Biomimetics, Micro-design, Arctium minus et al Hook and Velcro – A PhD and a Virtual Textbook on Biological Attachment Mechanisms and their Mimicking

Home » 2014 » May

Monthly Archives: May 2014

Transfer Paper part i

 

        

PhD Transfer Report

 

 

 

 

A Study of the Functional Ecology and Mechanical Properties of Hooks in Nature

A Biomimetic Approach

Submitted by

Bruce Edward Saunders

July  2005

 

University of Bath

Centre for Biomimetic and Natural Technologies

Department of Mechanical Engineering

Faculty of Engineering and Design

BA2 7AY

 

 

 

 

Research Funded by the Engineering and Physical Sciences Research Council (EPSRC)

Project no. EN042
Summary

 

The functional ecology and mechanical properties of hooks in nature is a vast subject area – too large to be encapsulated in a single thesis.  For this reason this investigation has been developed as a foundation paper for instructing further work in this field.

 

From an evolutionary perspective, a hook shape is a fundamental shape which has existed for millions of years, first seen in fossils from the Cambrian age. There are a finite number of biological materials that grow into hook shapes. Any environmental influences and changes are facilitated by the initial self-assembly of molecules during growth at a cellular level, when the structural materials are manufactured.

 

A study of a biological structure can be separated into parts.  First there is the study of shape, then the material properties and finally the modelling of the structure’s behaviour in concert with its substrate. Thereafter appropriate artificial materials are selected and a prototype device is manufactured.

 

Five specimens of three biomaterials were selected and three types of experimental procedures are conducted upon them.  The following structures were studied: plant hooks composed of cellulose, bird claws composed of avian keratin and insect hooks composed of insect cuticle. Discussion then proceeds to the design value that could be derived from each.

 

Appendices to this report include biomaterials, a zoological database of examples and a description of the progress and utility of recording biological morphologies.

Research upon the following topics is presented:

 

  1. The behaviour of biological structures and the implications of the principle of adaptive growth and its applications to engineering design.
  2. The imaging of biological structures, in particular, the use of confocal microscopy to directly obtain the 3-D voxel image of a hook with radius of curvature of approximately 200mm at the neutral axis made of cellulose and dual-hook tarsi of insect cuticle, which has never been done before. Further, there is discussion of the use of atomic force microscopy to record substrate morphology to examine hook/substrate correspondence,
  3. A mathematical hypothesis is developed to describe the set of all biological hooks using their component bio-material as a dominant parameter,
  4. An evolutionary hypothesis on the development of hook-shaped structures is discussed,
  5. The design process for the study of miniature attachment devices is examined as per Gorb,
  6. The application of the study of insect/tarsus/plant surface interactions to pest control and miniaturised robotic feet is discussed.

 

It is proposed to continue this research into developing a prototype robot based upon the morphology of an ant with the ambition of creating a robot that can walk up a vertical surface.

 

 

 

 

Table of Contents

 

1      Introduction. 10

1.1       Preamble. 10

1.2       A Description of the Experiments. 13

1.3       A Biomimetic Approach to the Study of Attachment Mechanisms. 15

1.4       A Review of the Appendices. 20

1.4.1        Appendix 1 – Library of zoological examples of attachment mechanisms classified according to shape and function. 20

1.4.2        Appendix 2 – Biomaterials terminology, cellular biology and organic chemistry, fibrous composites cellulose, keratin and cuticle. 20

1.4.3        Appendix 3 – The plant cell wall, epidermis and trichomes. 21

1.4.4        Appendix 4 – Studies of atachment mechanisms and probablistic fasteners in Nature  21

1.4.5        Appendix 5 – Morphological studies – methods of recording shape for biomimeticists  22

1.4.6        Appendix 6 – Shape optimisation in biological materials. 22

2      The Ecology of Plant Hooks. 23

2.1       Introduction. 23

2.2       The Advantages of Dispersal:24

2.3       Abiotic and Biotic factors in Evolution. 26

2.4       Four Aspects of the Adaptation Process. 27

2.5       Have Hooks Evolved Adaptively?. 28

2.6       Seed Dispersal on Animals. 31

3      The Paleontology and Evolution of Hooks. 32

3.1       Are Nature’s Hooks Perfect?. 37

4      Hypothesis for an Ordering of Hooks in Nature. 39

4.1       Introduction. 39

4.2       Establishing Relationships Between Two Hooks Within a Fundamental Group:41

4.3       Expanding This to the Set of N Fundamentals F1 to Fn44

4.4       Mapping Artificial Composite Performance onto this Matrix. 44

4.5       Comment on the Above. 45

5      Experiment 1 – 2-Dimensional Digitizing and its Applications. 46

5.1       Introduction. 46

5.2       Aim.. 48

5.3       Apparatus. 48

5.4       Method. 49

5.4.1        Experimental procedure:49

5.5       Results. 52

5.5.1        Robin claw.. 52

5.5.2        Thrush claw.. 52

5.6       Discussion and Conclusions. 53

5.6.1        2-Dimensional image acquisition of bird claws as a shape acquisition technique  57

5.6.2        The general use of 2-dimensional digitising in a functional ecological study and its application to burdock hooks – a proposal for further experiments. 58

5.6.3        Subsequent experiments to complete the analysis of burdock. 59

6      Preamble to Experiments 2 and 3. 60

6.1       Introduction:60

7      Experiment 2 – Confocal Microscopy and its Application to Recording Small Biological Morphologies  62

7.1       Introduction. 62

7.2       Imaging at Bath University. 63

7.2.1        Touch probe digitising. 65

7.2.2        Laser scanning. 65

7.2.3        Micro CT Scan. 65

7.3       Notes on Imaging with the Confocal Microscope. 66

7.3.1        Comments from Sanson et al [‎7]67

7.4       Aim.. 69

7.5       Method. 70

7.5.1        Specimen orientation (microscopy technique)71

7.6       Apparatus and method. 71

7.7       Results. 71

7.7.1        Burdock hook. 72

7.7.2        Bumblebee and grasshopper tarsi76

7.7.3        Grasshopper tarsus. 79

7.8       Discussion. 81

7.8.1        Atomic force microscopy. 84

7.9       Conclusion. 85

7.9.1        Applications. 86

8      Experiment 3 – Tensile Testing and its Applications. 89

8.1       Introduction. 89

8.1.1        The functional ecology of Arctium minus (burdock)89

8.2       Aim.. 96

8.3       Method and Apparatus. 97

8.4       Specimen Preparation. 98

8.5       Results. 99

8.5.1        Graphs of the fracture loads of specimen hooks. 102

8.6       Discussion. 105

8.6.1        Images of fracture. 105

8.6.2        Force results. 106

8.6.3        Statistical methods. 106

8.7       Conclusion. 108

9      Design Conclusions for a Shape Optimised and Materially Economical Hook Based upon a Plant Hook  109

10    Future Work. 111

10.1.1      Design considerations of a reusable fastener based upon a biological specimen such as burdock  112

11    References. 115

Appendices. 118

 

 

 

 

 

 

 

Table of Figures

 

Figure 1 – A Burgess Shale Fossil taken from Smithsonian website  32

Figure 2 – Shape Influences on a Biological Structure  39

Figure 3 -A tiger’s claw overlaid with an image of the shape optimized hook constructed of two logarithmic spirals from [‎6] as it appears in Appendix 6  46

Figure 4 – Profiles of the hindtarsal of a beetle taken from [‎15] as it appears in Appendix 4  47

Figure 5 – Result of digitising Robin Claw and exporting data to Excel52

Figure 6 – Result of digitising Thrush Claw and exporting data to Excel53

Figure 7 – Examples of two slice images from Sanson et al [‎7]69

Figure 8 – A specimen of Burdock  70

Figure 9 – Sterogram 1 of the burdock hook specimen  73

Figure 10 – Stereogram 2 of the burdock hook specimen  73

Figure 11 – Stereogram 3 of the burdock hook specimen  73

Figure 12 – 1 – 20 The individual .tif files that make up the stereogram of the burdock hook (Figure 8) above (the scale bar defines 200 mm)75

Figure 13 – 1 – 30 confocal microscope image “slices” of hooked bumblebee tarsus (scale bar indicates 200 mm)79

Figure 14 – 1 – 29 consecutive confocal microscope image “slices” of the hooked grasshopper tarsus (scale bar indicates 200 mm)81

Figure 15 – Image number 18 taken from Figure 14  82

Figure 16 – velcro, from [‎19]      Figure 17 – SEM of burdock hook  91

Figure 18 – Burr variables from Gorb [‎9]94

Figure 19 – Micro-testing of hook tensile fracture force from Gorb [‎9]94

Figure 20 – Showing the calculation of elastic modulus of the hook material from Gorb [‎4]95

Figure 21 – One of the burdock bushes from which samples were collected  97

Figure 22 – mounting the bracts for testing  99

Figure 23 clockwise from top left: the rack of prepared specimens, testing the hook fracture force with silk thread, a fractured hook.100

Figure 24 – SEM’s of the fractured hooks  101

Figure 25 – Specimens 2 – 7, Mean hook fracture forces vs Burdock fruit diameter103

Figure 26 – SEM of a burdock hook with scale bar reproduced from figure 1  104

Figure 27 – velcro, from [‎19]      Figure 28 – SEM of burdock hook  113

 

 

 

 

 

1      Introduction

 

1.1    Preamble

 

Some may say that I have cast too wide a net in preparation of continuing my research. I personally feel that this was necessary in order to fully appreciate and understand the topic area as well as possible.

 

There are two ways of learning chess: studying a single attacking strategy in the hope that it works first time, or learn the rules of the game and after consolidation, utilizing the knowledge with confidence.

 

This report is my consolidation.

 

The Journal of Bionics Engineering, Vol. 1 No. 1, 1-3 contains, an opening paper entitled “Significance and Progress of Bionics” by Yongxiang Lu [‎1].

 

To quote directly from the abstract, the subject of that paper is;

 

“the driving force and source of the scientific and technological creation, the definition and history of bionics, the important significance of bionics in the development of the human beings, and the leading edge and progress of bionics.”

 

In his paper Yu asserts that many structures in nature have been shape optimized including “the macroscopic and microcosmic structure” of organisms and their configuration and function.  This follows from the theory of adaptive growth, that elastic biomaterials are able to increase and discard material in accordance with the stresses applied to them.

 

Further, again quoting directly from Yu’s paper:

 

“The leading edge of bionics, in the age of knowledge, mainly comprises:

 

Bionics of micro and nanometer structure and system driven by the development of molecular biology and systems biology, nanometer technology, and MEMS technology.

 

(1)   Bionics of intelligence, cognizance, sustainable economy, and management progress thanks to the development of network, intelligentization (sic) in the information technology and neural growth biology.

 

(2)   Bionics of process and bionics of energy owing to the increasingly attention for the people to the environment protection.

 

(3)   Bionics of calculation for the purpose of unscrambling the secret of the life information promoted by the cognizance of DNA, structure of protein, and the structure and function of brain and nerve.”

 

This is a verbatim quote, grammatical anomalies included.  The first is, in part, the main goal of this thesis.

 

From S N Gorb’s paper on miniature attachment mechanisms [‎2] (see Appendix 4 for a detailed review):

 

“The goal of biomimetics is not to imitate the entire system, but to use interesting principles or design details for new applications, or for improvement of existing ones.”

 

This is a secondary goal of this paper on hook-shaped biological structures and hopefully something of this nature will derive from further work.  However I have concluded that pure biomimetics is not an easy subject to utilize.  It is believed, in fact, that it is far easier to use conventional engineering to solve a problem than it is to approach biology directly in search of a successful idea.

 

Biomimetics is easy to understand and difficult to implement successfully without sufficient knowledge to recognize that which one is observing. Searching for a solution for a problem is the wrong approach.  One needs to see what is before one and how it can best be applied and where.

 

The appendices are, it is now realized, the opening chapters to this report and they can be read before the experimental description and hypothesis.  For directness it is preferred to keep this, the main body of the report which contains the results and the discussion of the experimentation, separate as this enables the knowledgeable reader to “plunge” straight into the work. Each appendix is written to be complete in its own right but it is believed that further reading will enable their content to be augmented and improved.  The requirements of biomimetics as a cross-disciplinary research topic are reflected by the topics of these appendices. Further, the introduction to each experiment directs the reader to the appropriate appendices for referral.

 

For the author, this Phd was an opportunity to augment his engineering knowledge with that of a new science, biology and to combine the two.  Thereafter it would be possible to utilize the knowledge over and over again and furthermore, to pass this knowledge on to others.

 

This paper has become the book that would have accompanied this proposal.

 

 

1.2    A Description of the Experiments

 

A different apparatus or technique is illustrated with each experiment:

 

  1. 2-Dimensional Digitizing
  2. Confocal Microscopy
  3. Structural (tensile) testing in laboratory conditions.

 

Specimens of five individual species, three different biomaterials and three types of hook have been examined.

 

  1. A robin claw (avian keratin)
  2. A thrush claw (avian keratin)
  3. A burdock hook (cellulose)
  4. A grasshopper tarsus (insect cuticle)
  5. A bumblebee tarsus (insect cuticle)

 

None of these specimens was used consistently in all three experiments.  This could be viewed as unfortunate since this would have been suitable for illustrating the complete biomimetic design process yielding a single product.  However as stated above, product design through searching for a solution to a prescribed problem is not the correct approach. Instead the view was taken of understanding the field and of consolidating and developing better means of studying hooked structures and small attachment mechanisms, as well as identifying fields of utility, one of which (in the long term) is pest control and another of which is small robotic attachment devices (robot feet!).

 

Further, since all biological materials are composites with demonstrating anisotropic behaviour, in order to make use of the shape optimized benefits of a biological structure one concludes that only artificial composite materials that can mimic the behaviour of these composites are suitable.

 

Note that a master of the field of micro-biological structures and biomimetics, Stanislav Gorb of the Max Planck Institute, says that “in the field of micro-fasteners it is parabolic element fasteners and not hooked element fasteners that offer the greatest possibilities in the field of micro-fasteners” [‎3]. This is an important design indicator for fasteners and excludes all but one type of hooked structure which is commented upon in Experiment 3, from Gorb.

Experiment 1 relates to the claws of two common British birds, the robin and the thrush.  These are examples of macrostructures (>5mm). Combining understanding of the property of adaptive growth (see Appendix 6) and the use of 2-dimensional digitizing, there is a description of a possible utility of bird’s feet and claws to illustrate the biomimetic design process. There also appears to be information that would be of interest to Earth Scientists since claws are well preserved in the fossil record.

 

2-D digitising is the only experimental technique that was not used with Arctium minus, and so there is a description of the manner in which 2-D digitizing could be used in the process of optimizing the performance of a hooked attachment mechanism, imitating burdock’s hook/substrate interaction.  In this way, Arctium minus is used to demonstrate the biomimetic design process through all experimental techniques in this paper: 2D digitizing, 3D imaging and tensile testing.  Further experiments are required to complete the study from a biological perspective and these are described in context.  These include a proposal for the study of the material properties of the cellulose hooks after methods developed by Gorb.

 

Experiment 2 was an investigation into using imaging techniques to digitize micro-sized hooks (<0.5mm).  Given that the first rule of biomimetics is to copy the structure (from the Bath University Biomimetics website)  it was decided to attempt to image structures of two different biomaterials to see if they would fluoresce naturally in the laser of the microscope. In this case a burdock hook and the tarsi of a grasshopper and a bee were imaged. From scrutiny of the literature it is clear that the confocal microscope has not been used for this purpose before, directly imaging a biological structure of the order of 200mm.

 

Experiment 3 was an investigation into the tensile testing of a burdock hook, or more generally, a hook made of the plant material cellulose.  It served to confirm the assertion of Gorb that in a hook that grows under the principles of adaptive growth the larger the span or radius of a hook, the greater the strength. (see Appendix 4).

 

1.3    A Biomimetic Approach to the Study of Attachment Mechanisms

 

S N Gorb has produced many papers and a book [‎4] in this field of research.  Three of these papers are cited below.  The first describes a design process for developing a miniature attachment mechanism from a biological specimen which is equally applicable to large biological structures, the second discusses probabilistic fasteners with parabolic and not hooked structures and the third demonstrates the implementation of the process for a hooked structure:

 

  1. “Miniature attachment systems; exploring biological design principles” [‎2],

 

  1. “Probablistic fasteners with parabolic elements: biological system, artificial model and theoretical considerations” [‎3], and

 

  1. “Natural hook-and-loop fasteners: anatomy, mechanical properties and attachment force of the jointed hooks of the Galium aparine fruit” [‎5]

 

(see ‎1.4.4Appendix 4 – Studies of attachment mechanisms and probabilistic fasteners in Nature for a detailed review of these and other papers on the topic.)

 

In the first paper Gorb ascribes different parts of the process to different fields of science:

 

  1. The biologist starts the process by studying and identifying the structure which demonstrates the property of interest. With reference to hooks this property of interest can be re-defined as the function such as attaching things to clothing, robot feet or structures to pierce or anchor.

 

  1. The material scientist continues the journey by studying the qualities of the biomaterial of which the structure is composed in preparation of seeking the artificial material that will adequately mime the performance characteristics within the system.

 

  1. The engineer continues the process by mathematically modeling the structure’s performance in a form that can be readily understood, analyzed and communicated.

 

  1. Thereafter the logical step is to move onwards to prototyping and this is where the use of computer aided microscopy teamed with rapid prototyping such as demonstrated in Experiment 2 is a powerful resource.

 

The second process, that of the material scientist, is fulfilled, in part, by knowledge of biomaterials, their performance characteristics and how to assess them and this is demonstrated by Gorb in his paper on the Galium aperine fruit. The third step in the process, the modeling of performance characteristics, is also demonstrated in his paper on the Galium aperine fruit as well as in his paper on parabolic fasteners [‎3].  These are all presented in Appendix 4.

 

Developing a biomimetic study and applying it to a hooked structure requires a study of

  • the structure,
  • its parent organism/substrate relationship/interaction,
  • its environment,
  • material and internal structure,
  • mechanical properties, and
  • its organizational relationship to other structures.

 

To utilize current biological information as it appears in the scientific literature requires understanding of both biological terminology and the defined fields of study and how to apply them in an engineering study. There is always a commonality in all academic fields of study which is language and communication.  It is both the unifier and the divider.

The association between biology and engineering is less obscure than it may at first appear to a layperson.  A selection of manufactured products can be grouped, differentiated and described in the same way as a group of similar biological structures can be taxonomically defined and indeed this is commonplace in manufacturing systems where efficiencies are enhanced by seeking commonality between parts for materials handling and avoiding redundancies in design.

Experiment 2 – 3-D digitizing demonstrates the potential for imaging small objects using laser microscopy. A paper by Sanson et al [‎7] provides guidance on the critical parameters in the use of a confocal microscope for the generation of a virtual model.  Gorb does not use confocal microscopy, his images are generated from physical sectioning and he generates his objects from these cross-sections [‎3] and then using solid modeling whereas Beraldin et al [‎8] suggest the linking of 3-D imaging to a rapid prototyping device (see Appendix 5).  His images are used for larger structures and use laser scanning, not confocal microscopy

Of course, there is a major difference between biology and manufacturing engineering which is that engineered parts are manufactured to a design and placed within a system of designed parts.  Nature’s structures have elements of commonality but their design and assembly is left to natural processes both internal and environmental.

 

From a biomimetic perspective that includes a desire to manufacture, biological information needs to be streamlined down and redefined such that it is useful to the design process, identifying design indicators if the solution is not directly forthcoming from exact replication.

 

The three experiments have been conducted upon five different specimens of three types of hooks of three different biomaterials.  This presents a difficulty: presenting the results in a linear manner required for the written page.  In actual fact the results and their implications have a matrix-like relationship and so it is inevitable that subjects will be visited and re-visited through the course of this paper. Experiment 1 using 2-D digitising is helpful in illustrating the principle of shape optimization in biomaterials.  A paper by C Mattheuk and S Reuss entitled“The Claw of the Tiger: An Assessment of its Mechanical Shape Optimization” [‎6] provides guidance to the principles investigated in this experiment and it is described in detail in Appendix 6.

 

 

 

 

 

 

 

 

 

 

 

Experiment 3 – The tensile testing of burdock is a form of test that Gorb has already conducted upon five other specimens of hooked plants. (see [‎4] and [‎9]) which are described in detail in Appendix 4).

 

The conclusions of this report suggest applications for further study in the application of biological attachment mechanisms: pest control and insect tarsi/plant strata interactions which form a class of re-usable fasteners, robotic attachment structures.  It is Gorb (again) who proposes these avenues with potential in his paper “Miniature attachment systems: exploring biological design principles” [‎2].  He also suggests microsurgical devices and micropart manipulators as possible applications but it should be noted that often small natural structures utilise secondary and tertiary properties.

 

It is recommended that the Appendices be read first by unschooled readers, prior to the experimental work.  Alternatively, pertinent appendices to each experiment are cited in each introductory discussion.

 

1.4    A Review of the Appendices

 

1.4.1    Appendix 1 – Library of zoological examples of attachment mechanisms classified according to shape and function

 

This is a summary of information from the two prime biological sources ([‎4], [‎9] quoted as reference in many of the scientific papers in this area of research), on attachment mechanisms including images from the text and the web.  These texts define attachment mechanisms first in terms of morphology by defining and grouping attachment mechanisms according to their type of attachment and their common mechanism qualities i.e. a permanent attachment functioning as a glue or a temporary attachment functioning like a snap-lock fastener and the by function.

 

Later in this, the body of the report, there is a development of a hypothesis for an alternative method of mathematically classifying hook-shaped structures based upon the component material which, it is hypothesized, could be used in the development of a knowledge-based design decision support system for matching hook shape and performance with artificial composite material.

 

1.4.2    Appendix 2 – Biomaterials terminology, cellular biology and organic chemistry, fibrous composites cellulose, keratin and cuticle

 

This appendix includes a description of some general material property definitions and an investigation into the structures and properties of cellulose, keratin and insect cuticle because specimens of these three materials were the subjects of the experimental investigations.

 

1.4.3    Appendix 3 – The plant cell wall, epidermis and trichomes

 

The plant cell wall is discussed here because of its application to the structure of a trichome, a term used to describe all outgrowths from the plant epidermis.  From the perspective of an investigation into the interactions between insects and plant surfaces this is pertinent to the experimentation because the plant epidermis and the trichomes it supports form the substrate with which insect tarsi hooks interact. This appendix has been prepared in anticipation of further research into insect/plant substrate interactions with regard to pest control applications, reusable fasteners and robotic adhesive/climbing structures.

 

 

 

1.4.4    Appendix 4 – Studies of atachment mechanisms and probablistic fasteners in Nature

 

This appendix contains detailed descriptions of experimental procedures that have been used in the study of small attachment mechanisms. These have been used in order to guide experimental procedures used in this research.  Further they contain valuable experimental guidance, description and discussion that is of importance to research into biological structures.

 

1.4.5    Appendix 5 – Morphological studies – methods of recording shape for biomimeticists

 

This appendix contains a description of the chronological progression of developments of methods of describing and recording biological shape. It draws upon papers from biology, computing and manufacturing.  Imaging is a fast moving field.  Here it is small, simple structures that are focused upon as the structures of interest.

 

1.4.6    Appendix 6 – Shape optimisation in biological materials

 

Adaptive growth is a key generalized assumption in research into biological structures (see [‎1]), that the shape of structures adapt to the applied stresses for reasons of economy.  This appendix describes a paper that demonstrates this principle by studying the profile of a tiger and bear claw (both predators) and subjecting the shape to finite element analysis under an extreme loading condition, proving that the profile is shape optimized and that there are no stress concentrations. Further, it shows that the inner and outer curves of the claw follow a logarithmic spiral which has (apparently) long held fascination amongst biologists since the early 1920’s when a renowned biologist named D’Arcy Thomson first discussed this in his book called “On Growth and Form” (as cited by [‎6]).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2      The Ecology of Plant Hooks

2.1    Introduction

 

 

As will be seen from the following, research has shown that it is difficult to isolate the precise reasons why plant hooks are shaped as they are.  General trends are identified and efforts are made to develop global rules, thus far without success.

 

 

The majority of examples of plant hooks are associated with reproduction and the dispersal of seeds and fruits through mechanical interlocking. It is pertinent therefore to consider studies of seed dispersal and their underlying theory.  The following derives from “The Ecology of Seed Dispersal” by H F Howe, J Smallwood [‎10].

 

This is a general review paper that discusses the “why’s” of seed dispersal:

 

  • Is one mode of dispersal preferred over another?
  • Why are there different dispersal structures and is there any benefit of one form over another?
  • What causes the differences i.e. climate, seasons?

 

It states that adaptation is regarded as having evolved through natural selection to enable an organism to reproduce and ultimately survive as a species.  It implies a functional configuration and not accidental advantage.

 

With regard to seeds and fruits such as burdock, hooks are termed morphological adaptations but, the paper says, little is known about the selective forces that produce them.

 

There is discussion upon the reasons for dispersal and the different methods, such as the fact that that the family Leguminosae, of which there approximately 17000 species, has seeds that have adapted to be dispersed by birds, bats, rodents, water, fur, feathers, wind, ballistics or simple gravity.

 

2.2    The Advantages of Dispersal:

 

There are three hypotheses discussed:

 

The Escape Hypothesis asks if there is a selective advantage to seeds being scattered further from the parent plant.

 

The Colonization Hypothesis says that the goal of dispersal is to find suitable habitats to colonize.  Habitats and their conditions change over time and the “goal of the parent plant” is to find another suitable habitat, hence dispersal.

 

The Directed Dispersal Hypothesis says that seeds are taken to non-random places that are suitable for dispersal.

 

This paper continues with a very specific ecological and evolutionary approach which is not very applicable to a work on the mechanical properties and functional ecology of hooks.  It may be considered to investigate this aspect of the work further in the future.  Experiment 3 later in this report (Section 8)  deals specifically with the mechanical properties of burdock, and during collection of the tested specimens precise notes were taken of the positioning of the collected specimens on the plant for possible analysis.  However, there has already been an in depth study of the ecology of Arctium minus but it appears that this report has gone missing from the British Library.

 

The discussion now moves to: “Plant Biomechanics – An Engineering Approach to Plant Form and Function” by K J Nicklaus [‎11] and particularly Chapter 10.

 

This describes the evolution of form and function and their relationships. Paleobiology (it says) allows for the development and testing of hypotheses through the study of fossil records and the utilisation of knowledge and principles that are equally applicable today.

 

Paleobiology makes use of a geologic column, a chronological ordering of the ages of the planet.  Fossil organisms are recorded chronologically on this column in their order of their appearance in the fossil record and this information is used to attempt to develop or prove hypotheses such as that of natural selection.

 

Darwinian evolution suggests that organisms exhibit adaptive responses (through the process of natural selection) to the challenges imposed upon them by the environment.  The environment is described to operate like a semi-permeable membrane over time through which some phylogenetic variations survive, whereas other do not.  The environment therefore imposes challenges that alter the genetic composition of populations, leaving the surviving phenotypes that manifest the appearance, structure and other properties that influence future generations.

 

Niklas says

 

“It is important, therefore, to see that natural selection is not the fountainhead of the genetic changes within organisms; it operates to eliminate, not engender, genetic alterations.” (p466)

 

In other words the environment operates to eliminate the weak and not to engender alterations.  But it is only those genetic alterations that are phenotypically expressed and that affect survival and reproduction that can be eliminated…others that do not immediately manifest themselves in an organism can pass through the “membrane” undetected and survive until they manifest themselves and are tested.

 

It must also be born in mind that the environment changes over time and so the long-term survival of a species is not assured simply by passing through this environmental filter.

2.3    Abiotic and Biotic factors in Evolution

 

The environment consists of abiotic and biotic factors.  The biotic component of the environment consists of the coexisting organisms and their interactions.  The abiotic components are the purely physical features.

 

Over time both of these components change and both have an influence over the growth, survival and potential for reproduction of every individual.  The biotic component changes through the process of evolution and the abiotic factors, too, may change; the global climate can change, continents can move.

 

Darwin believed that it was the biotic factors that provided the vector or directionality of natural selection since he felt that the changes to the abiotic component occurred too randomly.  Allmon and Ross (1990) as cited in Niklas, say that it is the biotic component that is the most influential in the evolution of biomechanical improvements in animal lineages.  But Niklas says that such a rigid regard for the relative influences is incorrect and that there must be a consideration of the fact that over time, the relative influence of the biotic and abiotic components can change.

 

Paleontologists concentrate on plants to seek the answers to the frequency of the relative influences of biotic and abiotic factors since plants constitute over 90% of the biomass.

 

2.4    Four Aspects of the Adaptation Process

 

 

  1. Adaptation cannot be evaluated outside the context of the environment,
  2. Adaptation is a relative attribute and depends upon an individuals capacity to function as well or better than its contemporaries,
  3. Characters or attributes of an organism cannot be regarded in isolation, they are part of all the attributes of the entire organism, and
  4. Adaptation allows comparison between individuals within a single population, among individuals from different species of the same character states and among individuals from different species that have different character states.

 

A further useful assertion from Niklas (p490) is that the first plants dispersed their spores using the wind, in other words dispersal by hooks is a relatively recent development on the evolutionary timescale.  Further, if one considers the order of appearance of plants upon the evolutionary timescale as being algae, mosses, ferns and then conifers and mosses, hooks make no appearance in their morphologies.

 

2.5    Have Hooks Evolved Adaptively?

 

There is an ongoing search for a global explanation to the patterns of evolution. The fact that evolution does actually occur is illustrated by

 

  1. Genetic composition and appearance of individuals changing,
  2. New lineages appearing, and
  3. The structure of communities changing as the frequency of occurrence of organisms changes.

 

The two opposing views are described as either being driven “from without” or “from within”.

 

The argument presented in this paper compares an organism and its properties to a material of either isotropic or anisotropic behaviour.  If an organism behaves isotropically then it has the propensity to develop in any direction at any point in its evolution, limited by the biotic and abiotic circumstances at that time and the characteristics that have survived the evolutionary filter.  If an organism behaves anisotropically then it has an intrinsic directionality to its development which again is limited by biotic or abiotic factors at that time and again, the inherent characteristics that have survived the evolutionary semi-permeable filter.

 

Niklas says that neither of these models would seem to be entirely true.

 

Isotropic behaviour would suggest an anything-is-possible at any point in time of evolution, which (he says) does not occur from observation.  Anisotropic behaviour would suggest that an organism is in control of its own evolution by the nature of its constituent properties, again which is not illustrated in reality.

 

It must also be recognized that at any point in the evolutionary development of an organism, further changes are measured against a relative axis and not an absolute axis of development.

 

“Thus evolution involves a reciprocity between the properties of the external environment and the properties of the things we call organisms.” (p527)

 

When considering the relative importance of these biotic and abiotic factors, Darwin’s “survival of the fittest” suggests that it is the influence of biotic factors that most influence evolutionary trends.  This hypothesis seems to be most valid in the case of complex organisms like birds and animals but plants are more responsive to abiotic factors.

 

BUT, and this is important for the hypothesis development of the next section, Niklas says:

 

“The force of these arguments is radically diminished if we accept that the laws of physics and chemistry, whose consistency appears assured, are abiotic agents….”

 

Niklas says further:

 

“Thus the question before us is not whether evolution involves the operation of abiotic or biotic agents for selection or whether the magnitudes of these components differ over time, but rather whether the relative magnitudes of the resulting deformations differ among different types of organisms and whether these deformations reflect long-term adaptive trends.” (p534)

 

What has been sought through the previous discussion is an answer as to why plants evolve hooks.  The result is a combination of factors none of which is conclusive.  Plants are more sensitive to abiotic factors and because plant hooks are multicellular structures, there are abiotic factors that involve the laws of physics and chemistry which relate to the mechanisms of self-assembly and other methods of growth of plant hooks that have a greater impact than biotic factors that affect more complex organisms.

 

 

 

 

2.6    Seed Dispersal on Animals

 

There has been some study of the dispersal of diaspores on animals. The papers “Comparative Experimental Study of Seed Dispersal on Animals” by S H Bullock [‎12] and “A Study of Adhesive Dispersal of Three Species Under Natural Conditions” by K Kiviniemi [‎13] are used as a resource to the following discussion.

 

The seed shadows of seeds that attach themselves onto animals, seed morphologies and the morphologies of host animals were studied for insight into the nature of plant reproduction and evolution.

 

The purpose of such studies is, in part, to assess the purpose of seed dispersal in the light of the hypotheses described in the introduction to Section 2.2.  It is found that dispersal distance depends strongly upon the habits of the host animal and the morphology of the seed attachment.  Further there is a contribution from the height of attachment on the host animal and the morphology of the plant inflorescence that bears the seeds.

 

It is observed that the nature of the diaspore morphology has an impact upon not just the attachment strength and density of diaspores on the host but also upon the host reaction it.  A host animal will seek to groom off a discomforting diaspore whereas one that does not interfere with the hosts activities has a greater chance of being dispersed further.  A diaspore that attaches to the host in a region that is inaccessible to grooming similarly will be carried further and so the height at which the seeds or fruits are presented to the host has an impact upon the distance that it is carried.

 

3      The Palaeontology and Evolution of Animal Hooks

 

 

In the light of the information of Section 2 it should now be possible to develop a hypothesis for positioning manifestations of various forms of hook on the geologic calendar.

 

 

The Museum of Natural History in London was visited for viewing of the fossils of the Archaeopteryx as well as the Smithsonian Institute in Washington DC where fossils from the Burgess Shale, a famous archaeological site discovered in 1907 in Canada, have been observed.  These visits afforded a viewing of some of the earliest hooks to occur in the history of the earth, those of the Archaeopteryx being the claws of the first bird in an evolutionary transition from a ground-dwelling reptile, while the Burgess Shale fossils are examples of some of the earliest fossils of soft bodied organisms. These organisms resembled wood lice with hook-shaped feeding mandibles – the first known hooks on the evolutionary calendar [Figure 1 – A Burgess Shale Fossil].

 

Figure 1 – A Burgess Shale Fossil taken from Smithsonian website

 

The hooks of the early Burgess Shale organisms, some of which were clearly used by predators for grasping prey, were distinctly hook-shaped.  The hook as a shape had appeared by the Cambrian Age, in living organisms. So there is not an example of an under-developed hook i.e. a structure that is desired to be a hook but which fails in this requirement. [Note: Burgess Shale has the earliest known fossils of soft bodied aquatic organisms known, resulting from them being fossilised in a silt layer which preserved even some evidence of plant life.]

 

What does distinguish and influence the shape of these early hooks is their component material which was primitive cuticle.  Cuticle can become “scleritised” or matured through exposure and age causing it to toughen (see Appendix 2 and the tanning process of cuticle).  Cuticle can possess scatterings or coalescences of elements that produce toughening characteristics such as surface hardening.  So, at this time in the evolutionary timescale the self-assembly and shape adaptive growth processes required to form hooks had evolved.

 

The book entitled “In a Blink of an Eye: the Cause of the Most Dramatic Event in the History of Life”[‎14] by Andrew Parker discusses the “Cambrian Explosion”, so-called because it was during the Cambrian period of the earth’s development that the diversity of life on earth exploded in numbers and the differentiation between organisms increased greatly.

 

Dr Parker expresses the view that it was the development of vision and the change from a blind world to a world of organisms that could see that led to organisms responding to the change by developing armour, limbs, mating patterns, defence mechanisms, colour and more, in a period of time (5 million years by his estimation) that is relatively short in the history of the world.

 

It is his book that translates the research proposal: “The functional ecology and mechanical properties of hooks”. Dr Parker’s book could have an alternative title: “The functional ecology and physical properties of vision”.  He discusses the development of vision and the different forms of vision systems that organisms employ as well as their interactions with colour.  There are five fundamental types of eyes which employ different physical principles in order to perform the common function, seeing.  These types of eyes evolved in different species at different times on the evolutionary time-scale.  Some types of eyes he describes occur in completely different species yet still obey the same physical principles, such as the eye of the octopus and the human eye.

 

Clearly in this hypothesis Dr Parker is emphasising the influence of abiotic factors in the development of vision, vision developing under the influence of the abiotic factors of physics.  Thereafter the ability to respond to the biotic factors that became visible (organisms to hunt or be hunted by, for instance) led to the “explosion” of diversity and form.

 

However it is suggested that the shape of a hook may not have evolved through a “survival of the fittest” scenario but instead that it evolved with the evolution of a self-assembly process that could produce a hook-shape.  From basic chemistry, chemical reactions require the presence of basic component materials and a gradient that induces the reaction, be it electrical potential, relative molecular concentration or some other form of differential.  Without these there can be no reaction.  If growth through cellular self-assembly is understood to have limited structural patterns then there is a limit to the shapes that can be produced from a parent material whilst maintaining the property of shape optimisation as discussed in Appendix 6 and Experiment 1.

 

Thus it is proposed that the biological structures known as hooks equally evolved through the abiotic factors of chemistry and physics due to changes in the environment which made the conditions available for the development of these structures and under the stresses of usage that influenced shape into a shape optimised curve that was materially efficient.

 

[Note: It is necessary to refine what is meant by materially efficient.  This can not only mean that for any individual hook, unnecessary material is physically gained or lost under ambient conditions of stress as occurs with materials such as bone, it also means that the material that is present can be strengthened through such processes as fibre alignment to produce maximum strength from the same finite volume of material that  remains unchanged.]

 

Therefore it is quite possible that hook-shaped structures evolved at the same time as vision structures or even prior to vision structures.  Vision could have developed as a protection mechanism from organisms with hooks.  The more that one considers these issues the more inclined one is to forsake the cause-and-effect theory in the development of the hook as a shape in favour of the randomness of an isotropic material in a suitable abiotic environment acting within the limits of the laws of physics and chemistry. It must be borne in mind that a hook is a relatively simple structure utilising “straightforward” chemical reactions in its formation without the complexities of the physics of light associated with vision systems.

 

Further, although the external and internal structures of a hook are relatively simple, if a hook is not a static structure (mandibles, motive organs) then there must be a developed musculature to enable attachment and manipulation.

 

The question is then asked: Is there a pre-vision organism with active mandibles and if there is, is there any reason why hooked structures should be restricted only to such parts?  For if a hooked structure could develop in that environment from a material such as cuticle then why should the possibilities be restricted to mandibles?  The answer must lie within fossil records.

 

It would seem that the first organisms with hooks, on record, were those of the Cambrian age as found at Burgess Shale.  These were made from cuticle.  Thereafter the search must continue for fossils of later aquatic organisms that may have evolved prior to the first land organisms with hooks developing, and these must be from materials besides cuticle.  It would seem that teeth could be a promising possibility which would then include dental ceramics.

 

Here hooks are being considered as primarily a function of biotic chemical and physical factors that enable the growth of the shape.  Hooks have a simplicity of structure that goes beyond the external morphology.  Their internal structures, too, are simple without musculature and nervous system.

The first land plants began with unicellular algae.  Thereafter came the development of ferns, conifers and mosses, none of which have hooks and by the time of the development of the first flowers and berries, dinosaurs were wandering the planet.

 

By this process of elimination one can produce an ordered list of the emergence of hooked structures from different biomaterials:

 

  1. primitive cuticle (primitive branchurians)
  2. enamel (teeth of prehistoric aquatic organisms)
  3. reptilian keratin (dinosaur claws)
  4. avian keratin (bird claws and feather hooks)
  5. mammalian keratin (warm blooded animals with claws)
  6. cellulose (seed hooks)

 

3.1    Are Nature’s Hooks Perfect?

 

The environment can interfere with a structure’s development but equally the environment can contribute to a structure’s development through effects that are utilised to the benefit of the structure’s functioning, influencing the composition and properties of the component material in a manner which is reflected in the structure’s final shape. But the initial shape evolves from some pre-defined coding that inhabits its growth tissues.

 

If one assumes some form of shape optimisation has occurred then it follows that for some strength to weight optimum the biological material itself has been optimised, whether it is through fibre alignment or some other process such as surface hardening.

 

But if all organisms are in the midst of a dynamic yet long term evolutionary process, can it be assumed that at any point in time natures design is an optimum?  Is there a method of testing this?

 

It is suggested that there is merit in comparing the performance of a structure such as a hook acting in its ecological environment with its performance in isolation, in laboratory conditions.

 

It is proposed that if a structure such as a claw is a form of some unit structure, a structure that appears or develops from some genetic interactions and constructed from a finite materials, then the process through which a hooked structure is manufactured is one of a finite number growth processes available and is repeated through species.  This links the concepts of shape and material across species and classes since it is the process of growth that yields the shape in a material-optimised manner.

 

This is a somewhat “robotic” approach to the structure, that hooks are biologically manufactured in similar fashions and can be grouped accordingly as per manufactured engineering parts as a set of primitives based upon their material and other parameters arising from the loading conditions and some fundamental dimension such as distance from root to tip.

4      Hypothesis for an Ordering of Hooks in Nature

 

4.1    Introduction

 

 

Figure 2 – Shape Influences on a Biological Structure

 

 

The previous section ended with the discussion of a manufacturing approach to the classification of hooks.  Figure 2 above shows the parameters that will now be ordered within a hypothesis for a hook classification system.

 

Consider the set of all hooks in nature. This set can be divided into subsets of similar hooks, chosen to be described as the hook fundamentals, F1-n. Each hook fundamental Fi is defined by a characteristic material and a fundamental, dominant parameter. It is proposed that the presence of environmental factors such as the substrate to which the hook is to attach and other properties of the organism from which it arises (such as the mass of the supporting structure) contribute to the variation of the hook shapes through changing the loading conditions which can include fatigue or cyclic loading.

 

Some examples of hook fundamentals:

 

  • The set of plant hooks for attachment (of cellulose)
  • The set of bird claws (of keratin)
  • The set of insect tarsi (insect cuticle)
  • The set of insect mandibles (insect cuticle)
  • The set of feline claws (of keratin)

 

In the first instance consideration has been restricted to those examples of hooks that interact with a substrate i.e. they have adapted for a function other than the interaction of parts of the same organism or for attaching organisms of the same type as in the mating systems between male and female parts.

 

The set of plant hooks is different from the other four in that plant morphologies, as discussed by Niklas and described in Section 2, are more susceptible to abiotic factors and the reasons behind the development of their morphologies are more difficult to define.

 

4.2    Establishing Relationships Between Two Hooks Within a Fundamental Group:

 

Consider the group of cat claws and let it be known as fundamental group F1.

 

 

 

Let there be n different species of cat all of which exhibit types of hook. Therefore hooks f 1-n, are members of a fundamental group F1,where the group is defined by the material mammalian keratin. 

 

Each hook fi in the set F1 will have evolved to its final shape through the properties of the component material and its loading conditions as well as the dimensions of its growth region and cells.

 

Experiment 1 discusses the loading and effect of loading upon adaptive growth.  For the moment let it be stated here that the loading condition of all the feline claws shall be point loads perpendicular to the tip but this is not to be assumed as a universal condition.

 

This information, that is f1 = f(biomaterial, dimension, loading) should now be sufficient to describe the hook in its entirety.

 

However, there is still a question remaining concerning the loading condition which was partially addressed at the end of Section 3.  And this relates to the perfection of the design and the loading condition that will produce the expected shape.

 

For is it an extreme loading condition that occurs infrequently that produces the characteristic shape? Or is it a high frequency loading cycle at a lower loading amplitude that produces the shape?

 

To assess for the correct condition requires a comparison between different loading conditions to ascertain which condition or range of conditions fulfils the requirement to produce the correct shape.

 

  • The first is to assess the ultimate failure strength of the hook in a laboratory environment using an Instron testing machine or some other engineering tensile tester.

 

  • The second is to test a hook in a system that replicates the natural system as closely as possible. In the case of a cat claw, measuring the stress produced by a cat on a scratching post could give an indication of a lower frequency stress as a cyclic load.

 

Each form of test would give us data that could be interpreted in different ways, in the realm of engineering and the functional ecology realm.  The product of these tests would resemble the fatigue diagram of a structure but in reverse, the cyclic loading to shape instead of cyclic loading to failure.

 

Further, if both of the above forms of experiment are conducted upon samples of a hook-type  fi then assessing the differences between the results gives an insight into assessing the “perfection” of nature’s design. (see Experiment 3 – The Fracture Force on a Burdock Hook earlier in this report and compare this with an experiment using a natural fur substrate.)

 

The ultimate fracture strengths of the n claws of F1 can be plotted on the graph of size versus strength implying that function and material have thus been linearised since all the specimens are of the same material and function. A line can then be drawn between them to represent a transition between their relative performances. This line should represent a continuous transition between the group of hooks similar in material and composition and under normal conditions it should be smooth, taking into account the scaling relationship mentioned in the introduction and the performance of each hook that is now a mathematical function of the size and assuming material homogeneity.

 

Where the test reveals a “glitch” or discontinuity, that specimen warrants further study to understand the hidden property from which this behaviour derives such a strength-supplementing additional mineral.

 

A second experiment is then conducted upon the same n types of hook specimens. This time the strength of the attachment is measured in a modelled system including the natural substrate or a close approximation, such as the scratching post mentioned earlier.

 

The results of the two experiments can be compared and it is predicted that this data will provide an insight as to the efficiency of the hooks as natural designs.

 

4.3    Expanding This to the Set of N Fundamentals F1 to Fn

 

 

We can then repeat similar tests on sets of materially and functionally similar hook specimens F 1-p that is, of different fundamentals such as those listed in Section 4.1.

 

It is suggested that, in theory, the process can be continued for all hook fundamentals in nature to establish a matrix of relationships of hooks of all biological materials.  This will be a 3-dimensional matrix due to differing material properties and functions (=> shapes) but all will be composed of biological composites.

 

4.4    Mapping Artificial Composite Performance onto this Matrix

 

 

Once such a matrix has been established which shows the n relationships between hooks of similar function and materials (of the same Fundamental Group), and the p relationships between the Fundamental Groups then the performance properties of synthetic composites can be mapped onto the system to give a performance indicator that would aid designers wishing to design hooks using composite materials for specialised applications that require high strength and weight minimisation.  (Note that n and p are used here for simplicity but, of course, there is no reason that each of the p Fundamental Groups will contain the same number of elements n.)

 

Further, this process can be expanded to include hooks of differing materials yet similar functions or similar materials and differing functions, and gradually a 3- dimensional matrix can be developed of the space of hooks.

 

4.5    Comment on the Above

 

 

This hypothesis is very much simplified for the purposes of illustration.  Any biologist would recognize that I have in effect utilised cladistic studies in reverse, working with the manifestation of phenotypic differences that are ordinarily utilised by biologists for taxonomic work (see Appendix 1).

 

Exactly how complex this matrix would be is defined by the number of materials (six, by Section 3) and functions as well as the number of elements to each set.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5      Experiment 1 – 2-Dimensional Digitizing and its Applications

 

5.1    Introduction

 

For this experiment the reader is requested to refer to Appendices 2, 5 and 6 which discuss biomaterials, morphological studies and shape optimization.

 

Appendix 6 discusses an experiment into the two dimensional digitizing of a tiger’s claw in detail, in particular, the occurrence of a logarithmic spiral in its growth pattern and its apparent state of shape optimization. Refer to Figure 3 and Figure 4 below.

 

Figure 3 -A tiger’s claw overlaid with an image of the shape optimized hook constructed of two logarithmic spirals from [‎6] as it appears in Appendix 6

 

 

Figure 4 – Profiles of the hindtarsal of a beetle taken from [‎15] as it appears in Appendix 4

 

There are important differences to note from Figures 1 and 2.

 

The tiger’s claw (Figure 1) and others like it in the Mattheuk paper are all similar in that they come from predators and therefore it is assumed that the maximum loading condition occurs at the tip of the claw from a direction that is normal to the tip.  They are also composed of the biomaterial animal keratin which is an intracellular material.  It forms from the protoplasts of the cell and the cell walls deteriorate around the material.  Therefore it is not fibrous and can be taken to be approximately isotropic in behaviour prior to any work hardening effects arising through use. The authors found that the inner and outer curvatures of a tiger’s claw are formed of sections of two logarithmic curves.

 

But biomaterials are generally not homogenous (see Appendix 2). The beetle tarsus is made of insect cuticle. It is an extra-cellular material made up of chitin microfibrils in a matrix of protein.  Hence it is not to be assumed that the tarsi of an insect, while shape optimized, should exhibit the mathematical property of logarithmic curvature.  There are other ways in which the strength of the material can vary through varying the density of the chitin fibrils in the matrix or the qualities of the matrix (from discussions with J Vincent, zinc as a trace element is a hardener in insect cuticle).  This can be observed in Figure 2 where the curvature of the insect tarsi are described by adjoining radii of curvature since it is clear from observation that their curvatures are uneven and non-logarithmic in nature.

 

5.2    Aim

 

To investigate the use of 2-dimensional digitizing in a functional ecological study and adaptive growth.  The subject of the study was the claws of a robin and a thrush.

 

5.3    Apparatus

 

  1. An axioscope light microscope.
  2. An Apple PowerMac with Nih Image software installed. Nih Image is a commercial software package used for 2 dimensional image analysis and manipulation.
  3. Software called “hook-fit” was written by an engineering lecturer (Dr G Mullineux) and inherited from a predecessor but it was not utilised for reasons of being an inappropriate approach to the experiment.

 

 

 

5.4    Method

 

Claws were placed under the microscope and imaged using Nih-image on the AppleMac.  This image was then digitized to produce the profile image.

 

The process of converting the image to a digitized shape is below.

 

5.4.1    Experimental procedure:

 

5.4.1.1  Mounting the specimen

 

  1. Image the specimen prior to isolating the claw/hook structure.

 

  1. Use a sharp blade to separate each claw from its respective toe. The procedure that follows should be applied to each claw respectively.

 

  1. Place claw in profile position under the Axioscope microscope together with a section of a ruler for scaling purposes. Adjust the lens and magnification to optimise the size of the image in the frame grabber. Save the image prior to analysis and save a further copy of the image, that is to be used for the analysis.

 

  1. Use the grow box (bottom right hand corner of window) to make the window larger than its original size. The zoom box switches to “scale to fit” mode to make the window as large as possible while still maintaining the aspect ratio.

 

5.4.1.2  Navigating around the image

 

  1. Click in active window to zoom. Double-click on magnifying icon to revert to 1:1 magnification. Or hold down the option key to zoom out. Switch to the grabber tool using the space bar to scroll through an image.

 

  1. Use the rectangular selection tool to isolate the portion of the image to be analysed. This rectangle can be saved to file and re-opened for analysis.

 

5.4.1.3  Setting the measurement scale

 

  1. Using the copied image file set the scale. Use a line measurement on the ruler to establish the pixel: millimetre ratio. This converts all measurements to millimetre values.

 

5.4.1.4  Thresholding the shape

 

  1. Use Thresholding to convert the image to grey scale, following the process outlined in the Nih image manual to get as clear an image of the profile as possible. The map window is used for adjusting the contrast and brightness. See manual on “map window” for thresholding controls. (Click in the lower left hand corner and drag horizontally to the right until the image starts to saturate).

 

Note: use a screen to reduce the extraneous light onto the specimen which could cast unwanted shadows in the image. Make a note of the thresholding values.

 

  1. Convert to binaryto get a black and white image and use the erode function to discard edge pixels to give a firmer outline to the image.

 

  1. Use the crosshairs to pick out points on the curve of the hook, printed to the Results window and save results to floppy disk. The cross hair tool counts objects, marks them and records their X-Y co-ordinates. The results window can be emptied using “Reset”. The crosshair tool leaves markers (sized according to the current linewidth selection) in the current foreground colour. Hold down the control key to display X-Y co-ordinates.

 

 

5.4.1.5  Outlining the shape

 

The wand tool automatically outlines structures isolated during “thresholding”. Click inside the object near the right edge or outside to the left of the object. Then subtract background to get rid of unwanted shapes.

 

5.5    Results

5.5.1    Robin claw

 

Figure 5 – Result of digitising Robin Claw and exporting data to Excel

 

5.5.2    Thrush claw

 

Figure 6 – Result of digitising Thrush Claw and exporting data to Excel

5.6    Discussion and Conclusions

 

If the intention had been to follow the procedure of the experiment on the tiger’s claw, then it would have been appropriate to compare the digitised points with logarithmic spirals to investigate if the rule held true.

 

Growth in the shape of a logarithmic spiral has the quality that a structure retains its shape as it grows, such as demonstrated in snail shells.  The discussion of some structural materials and their development is contained in the Appendix 2 and 3.

 

The tiger’s claw is one of a predatory mammal, made of mammalian keratin, which experiences maximum loading at the tip. Further, from personal observation, such claws retain a narrow cross-section with rounded ends as the distance from the tip increases.

 

From observation it is clear that bird claws operate in a similar fashion when co-ordinated into the grasping mechanism of the foot.  A bird’s foot commonly consists of three toes pointing forwards and one foot pointing backwards.  This creates a grasping mechanism.  The claw of each toe protrudes in a manner such that the point is available to insert into the surface of the perch.  In this manner the foot grasps the perch and the claws have the function of preventing rotation.

 

However it was decided not to proceed with the experiment in this manner, that the fact that the curves may or may not exhibit logarithmic qualities has little engineering or biomimetic application or rather, that mattheuk and Reuss have already proved the effect.  From first-hand observation of various species of birds in the London Science Museum, it is clear that different claws have different cross-sections, i. e. some are round in cross-section, some are oval and some even approximate triangular.  The claws of raptors in particular have an ovoid section with a “bulging” base. The profiles of these claws as well as their shapes in cross-section must  be due to shape optimisation and the properties of avian keratin as a material. The bending equation for beams says that a non-symmetric cross-sectional area will influence the radius of curvature and stress distribution leading this researcher to suppose that the logarithmic qualities attributed to the Tiger’s claw, while true, must be due to the researcher’s choice of specimen with a bi-axially symmetric cross-sectional area (ellipsoid).

 

Mathematically speaking, if a curve or arc is smooth and continuous yet is not of constant radius, but instead is of constantly changing radius at a constant rate, then it will fit some part of some logarithmic spiral.  Combine this with a homogenous material of symmetrical cross-sectional area that grows (or is formed) under the law of adaptive growth and one arrives at a shape optimised structure.  This gives a useful design indicator for ideal hook design for a hook with symmetrical cross-section about the neutral axis (noting that the neutral axis divides the cross-section into two equal areas by definition, for a homogenous beam).

 

Differences stem from the root of the claw and the size and cross-section of the growth region of keratin-producing cells. It is this root area that defines the cross-section of the claw and this develops in response to the system and the stresses through it related to the grasping system within which the claw functions.  This arises through the process of adaptive growth.

 

Personal observation has distinguished four main types of bird claw (see Appendix 1 for more on claws and beaks):

 

  • Small non-predatory birds have a claw which is long and slender.  These claws are for assisting with the grasping of twigs and preventing rotation when operating as part of a grasping system.

 

  • A talon type of claw is found in birds of prey. These have a more pronounced curvature of the neutral axis at their tip but the cross-section of these claws is significantly different due to the stresses to which they are exposed, either through the force of grasping and holding their prey or because of the sheer size of their own bodies which leads to a requirement of strength in order to hold onto their perches while supporting their mass.  Their claws have a thick cross-sectional area for piercing with a sharply hooked pointed tip for piercing.

 

  • The triangular sectioned claws of heavy and flightless ground-dwelling birds, such as those of an ostrich.  These claws have to bear significant stresses during the process of walking and running particularly if the bird’s bodymass is high. This leads to a triangular section with a flattened base where material is concentrated in order to bear the weight of the bird.

 

  • The swift is a bird that has all its toes pointed forwards and it is unable to perch on a branch.  In fact some swifts have legs so weak that they are unable to stand on a surface (when their legs would be subjected to compressive forces).  Instead their legs are always in tension as they hang from their vertical perches. Their claws have extremely sharp points which enable them to hook into the small irregularities of surfaces such as rock faces (see the chimney swift) or the fibrous surfaces such as the underside of palm leaves (see the palm swift). This means that their claws have loading angles that are approximately at right angles to the sharp tip.  This would make the claw of the swift shape-optimised for a grasping tool for an object with hard, flat and relatively smooth surfaces where the artificial claw is in a state of tension with a reduced bending moment.

 

All of these shapes arise from the manner in which the claws interact in the biological system of organism, surface and environmental medium (air).  The biological system consists of the entire foot, the muscular attachments and the substrate.

 

No single toe acts on its own. All toes interact in the system that makes up the foot.  The shape and size of the individual claws develops to absorb the stresses incurred during normal usage.  Since the stresses arise through the muscular activity of the attachment muscles it is reasonable to suppose that the cross-sectional areas through the claws derive from the properties of the material and the muscular activity of the leg muscles/tendons (or in the case of the swift which can’t stand upright, from the tension of a dangling bodymass as it hangs from its claws).

 

If one takes the four types of claw identified and assigns appropriate mechanisms to them, then we have

 

  1. A holding mechanism – countryside, perching birds
  2. A piercing mechanism – predatory claws
  3. A supporting, walking mechanism – ground dwelling birds
  4. A wall climbing mechanism – the claws of a swift

 

5.6.1    2-Dimensional image acquisition of bird claws as a shape acquisition technique

 

In measurement, a single bird claw can twist out of plane making it difficult to reliably obtain a true silhouette of the claw. Therefore from the perspective of shape acquisition it was felt that it would be possible to improve upon the results obtained here, leading to Experiment 2 in 3-dimensional image acquisition.

 

However, from a biological point of view, there are statistical methods that make it possible to compare a number of claws of the same species.  This would consist of locating similar points upon the profile relative to each other, such as the tip, the aphelion of the arch and the base of the claw with some intermediary points and comparing them statistically to obtain an average “best” shape.

 

5.6.2    The general use of 2-dimensional digitising in a functional ecological study and its application to burdock hooks – a proposal for further experiments

 

In studying the attachment interactions of a biological attachment mechanism it is necessary to study both the biological structure and the structure of the substrate and their interactions.

 

To this end it is necessary to study the engagement of the attachment mechanism.

 

In order to utilise 2-dimensional digitising to study the interactions of a burdock hook (Arctium minus) and substrate it would be necessary to immerse the attachment in a clear resin which could harden.  Thereafter, a section must be taken through the hook and examined under a microscope.

 

The relationship of principle interest would be the ratio of proportion between the hair follicle diameters and the radius/diameter of curvature of the hook and this would be related to the attachment force.

 

Further, the qualities of the substrate would require study including the extent of entanglement during attachment and the frictional relationship between the materials.  Gorb [‎9] has already studied the critical criteria for hook strength which he has concluded experimentally to be the length of the shaft for a given material and hook radius, i.e. taking two hooks of the same material, from the same plant and testing them for fracture strength, it was the shorter of the two that would fracture first. This is due to the energy absorbing qualities of cellulose as a biomaterial and the mode of fracture (see experiment 3 for more on this topic). Combine this information with a comparison of attachment strengths for different substrates and materials and one should arrive at an optimum performance.

 

5.6.3    Subsequent experiments to complete the analysis of burdock

 

From a functional ecological perspective a study could be made of the relative strength of attachment of burdock to the fur of indigenous species, including rabbit, deer, sheep, goat and badger.  The fur of each species will have different qualities.  Further, the test could be made using both wet and dry fur, to compare performance under different conditions.

 

The outcome of the experiments would provide a biomimetic indicator as to the quality of substrate that best suits burdock and the attributes of that substrate.

 

 

 

 

 

 

 

6      Preamble to Experiments 2 and 3

 

 

6.1    Introduction:

 

 

The next two experiments can be viewed separately and together as being part of the development of an experimental procedure for the biomimetic study of small attachment mechanisms. Arctium minus or burdock has been chosen as the subject because of its availability. It is commonly regarded as having been the inspiration behind Velcro.  This does not mean that all aspects of this species have been studied nor that they have been studied in the manner in which Gorb prescribes from his biologist perspective with regard to miniature attachment mechanisms.  For instance, a mathematical model for the interaction of a hooked structure and a simulated piece loop of hair/fur, and for a field of these, has yet to be discovered in the literature (but this research has not yet been declared conclusive).

 

Background materials that should be read prior to these experiments are:

 

Appendix 2 – Biomaterials etc

Appendix 3 – The plant cell wall etc

Appendix 4 – Studies of attachment etc

Appendix 5 – Morphological studies etc

 

It bears repeating here that small structures are generally viewed as being shape optimized from [‎1].

 

The design process for small biological attachment systems is described in Gorb [‎2].

The first experiment on imaging small biological structures has further applications.  The conclusion to the experiment includes descriptions of the directions that this research can take from here [Section ‎7.9].

 

Experiment 3 on the tensile testing of burdock hooks was to confirm the conclusion of Gorb that it is the span of the hook that is the dominant parameter with regards to the separation contact force of a biological hook. Further it served the purpose of being an introductory study into the fracture of biomaterials, (in this case cellulose).

 

The apparatus available for this test was an Instron tensile tester.  Gorb prescribes the use of a micro-force tester with an optical sensor for this form of experiment for its increased sensitivity and this is discussed and described in Appendix 4.  He uses the micro-force tester in order to assess material properties which is difficult and cumbersome using a tensile tester of the size and shape of the Instron.

 

 

 

 

 

 

 

 

 

 

7      Experiment 2 – Confocal Microscopy and its Application to Recording Small Biological Morphologies

 

7.1    Introduction

 

This experiment was conducted early in the research, prior to reading background material on the subject. For this reason there are errors in the method in which it was conducted.  Nevertheless the results are adequate to illustrate the principles of an experiment that can be repeated easily and swiftly and to discuss applications.  Improvements to the methodology are completely specified. Below, Section ‎7.3 contains notes from an important paper on confocal imaging by G Sanson et al [‎7] which was not available at the time of the experiment.

 

It has been possible to do much more background research post-experimentation.  For a more detailed description of the development of the recording of morphologies see Appendix 5. Appendix 4 on insect attachment mechanisms and Appendix 3 on plant surfaces are also appropriate.

 

A reminder here that Gorb has asserted that in the field of micro-attachment devices it is those parabolic fasteners such as the dragonfly head arrestor mechanism that are more important than hooked devices [‎3] and these are the attachment devices that will be of more interest to engineers.  However, there is room in the field of pest control and insect/plant interactions that can be studied (see Section ‎7.9.1.2) for alternative forms of interactions of re-usable attachment devices for moving parts instead of static attachment devices.

 

7.2    Imaging at Bath University

 

 

Apart from Appendix 5 on imaging biological morphologies, a review was made of the available means of recording morphologies that was available here at the university and at other nearby research facilities. The Biomimetics website http://www.bath.ac.uk/mecheng.biomimetics), written by Prof J F V Vincent, states that the first requirement for studying a structure is recording its shape.

 

This investigation was begun on the back of a six month investigation into 3-D vision, a final year project of an undergraduate mechanical engineering degree.  That project took the form of writing a program to link a stack of images, each image consisting of a profile of an object turning on a turntable about a central axis, in order to produce a 3 dimensional wire-framed model of said object.  In concluding that project the limitations and difficulties of surface imaging had been thoroughly investigated, in particular when dealing with internal curved surfaces and undercuts such as the inner radius of a hook.

 

The digital capturing of the shape of these small hooks became the first challenge of the project.  Investigations on the web and through discussion with colleagues revealed that in the world of microscopy and laser scanning there was a technology gap in the capturing of 3-D images of objects of the order of magnitude of approximately 0.1mm to 0.001mm, particularly flexible and fragile biological specimens with hooks that could form extremely small radii of curvature.  There was a possibility of success using the confocal microscope which is normally used for studying cells and organelles in the neurology department of the university.

 

The paper “3-D Modelling of Biological Systems for Biomimetics” by Shujun Zhang, K Hapeshi, A K Bhattacharya [‎16] has a complete discussion of biomimetic imaging methods, including the use of NURBS and laser scanning techniques. S Zhang saw the confocal image of a burdock hook in the main body of this paper prior to writing his paper which was published in Prof Vincent’s Journal of Biomimetics Vol 1. The following brief research was conducted by this researcher, into imaging methods currently available at this and nearby facilities, prior to this paper being published.  The experiment into confocal imaging was conducted before this student had encountered the paper of Sanson et al.

 

The results are therefore for demonstration purposes but the imaging, for reasons that will be explained, will have to be repeated.  For the purposes of discussion however, they are perfectly adequate.

 

Here follows a brief review of some of the imaging methods available in the Mechanical Engineering Department at Bath University.

 

 

 

 

7.2.1    Touch probe digitising

 

The Mechanical Engineering Department had recently acquired a touch probe digitiser from the company Renishaw of Wootton-under-Edge, Gloucester. The problem with using this machine for a small hook is apparent when one compares the size of the digitising probe tip and the radius of the typical insect hook. There simply isn’t the room to insert even the smallest probe to take a sequence of accurate points.

 

There is also the possibility when considering the digitising of a burdock hook, that the probe could bend the shaft of the bract, even with very small pressures and therefore cause inaccuracies.

 

7.2.2    Laser scanning

 

The department has acquired a laser scanner that functions with a turntable to produce 3-dimensional, accurately scaled and coloured images of objects. It does not have the accuracy required to scan the small hooks of my specimens.

 

7.2.3    Micro CT Scan

 

This sounds most suitable for the size requirement. It has all the accuracy required, there is one at Bristol University, but enquiries after using it prompted noises of funding. The confocal microscope investigation continued.

 

7.3    Notes on Imaging with the Confocal Microscope

 

The following has been taken from Sanson et al in his paper on the imaging of mammalian teeth [‎7].  It is essentially notes on how to take a suitable image of a small object for the purposes of digitizing and reproduction, both in virtual reality and for the purposes of manufacturing an artificial model. This paper is described in Appendix 5 as well but the details must be included here because of their direct relevance to this experiment.

 

The main benefits of using the confocal microscope are i) speed ii) ease of mounting the specimens and iii) accuracy at a micron scale.  Confocal microscopy and atomic force microscopy (see Appendix 5) both allow for specimens to be mounted upon a slide using distilled water as a medium.

 

In capturing an image it must be born in mind that the goal is an accurate 3-D model for both virtual reality applications and for the creation of an artificial model.  This makes it important to set the slice thickness accordingly.  The paper by Sanson et al details a method of taking a cast of a tooth which is more technically cumbersome than simply putting a microscope slide with specimen under the objective and so some of his paper is not relevant here (the details concerning the casting of the teeth).  However, there are details in this paper which are common to the goal of imaging and these are noted here:

 

  1. The make and model of the microscope is important to note.

 

  1. The type and size of the objectives e.g. x 5 (0.12 NA) and x 10 (0.3 NA) dry objectives.

 

  1. The optics e. g. rhodamine (excitation 568 nm and emission 590 long pass).

 

  1. The fields of view of the lenses e. g. 2 x 2 mm and 1 x 1 mm.

 

  1. The setting of the pinhole e. g. 1 optical unit.

 

  1. The measured axial resolution e. g. 35 mm

 

7.3.1    Comments from Sanson et al [‎7]

 

 

Optical slices were taken through the x, y plane where each slice was square (e. g. 256 x 256) pixel 8-bit image at medium scanning speed.

 

Slices must be taken at the same distance as the interval between pixels to make cubic voxels.

 

Software such as Zeiss is used to generate a 3-D image from the stack of slices, where pixel intensity represents height and the z-height is found by comparing the intensities for each x, y point (in fact, a column of pixels all with co-ordinates x, y)

 

In most of the tests run by Sanson et al, the cubic voxels (and z-interval) were 7.8 mm long, generated in one the two following ways:

 

  1. x 5 lens – a 256 x 256 pixel image was scanned at zoom 1 (field of view (FOV) of 2 x 2 mm), or a 128 x 128 pixel image was scanned at zoom 2 (FOV 1 x 1 mm)
  2. For the x 10mm lens, a 128 x 128 pixel image was scanned at zoom 1 (FOV 1 x 1mm)

 

In other words, using a lens with a field of view (FOV) of 2 x 2 mm at a setting of zoom 2 reduces the field of view to 1 x 1.

 

Surface noise can affect the image and give a false indication of where the true surface lies.  Sanson et al did experiments with the x 5 and x 10 lens to see how best to obtain the most accurate surface image. They used two techniques to try to reduce surface noise; accumulation and averaging.

 

Accumulation is to accumulate and average several images at each z height and then create an image from the accumulated image slices.  On the microscope this is termed, for example, an “Accumulation 2” scan where the 2 stands for the number of slices that are averaged.

 

The second method was to take the average of a number of reconstructed 3-D images of the same area.

 

This was tested using a specially prepared and dimensionally precise standard glass specimen and comparing resultant images. The specimen was cubic and so without any undercuts but with a 45o fillet.  Inner width was 1.3mm and outer width 1.7mm.

It was found that averaging produces better results than accumulation.

 

Sanson et al used a resin casting of their teeth specimens which was coated with eosin, a fluorescent dye.  Figure 7 shows two image slices obtained without any post-processing.  The outline of fluorescence is clearly visible.

 

Figure 7 – Examples of two slice images from Sanson et al [‎7]

 

7.4    Aim

 

To investigate the imaging of biological structures (hooks of plant and insect material) using a single photon confocal microscope.  This was to be a preliminary investigation into gathering a 3-D image that could be converted to a STL (stereolithography) file for export to a rapid prototyping device for the creation of an artificial model for the physical study of structure/substrate interactions as well as making it possible to model these interactions using virtual reality.

 

Figure 8 – A specimen of Burdock

 

7.5    Method

 

It was decided that the specimens were small enough and, possibly, translucent enough to laser light, such that it might not be necessary to use the casting method.  Instead it was decided to attempt to image a plain specimen.

 

Specimens of a burdock bract, a bee tarsus and a grasshopper tarsus were each mounted upon “well” microscope slides in distilled water (it is a feature of both confocal and atomic force microscopy that specimens are mounted easily without much treatment) and placed in turn under the microscope (with a large contribution of assistance from Ian Jones, the technician in Neuroscience in Biology). The results of the three scans are below.

 

 

 

7.5.1    Specimen orientation (microscopy technique)

 

With regard to the confocal microscopy, it was important to get the specimen in the right orientation on the slide to avoid displaying an undercut surface to the laser light.  Further, it is important to optimise the strength of the laser and reduce the required depth of penetration.  Alternatively it could be useful to remount the same specimen a number of times in different orientations in the slide to fully expose the complete detail of the structure.

 

7.6    Apparatus and method

 

  • A Zeiss single photon confocal microscope in the Neuroscience section of the Biology Department.
  • Well slides which are microscope slides with a bowl ground out in the centre to receive specimens that are not flat.
  • Distilled water as a medium for slide mounting.

 

7.7    Results

 

When infused with the laser light at three different frequencies it was found that the burdock hook fluoresced well under the green laser light (note that the cellulose hook is brown in colour, not green as the reader might suppose, see Figure 8 – A specimen of Burdock previously).  Under the red and blue light the resulting image was less distinct. The stacked image is then output to file and stored as a sequence of .tif files that are viewed in .avi format (see below for the full range of .tif images).

 

7.7.1    Burdock hook

 

Stereogram images of the hook are overleaf (Figure 9, Figure 10 and Figure 11). The data from the confocal microscope is a sequence of image slices that are then automatically reassembled (stacked). Evidence of the stacking can be observed in the images from the stepped outline of each image.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 9 – Sterogram 1 of the burdock hook specimen

 

Figure 10 – Stereogram 2 of the burdock hook specimen

 

Figure 11 – Stereogram 3 of the burdock hook specimen

 

The individual .tif images that make up the above stereogram are below (see Figure 12 – 1 – 20 The individual .tif files that make up the stereogram of the burdock hook (Figure 8) above (the scale bar defines 200 mm)).  The glow that surrounds the stereogram images derives from the fact that this view of the hook is assembled using standard confocal software and the viewer is looking through preceding and following images which are a result of the perspective of looking at angled images.  Only in a profile image does a stark outline of the hook show.  There is an artefact on the microscope slide that shows to the left of the hook.

 

 

1.   2. 3.  4.

5. 6.  7.   8.            9. 10.11.12.

13.14.15.16. 17.18.19.20.

Figure 12 – 1 – 20 The individual .tif files that make up the stereogram of the burdock hook (Figure 8) above (the scale bar defines 200 mm)

 

Figure 12 – 1 – 20 The individual .tif files that make up the stereogram of the burdock hook (Figure 8) above (the scale bar defines 200 mm) shows the component images that comprise the stereogram. Note that the images from the confocal microscope show internal structure of the hook, particularly the cellulose microfibrils.  These microfibrils are visible in the next experiment which fractures the hooks in a tensile tester.

 

7.7.2    Bumblebee and grasshopper tarsi

 

 

Figure 13 and Figure 14 shows the image sequences through a bee and grasshopper tarsi.  In both of these sequences the image starts in the furthest plane and the slices move towards the viewer.

 

Interest in imaging these two specimens comes from an interest in studying insect/plant surface interactions. (see Section ‎7.9.1.2).

 

Insect material doesn’t fluoresce as well as the plant material of the burdock hook but the tarsi as structures are more complex than the hooks. Attempts were made at all 3 wavelengths (red, blue and green) and combinations of the three. It is certain that a 2-photon microscope with its greater focus and depth penetration would improve the image making capability.  The laws of physics say that blue light has the highest energy but excitation of molecules is sensitive to the exciting frequency so exciting the molecules with all three colours gives a spread of frequencies that provoke the maximum excitation.

 

The results to the insect experiments have not been presented as stereograms.

 

The following sequence of images (Figure 13) shows a progression of the laser through the specimen.

 

The z-axis of the laser starts furthest away from the viewer and moves “closer” towards the viewer during the progression through the stack, from image 1 – 30.

 

A combination of all three wavelengths of light (red, green and blue) was used and these are visible in the images.  It is interesting to note that different structures in the tarsi fluoresce at different frequencies and that the combination of all three provides an opportunity to look “into” the structure and identify different structures through colour differences.  The plain of the laser is identified to the viewer by those parts of the image that reflect white light.

 

 

1.      2.  3.   4.  5.      6.  7.   8.         9.     10.11.12.

13.14.15.16. 17.18.19.20. 21.22.23.24. 25.26. 27.28.  29.30.

Figure 13 – 1 – 30 confocal microscope image “slices” of hooked bumblebee tarsus (scale bar indicates 200 mm)

 

7.7.3    Grasshopper tarsus

 

See images overleaf.

 

 

 

1.   2.  3.  4.

5.   6.  7.  8.

9.  10.11.12.

13.14.15.16.

17.18.19.20.

21.22.23.24.

25.26.27.28.

Figure 14 – 1 – 29 consecutive confocal microscope image “slices” of the hooked grasshopper tarsus (scale bar indicates 200 mm)

 

It is possible to see the setae (hairs) on the underside of the metatarsus (the structure that supports the tarsi) which aid in adhesion of the structure to plant surfaces through friction and adhesion (setae secrete tarsal fluid which aids with adhesion [‎15]).

 

7.8    Discussion

 

 

The first fact that should be noted is that the image slices here were too thick to obtain cubic voxels. These images were taken at z intervals of 19mm whereas Sanson et al advises a sectioning thickness of 7mm to obtain cubic pixels necessary for accurate conversion to an undistorted 3-D image.  This has the effect of increasing the memory requirement for storing the complete stack of images required to section the image [‎16].

 

If that fact is acknowledged and noted then the discussion can continue.

 

A comparison between the images that Sanson et al obtained (Figure 7) and those of Figure 12, Figure 13, and Figure 14 shows obvious differences.  Sanson’s images were obtained from a casting of clear resin painted with fluorescent dye hence the images are much clearer.  A problem with using the whole specimen mounted on a slide is that the laser picks up details that are off the plain of the laser through reflection and scattering of the light. This means that some preprocessing of the individual slices would be necessary before conversion to a STL file.  Consideration of Figure 15, a single image taken from Figure 14, will aid the discussion.

 

Figure 15 – Image number 18 taken from Figure 14

 

 

Imaging using a confocal microscope has the benefit of revealing internal structures, though not adequately enough to negate the requirement of physical sectioning for biological study purposes.

 

The process of transforming this and the other images in the stack could resemble that of the 2-dimensional digitizing using the AppleMac (see Section ‎5.4.1) if it was necessary to perform the task manually. The pixels of the greatest intensity show the plane of the laser light.

 

Alternatively the images could be subjected to an algorithm as follows:

  1. Each slice would go through a process of edge detection using the Canny edge detection algorithm for instance to locate the highest intensity voxels that make up the edge of the image data cloud.

 

  1. The resultant “step” shaped 3-D data set would then be put through a process of interpolation to obtain triangular facets for the object surface with a unit normal for each facet to show direction. In other words the voxels have now been converted to a triangulated surface mesh that is a vector graphic.

 

  1. This image would then be scaleable to a useful size for production of an artificial model.

 

  1. The resulting data file is thus converted to a .stl format suitable for export to a rapid prototyping device.

 

All these algorithms are described in detail in “Image Processing Analysis and Machine Vision”[‎17].

 

The confocal microscope on the mounted specimen enables the user to see the internal structures but it is plain to see that it would be beneficial to improve the technique and orientation of mounting the specimen to expose the setae to the laser.  This is possible under a confocal microscope but this has yet to be investigated fully.

 

 

7.8.1    Atomic force microscopy

 

 

Atomic force microscopy and its abilities are discussed in Appendix 5.  Of particular interest is the conversion of its output files to 3-D and then .stl (stereolithography) formats.  In the next section there is discussion of the study of pest control on plants.  In the reproduction of artificial models of tarsi/plant surface interactions, an ability to pair the abilities of confocal microscopy with the abilities of atomic force microscopy is of value.  This has a bearing not only upon pest control, since tarsi/surface interactions are attachment mechanisms and these have been effectively studied to find ways of preventing damaging pests walking upon host surfaces previously (see Section ‎7.9.1.2Pest Control below). But it also has application in modeling the hook/substrate using virtual reality.

 

Gorb’s model for designing miniature attachment mechanisms can be taken beyond solid modeling of approximations to truly investigating the variations in nature which may not be associated with repeated patterns as his models in his paper on parabolic fasteners suggests [‎3].

 

Appendix 4 on attachment mechanisms contains the observation that the pitcher plant makes use of trichomes and its surface wax platelets to interfere with and direct the movement of ants from [‎3].

 

 

 

7.9    Conclusion

 

The ease with which these preliminary images were obtained is fortunate although it could be predicted that some measure of success would be achieved from the physics of the microscope. It was fascinating and impressive to observe the speed with which the confocal microscope acquires and processes the images (15 minutes from placing the microscope slide under the objective to obtaining a 3 dimensional image on screen).

 

This experiment was conducted in order to get a 3-D digitised image of the specimen for two purposes:

 

a)      To have a suitable image that could be exported directly to ANSYS and analysed using 3-D finite element analysis after the paper on the tiger’s claw [‎6].

 

b)      To convert the data to a vector graphic file that could be enlarged and further, exported to a rapid prototyping machine to produce a scaled-up rendered model.

 

Considering the process of rendering a scaled model as outlined in the discussion, problems were foreseen with regard to paying for the resin (at that time the device in the biomimetics laboratory was not in place and the quote for the powder resin in the manufacturing laboratory was £800/kilogram) and at that time this researcher was not content with the preliminary investigations into the subject area that it was felt wise to diverge from the topic so early. However, Dr Dylan Evans used a slight variation on the technique to produce a life-sized model of the heart from MRI scans instead of the scan from a confocal microscope.

 

The product of an MRI scan is similar to that of a confocal microscope, namely a stack of 2-Dimensional images. It should be added that the process was not as forthright as it sounds, it was necessary for Dr Evans to do some smoothing of his 3-D image using ImageMagic software, prior to sending the image to the rapid prototyping device.  This is because the interval between the MRI scan images is approximately 1 cm and a human heart is approximately 18 cms hence the necessity for the smoothing for a 1:1 scale model.  It is expected that this will also be the case for a micro-sized structure when it is enlarged to a size that can be produced through a rapid prototyping device since invisible flaws in the curvature of the reproduced surface will be exaggerated by the enlargement.

 

7.9.1    Applications

 

7.9.1.1  The controlled manufacture of small (micro-sized) structures

 

From research it is clear that there is at present a technological problem with the controlled assembly of micro-sized structures.  Because of the scale of size of the image sections and the interval between them which is commensurate with molecular dimensions due to the accuracy of the confocal microscope, it is hoped that there might exist a potential to exploit this microscopy technique to generate a scaffold upon which to lay down layers of biomaterial in a “sandwich” effect.

 

In particular, the biomaterial keratin could be a suitable material to study since the structural material of keratin is not secreted from within the cell, instead it remains as an intra-cellular material.  At present the controlled assembly of structural biomaterials fibrils such as cellulose is not possible.  This means that an alternative means must be found of fusing structural bio-molecules together.

 

The question is asked would it be possible to use the series of sections (once the image sections had been cleaned up) as templates for the manufacture of membranes suitably engineered to support keratin cells.  The layering effect of the sections would give rise to structures completely consisting of bio-material that would be based on evolutionary design exhibiting (hopefully) predictable behavior and which would bio-degradable and bio-compatible.  With the biomaterial keratin, for instance, in its natural state there exists a problem with keeping the cells from coalescing in solution.  A membrane would act partly as a support structure and partly as a structure for dispersion of the cells in a controlled fashion.

 

7.9.1.2  Pest Control

 

Gorb’s paper “Miniature Attachment Systems: Exploring Biological Design Principles” [‎2] highlights another application of the study of miniature attachment systems, namely that of insect/plant interactions.  This is the reason why the preliminary research upon trichomes (see Appendix 3) has been included.

Further, Appendix 4 Section 1.8 describes the paper “Performance and Adaptive Value of Tarsal Morphology in Rove Beetles of the Genus Stenus (Coleoptera, Staphylinidae)” (2002) O Betz [‎18] and demonstrates some testing methodologies that have been used to examine insect/plant surface interactions.  These tests are somewhat biological in their emphasis (i. e. holistic and non-reductionist) however the manner in which the tests were conducted and the knowledge of the instrumentation used is useful.

 

The pitcher plant/ant interaction guides the ant towards the waiting trap through directional trichomes preventing the ant from retreating across the surface, as well as waxy plates interfering with the tarsi of the ant thereby causing a loss of traction (from [‎2]).  This could provide a biological example of a form of one way attachment system or it could provide a form of control, using the surface structures as guides to an autonomous but non-intelligent entity.

 

Another example cited by Gorb is the honeybee (see [‎2]).  A species of honeybee has been genetically modified to have a coating that prevents infestation by parasitic mites.

 

Combining Gorb’s work with the study of pest control provides an interesting research area which clearly has direct and indirect applications, particularly if one includes the use of atomic force microscopy (see Appendix 5 for more on microscopy).  It must be stated here that thus far insufficient reading has been done in this field for comment to be made with sufficient authority.

 

 

8      Experiment 3 – Tensile Testing and its Applications

 

8.1    Introduction

 

 

Appendix 4 contains detailed descriptions of papers on the study of hooked attachment mechanisms.

 

8.1.1    The functional ecology of Arctium minus (burdock)

 

[Note: As with the experiment on the confocal microscope, the procedure with which this experiment was executed was not with the precise methodology that would be expected of a biologist.  This was not of particular importance since this experiment was to confirm the result of S N Gorb et al in the paper entitled “Contact Separation Force of the Fruit Burrs in Four Plant Species Adapted to Dispersal by Mechanical Interlocking” [‎9], that it was the hook span that was the prime factor that influenced the contact separation force, that is, the larger the span the higher the contact separation force.]

 

Acknowledgement is due here to the papers by Gorb et al (Natural hook-and-loop fasteners: anatomy, mechanical properties, and attachment force of the jointed hooks of the Galium aparine fruit” [‎4] and “Contact Separation force of the fruit burrs in four plant species adapted to dispersal by mechanical interlocking” [‎9] for much of the following information and presentation style.

 

Higher plants use a variety of dispersal agents such as wind, water, animals and people.  Dispersal by animals is known as zoochory. Dispersal by fruit-eating animals (frugivores) is known as endozoochory or by ants is known as synzoochory.

 

The dispersal of seeds or fruit (known as diaspores, more often fruit than seeds) by attachment to animal fur or feathers is known as epizoochory.  Diaspores of this kind do not provide valuable nutrition to the animal to which they attach themselves nor do they actively attract animals to parent plants.  Instead they have special structures such as hooks, barbs, burrs and spines or sticky secretions and they detach easily from the parent plant.

 

That is, there are two mechanisms of diaspore attachment:

 

  1. Mechanical attachment.
  2. Attachment by glue.

 

In fur and feathers the diaspores may remain attached for a long period of time until animals groom them off or until the animal dies.

 

Arctium Minus is a plant indigenous to the UK. Its natural symbiotic partners in seed dispersal are wild animals and birds indigenous to the UK, such as rabbits, badgers, foxes, sheep and deer.  The diaspores of Arctium minus are adapted for dispersal by mechanical interlocking.

 

While it may be true that Arctium minus has been studied extensively by the inventors and manufacturers of Velcro, this does not necessarily mean that the species has been studied from a biomimetic perspective.  Certainly no paper has been written on the study of Arctium minus in the form as demonstrated by S Gorb in his papers on miniature attachment mechanisms and the design of miniature attachment mechanisms, and Velcro the product has significant structural differences compared to burdock the natural hook (see Figure 16 – velcro, from [‎19]      Figure 17 – SEM of burdock hook) below.

 

 

Figure 16 – velcro, from [‎19]                          Figure 17 – SEM of burdock hook

 

Therefore this study can be utilized in two ways;

 

  1. As a study of the fracture of plant material (cellulose), a biological composite.
  2. As part of the study of natural hooks to understand adaptive growth and shape optimization in nature and derive a design hypothesis for mechanical hooks.

 

In the biomimetic design process described by Gorb, the process of identification of the structure/species is obviously complete.  Gorb demonstrates a method of assessing the mechanical properties of the material. The mathematical modeling of a hook structure’s mechanism of attachment as it is produced in his paper on parabolic fasteners (apparently) has not yet been done.  He has highlighted the dominant feature of the hook fracture strength to be the shaft span (variable “sh” in Figure 1, Section 1.22. of appendix 4).

 

[Note: this is another possibility for insect tarsal/substrate study – developing a model for tarsal interactions with a substrate.  A tarsal claw (singular) is shaped like a bent parabolic fastener.  If one took the Gorb model for a probablistic fastener with parabolic elements [‎3] and inserted a curve perpendicular to the parabola plane to bend it, before angling the resulting hooked parabola at some angle to the vertical one would arrive at a descriptive model for a single tarsal claw.  This could then be expanded for multiple claws.]

 

In the burdock plant, the hooks are formed from the tips of specialised bracts that protect the seed pod. These bracts do not carry seeds individually. The entire fruit becomes entangled in a passing host such as the fur-coat of an animal and the fruit separates from its branch whereupon it begins to disintegrate, splitting apart as more hooks become enmeshed in the fur until seeds are revealed to either fall to the ground as the pod breaks up or be shaken out of the opening at the top of the pod.

 

The array of hooks that the fruit presents to the world is a probabilistic fastener, with a field of hooks just as the dragonfly head-arrestor mechanism has fields of microtrichia (bristles) [Error! Reference source not found.]. The field of systematics could be applicable here since the study of the number and dispersion of the hooks about the seedpod could, for instance, yield information indicating some optimisation such as hooks per arc of radius or optimum rows of hooks per sphere, with reference to fruit mass.

 

The flat bracts from which the hooks develop are flexible in a single plane.  This flexibility (from Gorb et al’s paper on the Galium aperine fruit [‎4]) increases the likelihood of attachment to a host since hooks are able to flex and bend to attach to a substrate that is not necessarily directly in contact, thereby participating in the attachment process.

 

The burdock hook will attach to a variety of substrates, even to skin, because of its differing structure to the conventional hooks of a Velcro system. The pointed tip at the end of a flexible tapering shaft penetrates many types of material with strength due to its toughened, desiccated state and its flexible shaft bends backwards to allow the needle sharp point to pierce the substrate.  This means that an artificial burdock made in this shape might not require a pre-defined substrate.

 

In the burdock plant, the hooks are formed on specialised bracts that protect the seed pod. These bracts do not carry seeds individually. The entire fruit becomes entangled in a passing host such as the fur-coat of an animal and the fruit separates from its branch whereupon it begins to disintegrate, splitting apart as more hooks become enmeshed in the fur until seeds are either revealed to fall to the ground as the pod breaks up, or they are shaken out of the opening at the top of the pod where the corolla of the pod used to be.

 

Consider Figure 18 and Figure 19 that follow:

 

 

Figure 18 – Burr variables from Gorb [‎9]

 

 

Figure 19 – Micro-testing of hook tensile fracture force from Gorb [‎9]

 

Figure 18 – Burr variables from Gorb [‎9] demonstrates the variables that Gorb used in his experiment that led him to conclude that the principle geometric variable determining the strength of a hook is the span of the hook (distance from shaft to hook tip equivalent to a diameter of a semi-circle).  Figure 19 shows the microforce tester that he used.  This piece of equipment is not available in the biomimetics laboratory. It is equipped with a sensitive optical sensor which aids deflection measurement.

 

Figure 18 – Burr variables from Gorb [‎9] shows the variables that could have been noted during the experiment if the purpose had been the study had been to ascertain the correct criteria. Figure 19 – Micro-testing of hook tensile fracture force from Gorb [‎9] shows the micro-force tester that should have been used because of its increased accuracy in measurement.

 

Figure 20 – Showing the calculation of elastic modulus of the hook material from Gorb [‎4]

 

 

Figure 20 above shows the use of the microforce tester to assess the elastic modulus of the hook material.  A bending force was applied to the top of the shaft which was treated as an inclined shaft.  The deflection was measured and from this, using the bending equation for beams, a result was calculated for Young’s modulus E.

 

The statistical analysis used by Gorb was Kruskal-Wallis one-way ANOVA on ranks with P<0.001 and Dunn’s Method of pairwise multiple comparison (see Section ‎8.6.3 below).  This is a method for comparing samples of data from similar specimens of different species and relating performance qualities.

 

8.2    Aim

 

To investigate the fracture force of hooks from the plant genus Arctium lappa or common burdock using an Instron tensile testing machine to observe any telling differences that could be observed from the conclusion of Gorb that the span of the hook was the significant factor in contact separation force by testing specimens of different radius of hook collected from burdock pods of varying diameters. Further, to observe the nature of fracture of the composite biomaterial and to use this information in developing a design hypothesis for the design of optimum performance hooks and attachment mechanisms.

 

8.3    Method and Apparatus

Figure 21 – One of the burdock bushes from which samples were collected

 

  1. Specimens were collected from four separate burdock plants that grow behind the University of Bath accommodation blocks. The plants all stand in a line next to a sandy path that passes between the University grounds and the golf course.

 

  1. Note was maintained of the conditions of collection and the regions of the individual plants from which specimens were collected. These specimens were collected late in October 2003 and tested in December. It was observed that the plants themselves were brown and dry with the leafy vegetation of early season growth disappeared and the seedpod fully developed.

 

  1. Specimen hooks were collected in the form of whole fruits. The specimens were stored in paper packets until it was possible to conduct experiments upon them. (~30 days).

 

  1. It was judged that the effect of the delay between the collection and testing of the hooks would have little effect on the relative performance of the hooks and probably little effect on the absolute performance of the individual hooks given that they were collected in a naturally desiccated state and maintained in a dry condition until ready for testing, thereby preventing/inhibiting decomposition. Their desiccated state also made them ready for SEM work.

 

  1. Five individual fruit specimens (each consisting of an array of approximately 100 hooked bracts) were collected from each plant giving 20 specimens in total. A selection of these specimens was then tested.
  2. At the commencement of each test the burdock fruit was sectioned in half and one half labelled and stored back in the specimen drawer. These are still available should any future measurements be required but of course, although they have been stored in a dry state, they are not truly ideal.

 

8.4    Specimen Preparation

 

Each fruit was sectioned into halves under a dissecting microscope. One of these halves was returned to the specimen packet in case more hooks from the same specimen would be required. The other hemisphere of bracts/ovary/seeds was separated to “free up” the hooked bracts that surround the ovary.

Ten individual hooks were taken from the dispersed hemisphere. These were mounted in preparation for testing in the Instron machine by gluing each, entire bract to a plastic mounting with 5mm of the bract shaft with its hook extended and exposed for interaction with a testing substrate (in this case a loop of silk thread as will be discussed).

 

Figure 22 – mounting the bracts for testing

 

 

Images were retained of all the stages of the experimentation.

 

8.5    Results

 

Below are the results for tests on approximately 60 specimens, from 6 different burdock fruits.

 

Graphs are included of the detachment force of each set of specimen hooks. The mean value of these results for each specimen is then plotted versus the diameter of the fruit.  There is also SEM images of the fractured surface of the hook.

1.               2.

 

Figure 23 clockwise from top left: the rack of prepared specimens, testing the hook fracture force with silk thread, a fractured hook.

 

 

 

 

 

 

 

 

 

 

 

1.  2.

 

3.  4.

Figure 24 – SEM’s of the fractured hooks

 

The process to fracture was filmed using a high speed camera and the footage has been retained but is not included here.  See the Discussion for more on this.

 

 

 

 

 

 

 

 

 

8.5.1    Graphs of the fracture loads of specimen hooks

 

Specimen No 2 3 4
Fracture Force (N) Fracture Force (N) Fracture Force (N)
1 0.00101 1 0.00114 1 0.00057
2 0.00104 2 0.00121 2 0.00108
3 0.00107 3 0.00099 3 0.0011
4 0.00103 4 0.00095 4 0.00083
5 0.00087 5 0.00098 5 0.00092
6 0.00085 6 0.00091
7 0.0009 7 0.00092
8 0.00093 8 0.00107
9 0.0009 9 0.00115
average detachment force 0.001004 0.000983333 0.00085375
std dev (s) 0.031685959 0.003401055 0.000150867
Height (mm) 17.5 10 14
Diameter (mm) 23.5 15 14
Specimen No 5 6 7
Fracture Force (N) Fracture Force (N) Fracture Force (N)
1 0.00135 1 0.00059 1 0.00139
2 0.00093 2 0.0011 2 0.00114
3 0.00112 3 0.0012 3 0.00112
4 0.00124 4 0.00088 4 0.00106
5 0.00114 5 0.00109 5 0.00105
6 0.001 6 0.00118 6 0.00131
7 0.00086 7 0.00127 7 0.00127
8 0.00113 8 0.00109
9 0.0012
average detachment force 0.001163333 0.001168 0.00117875
std dev (s) 0.002073291 0.000250516 0.000108428
Height (mm) 16 17 17
Diameter (mm) 26 25 23

Table 1 : Fracture forces of burdock hooks [Height and Diameter of fruit refers to the entire ball of hooks]

Figure 25 – Specimens 2 – 7, Mean hook fracture forces vs Burdock fruit diameter

 

 

 

 

 

 

 

 

 

Mean Hook Fracture Force (N) height (mm) diameter (mm)
0.001163

 

16

 

26

 

0.001168

 

17

 

25

 

0.001168

 

17.5

 

23.5

 

0.001179

 

17

 

23

 

0.000983

 

10

 

15

 

0.000854

 

14

 

14

 

Table 2 – Specimens 2-7 mean hook fracture forces and dimensions of whole burdock fruit

 

Figure 26 – SEM of a burdock hook with scale bar reproduced from figure 1

8.6    Discussion

 

8.6.1    Images of fracture

 

 

The SEM images of the fractured hooks (Figure 24) clearly show the fibrous nature of the hook material and the fracture surface indicates the material properties, noting how the inner surface of the fracture surface fractures squarely with no fibre “pull-out”.

 

From Prof J F V Vincent’s notes on the mode of fracture of fibrous composites from [‎20] (and see Appendix 2) the lack of fibre “pull-out” indicates that the fibre/matrix interface of the plant material, cellulose microfibrils, hemi-cellulose and lignin (see Appendix 2), is tightly bound.

 

It can be seen that all 4 specimens experienced failure on the inner curvature of the hook as would be expected for a hook of material experiencing a bending moment with the inner fibres under tension while the external fibres are in a state of relative tension about a neutral axis.  The surface is typical of a fibrous composite break in bending.

 

All hooks fractured at the region of the join between hook and shaft which is the region of the entire hook structure (both shaft and arced tip) that experiences the highest bending moment when the hook is placed in tension.

 

Image 3 of Figure 23 shows a typical hook fracture.  In this case the hook “head” did not become completely separated from the shaft, being retained in place by a thread of material, having folded back onto itself to release the loop of thread before separating completely.

 

8.6.2    Force results

 

With reference to Figure 25 it can be seen that the hook fracture forces are all of the same order of magnitude but that there is a levelling of the slope in the region of the diameter equalling 20mm.

 

The specimen size ranged from 14mm to 26mm in diameter with a “gap” in the spread of specimen diameters in the interval between 15mm and 23mm. This gap appears as the step in the graph.

 

The force results agree with Gorb’s conclusion that increasing hook span indicates a greater force to separation.  The separation force levels out at 1.2 mN which can be taken to indicate the ultimate tensile strength of the cellulose microfibrils an the point at which the crack accelerates across the fracture plane and the hook disconnects from the tip of the shaft or folds back sufficiently enough to release the loop.

 

8.6.3    Statistical methods

 

Gorb clearly states the statistical methods that he used: Kruskal-Wallis one-way ANOVA on ranks with P<0.001 and Dunn’s Method of pairwise multiple comparison which allows comparisons to be made between any number of sample means, all in a single test. The P value is the acceptable significance. For further information on statistics for biologists see [‎21].

 

However, due to the nature of this experiment, based upon a single species, burdock, it was deemed that such statistical methods were unnecessary particularly as the investigation was to confirm a conclusion already made by Gorb, that span was the dominant parameter.

 

Were the experiment to be repeated along the lines of the papers of Gorb, then the statistical methods would be applicable as well as precise measurements of various physical dimensions of the hooks prior to tensile testing.  He includes standard deviation in the presentation of his results which has not been done here.  It would clearly be possible to do this if required.

 

 

The basic assumption was made that the radius of the hook would correspond to the diameter of the fruit. If the fracture strength of a hook was dependent on the radius (or span) of the hook then it would show correspondence to the diameter of the fruit.  As has been previously stated in the Method (Section ‎8.3), the specimens have been retained and this assumption can still be assessed and confirmed should it be required.

 

The test images using the high speed camera were similar to those from Gorb’s paper ‎9] and not fast enough to capture the actual fracture (due to the speed of fracture).  The actual footage has been retained but it has been decided to rely upon images of similar tests from Gorb’s paper which is described including figures in Appendix 4 (see Figure 5 of Section 1.2.2). That figure contains images of the process of fracture of four species of hook.  The process seen there is the same as that of burdock hook fracture including initial extension before fracture and so these images suffice.

Why should span be the dominant criteria for hook fracture, as asserted by Gorb?  This result completely satisfies the laws of mechanics and shape optimization.  If the material composition is consistent including fibre alignment then the larger the span of the hook, the larger the bending stresses the hook can incur (bearing in mind that it is shape optimized from hook to the base of the shaft) and hence the higher the fracture strength (called the contact separation force in the paper).

 

8.7    Conclusion

 

This experiment confirms that the separation force of a natural hooked structure is dependent upon the span or radius of a hook.  From Gorb et al [‎4] this is not always necessarily true for cellulose hooks and this can be accounted for by variations in biological material composition from species to species.

 

It could be assumed in mechanical design of a hook that the smaller the hook the higher the separation force since this would reduce the bending moment due to the tensile force.

 

 

 

 

9      Design Conclusions for a Shape Optimised and Materially Economical Hook Based upon a Plant Hook

 

The following is concluded from the preceding experiments on a plant hook such as burdock:

 

  1. That, for a material of construction that conforms to the qualities of cellulose in terms of fibre or grain alignment and material properties, it is the radius of the hook span that dictates the fracture strength provided that the entire hook and shaft is shape optimized and within the limits of the strength of the composite material.

 

  1. The proportions and dimensions of both hook and shaft are derived (in part) from the maximum force that needs be held.

 

  1. The point of maximum bending moment is at the connection between hook and shaft and this is a design criterion for the cross-sectional area of the shaft (it is assumed to be a tapered shaft as per Gorb and this is the minimum, limiting width before the hook bends towards the point of force application).

 

  1. Thereafter a safety check must be made through the proposed curvature of the hook that the rate of decrease of material matches the reduction of bending moment to the point of force application to confirm that the hook will not fail at a region prior to the hook.
  2. A second check must be made with reference to the bending moment at the base of the shaft to calculate the rate of shaft taper.

 

In nature if one considers shape optimization to be an optimization of material usage as well as optimum stress distribution then we arrive at the conclusion that copying the biological design provides a method of withstanding the greatest force with the minimum of material (that is, a homogenous material which can still be a composite material as long as the structure of the composite is consistent).  It must not be forgotten that there is an assumption that a natural hook has evolved to be as strong as it needs to be.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10  Future Work

 

 

There are a number of avenues for further research that arise out of this foundation research but it born in mind that I am not a biologist by training, nor do I aspire to be.  Therefore it is felt that I have explored the limits of the biological background required, within which to seat the next phase of work.  This notwithstanding, some of the directions listed below still have biological work associated with them.

 

The dominant goal, for myself as a mechanical engineer, would be to follow the biomimetic approach as described by Gorb and to move on to the next phase, post mathematical modelling, which is the development of a prototype.

 

It is believed that this should consist of investigating the possibility of manufacturing a scale model of an ant, a robot that can climb a wall.  This would include:

 

  • Exploring insect/plant strata relationships for pest control, in particular the relation between ant tarsi and pitcher plant surface morphology.
  • Mathematically modelling the attachment relationship as passive control mechanism using directional surfaces al la pitcher plant/ant interactions.  This would include an exploration of the gait or walking mechanism to produce the correct attachment/detachment movement, with the maximum of attachment force but the minimum of detachment force through the directionality of the tarsal movement.
  • Explore the possibilities of transforming atomic force microscopy output to 3D data and hence to a rapid prototyping device for surface models.

 

Further work that is of less intrinsic value but which may nonetheless be of interest:

  • Developing the design data-base that inter-relates biomaterials, artificial composites and small structures (hooks initially but this could be expanded).
  • Exploring the possibilities of utilising the confocal microscopy output file for use as membrane templates for the self-assembly of biomaterial (keratin) hooks of the same order of size as the specimen.
  • Explore and develop the evolutionary hypothesis (for a biologist as it requires some specialist knowledge of taxonomy and classification).
  • Consider the design of an attachment mechanism such as outlined below.

 

10.1.1Design considerations of a reusable fastener based upon a biological specimen such as burdock

 

To illustrate a biomimetic approach to design using burdock is different from the approach utilized by George de Mistral in his development of Velcro.  It took a number of years (approximately 10) [‎19] for him to find the compromise between the idea and the manufacturing techniques to produce a workable, reusable attachment mechanism. He conducted his work during the 1920’s and 30’s when technology was significantly less advanced and his aim was not to produce a scientific work but to invent a useful attachment mechanism for production and marketing. Considering an analytical approach to derive both useful scientific knowledge and technological advantage requires a different approach, hence this paper.

It took George de Mistral years to develop a method of manufacturing an attachment device that imitated the burdock plant in principle. As can be seen from the above figures there are marked differences in the structures of the two hooks. This is due to the limitations of the manufacturing process to produce a cheap fastener in bulk quantities.

 

Nylon, when sewn under infra-red light, forms rigid hooks.  The hooks comprise the rigid part of the fastener.  The corresponding surface is made of textile tape consisting of thin, flexible loops.

 

As a short illustration before moving into the experimentation consider the figures below.  It can be plainly seen in the images below [Figure 27 – velcro, from [‎19]         Figure 28 – SEM of burdock hook], that there are structural differences between the conventional manufactured Velcro hooks and those of the natural burdock hook.

 

 

Figure 27 – velcro, from [‎19]                          Figure 28 – SEM of burdock hook

 

Manufactured Velcro comes in a variety of forms.  The type shown in Figure 27 is manufactured from whole plastic loops that are then separated using a hot wire to produce a hook and a leftover stalk.

 

Comparing this with the SEM of Figure 27 – velcro, from [‎19]         Figure 28 – SEM of burdock hook, one can see that the burdock hook is sharply pointed.  It would be interesting to manufacture a hook with the exact structure of a burdock hook from an artificial material (or, even better, an artificial biomaterial) and study its attributes, to possibly match its abilities to an application which would be a more appropriate biomimetic approach to product/engineering applications.

 

It is also plain to see in Figure 27 that the manufactured substrate utilized by the product Velcro only faintly resembles the qualities of the natural substrates of the natural transporters of the burdock pod of seeds, furry animals. It is a manufacturing solution, not a biomimetic one.

 

And it is believed that herein could lie the key to silent Velcro, investigating the manufacture of the substrate such that the correct combination of manufacturability, resonant frequency, hook:diameter ratio, friction and hair length/”tangle”-ability is found.  “Silence” is a relative measure.  Using the correct materials it could be possible to manufacture a noisy Velcro that no-one could hear.

 

 

 

 

11  References

 

  1. Significance and Progress of Bionics” Yongxiang Lu, Journal of Bionics (2004) Vol 1 No 1-3
  2. “Miniature Attachment Systems: Exploring Biological Design Principles” S N Gorb, Design and Nature, 2002
  3. “Probabilistic Fasteners with Parabolic Elements: Biological System, Artificial Model and Theoretical Considerations” S N Gorb, V L Popov, Phil. Trans. R. Soc. London A(2002) 360, 211-225
  4.  “Attachment Devices of Insect Cuticle”, S Gorb, 2001. Kluwer Academic Publishers. ISBN 0-7923-7153-4
  5. “Natural hook-and-loop fasteners: anatomy, mechanical properties, and attachment force of the jointed hooks of the Galium aparine fruit” (2002) E V Popov, V L Popov, S N Gorb, Design and Nature Review Paper DN02/40800
  6. “The Claw of the Tiger: An Assessment of its Mechanical Shape Optimization” C Mattheuk and S Reuss, Journal of Theoretical Biology (1991) 150, pp 323-328
  7. “Confocal imaging, visualisation and 3-D surface measurement of small mammalian teeth” , A R Evans, I S Harper, G D Sanson, Journal of Microscopy, Vol 204, Pt 2, pp 108-119, 2001
  8. “Real world modelling through high resolution digital 3D imaging of objects and structures” (2000) J Angelo Beraldin, F Blais, P Boulanger, L Cournoyer, J Domey, S F El-Hakim, G Godin, M Rioux, J Taylor, ISPRS Journal of Photogrammetry and Remote Sensing 55 (2000) 230-250
  9.  “Contact Separation Force of the Fruit Burrs in Four Plant Species Adapted to Dispersal by Mechanical Interlocking”, E Gorb, S Gorb, Plant Physiology and Biochemistry, 40 (2002), pp 373-381
  10. “The Ecology of Seed Dispersal” H F Howe, J Smallwood (1982) Annual Review of Ecological Systems 13 201-228
  11. “Plant Biomechanics – An Engineering Approach to Plant Form and Function”  K J Nicklaus (1992), University of Chicago Press, ISBN 0-226-58641-6
  12. “Comparative Experimental Study of Seed Dispersal on Animals” S H Bullock (1997) Ecology 58, 681-686
  13. “A Study of Adhesive Dispersal of Three Species Under Natural Conditions” K Kiviniemi ((1996) Acta Botany Neerdelands 45(1), 73-83
  14. “in the blink of an eye: the cause of the most dramatic event in the history of life”, A Parker, The Free Press, POPULAR SCIENCE, ISBN 0-7432-3988-1
  15. “Roughness-dependent friction force of the tarsal claw system in the beetle Pachnoda marginata (Coleoptera, Scarabaeidae)” (2002) Z Dai, S N Gorb, U Schwarz, Journal of Experimental Biology, 205, 2479-2488
  16.  “3-D Modelling of Biological Systems for Biomimetics”, S Zhang, K Hapeshi, A K Bhattacharya, Journal of Bionics Engineering (2004) Vol.1 No. 1 pp 20-40
  17.  “Image Processing Analysis and Machine Vision”, M Sonka, V Hlavac, R Boyle, PWS Publishing, London 1999, ISBN 0-534-95393-X
  18. “Performance and Adaptive Value of Tarsal Morphology in Rove Beetles of the Genus Stenus (Coleoptera, Staphylinidae)” (2002) O Betz, Journal of Experimental Biology, 205, 1097 – 1113 (2002)
  19. “Really Useful: the origin of everyday things”, J Levy, New Burlington Books, ISBN 1-86155-337-4
  20. “Structural Biomaterials”  J F V Vincent, 1982, The Macmillan Press, ISBN 0 3 3 3 26125 9
  21. “Practical Statistics for Field Biology” Fowler, Cohen, Jarvis, 1998 John Wiley and Sons, ISBN 0-471-98295-4

 

 

 

 

 

 

 

 


Appendices

The Biomimetic Study of Insect Cuticular Hooks: Grasshopper and Bumblebee pretarsii including design case study

None of these papers have been peer-reviewed so…nor published….so take them with a pinch of salt, do.

This one is incomplete – a project outline if you like. A fifth paper from my research into Biomimetic Hooking Structures over 3 1/2 years at Bath Uni, U.K. circa 2002-2005.

Sorry – as per usual, images need more work to get on here on the Blog and I haven’t got it together yet.

Signed

The Author
Bruce E Saunders, MEng

brucesaunders23@hotmail.co.uk

A lack of funding curtailed my completion of the Phd and publication and subsequent investment in some ideas that I have in a small industry, so if anyone has a half mill to spare…

The Biomimetic Study of Insect Cuticular Hooks: Grasshopper and Bumblebee pretarsii including design case study

_____________________________________________________________________

Abstract: This paper follows Parts 1: A Biomimetic Study of Cellulose Hooks – Arctium Minus. The generalised ecology of insect pretarsii is described with the view to extracting design guidelines for the production a silent reusable probabilistic or non-probabilistic fastener. The same guidelines as described by S N Gorb are applied here, namely morphology, material, modelling, material and design. In this case the design draws from both Parts 1 and 2. Confocal microscopy is used to obtain the pretarsii morphologies of a common bee and a grasshopper and the process is fully described. Description is included of common plant surface structures.

 

_____________________________________________________________________

1      Introduction

It outlines the continued development of a silent releasable hooked attachment mechanism using structural mimicry, static modeling and finite element analysis. It is suggested that the previous paper The Functional Ecology and Mechanical properties of Biological Hooks: A Biomimetic study of Burdock (Arctium Minus”) be consulted. Further, direct reference is made through this to the author’s paper entitled the “Functional Ecology and Mechanical Properties of Hooks in Nature” and appendices.

Insect morphologies are characterized by structures supporting reduced energy expenditure; moving parts are simple in terms of musculature and augmented by physical structures to reduce energy requirements.  Frictional attachment devices are a prime example such as the head arresting mechanism of the dragonfly which is a frictional device made up of two opposing surfaces of parabolic structures that interlock and release through the insect’s cycle of common activities.  Once the head is retracted and locked into position on the anterior face of the thorax the neck muscles can relax. (See “Evolution of the Dragonfly Head Arresting System” by S N Gorb, [‎1] as described in Appendix 4 Section 6) and (“Attachment Devices of Insect Cuticle” by S N Gorb [‎2] as described in Appendix 1)

Gorb concludes his description of the functions of hooks in insect species with the following description (p50):

The hook mechanism is usually comprised of two complementary surfaces. These surfaces are not necessarily mirrored copies of each other but some dependence on the corresponding surface does exist. If both surfaces bear hooks (wing-interlock) their dimensions are usually predefined in order to optimise attachment and the probability of attachment as well. When only one surface bears real hooks, they could only attach efficiently to a particular range of textures (tarsal claws, hooks of phoretic and parasitic animals). The hook design can range from unicellular acanthi and multicellular setae to spines and cuticular folds.”

 

In the final sentence of the above quote we have an example of the deceptiveness of the human language; a hook design with spikes?  This derives from the verb “to hook” where a spike can be used “to hook onto” something.

But it is emphasised that for the purposes of this research topic, the structure being studied has been rigorously restricted to hooked shapes, pointed tapered shafts with a demonstrable curvature.

            Background

  1. Biologist
  2. Material Scientist
  3. Engineer
  4. Material Scientist
  5. Engineer

2      The Ecology

Insect environments and plant surface structures

3      The Biologist

Specifically it is the structure of the pretarsii irrespective of aspects such as gait that are being considered here.

Insect tarsi. Morphology and confocal microscopy.

Bumblebee and grasshopper tarsi

Figure 13 and Figure 14 shows the image sequences through a bee and grasshopper tarsi.  In both of these sequences the image starts in the furthest plane and the slices move towards the viewer.

Interest in imaging these two specimens comes from an interest in studying insect/plant surface interactions. (see Section ‎7.9.1.2).

Insect material doesn’t fluoresce as well as the plant material of the burdock hook but the tarsi as structures are more complex than the hooks. Attempts were made at all 3 wavelengths (red, blue and green) and combinations of the three. It is certain that a 2-photon microscope with its greater focus and depth penetration would improve the image making capability.  The laws of physics say that blue light has the highest energy but excitation of molecules is sensitive to the exciting frequency so exciting the molecules with all three colours gives a spread of frequencies that provoke the maximum excitation.

The results to the insect experiments have not been presented as stereograms.  

 

The following sequence of images (Figure 13) shows a progression of the laser through the specimen.

The z-axis of the laser starts furthest away from the viewer and moves “closer” towards the viewer during the progression through the stack, from image 1 – 30. 

A combination of all three wavelengths of light (red, green and blue) was used and these are visible in the images.  It is interesting to note that different structures in the tarsi fluoresce at different frequencies and that the combination of all three provides an opportunity to look “into” the structure and identify different structures through colour differences.  The plain of the laser is identified to the viewer by those parts of the image that reflect white light.

  1.  2.  3.   4.  5.      6.  7.   8.         9.     10.11.12.

13.14.15.16. 17.18.19.20. 21.22.23.24. 25.26. 27.28.  29.30.

Figure 13 – 1 – 30 confocal microscope image “slices” of hooked bumblebee tarsus (scale bar indicates 200 mm)

Grasshopper tarsus

See images overleaf.

  1.  2.  3.  4.
  2.  6.  7.  8.
  3. 10.11.12.

13.14.15.16.

17.18.19.20.

21.22.23.24.

25.26.27.28.

Figure 14 – 1 – 29 consecutive confocal microscope image “slices” of the hooked grasshopper tarsus (scale bar indicates 200 mm)

It is possible to see the setae (hairs) on the underside of the metatarsus (the structure that supports the tarsi) which aid in adhesion of the structure to plant surfaces through friction and adhesion (setae secrete tarsal fluid which aids with adhesion [ REF _Ref111113328 \r \h ‎15 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003100310031003100310033003300320038000000 ]).

4      The Material Scientist

5      The Engineer

Modelling

6      The Material Scientist

7      The Engineer

7.1    Silent Velcro

The term “Silent Vecro” is quite non-specific in the light of the above.  Velcro as a generic term means different things to different people.

Conventional Velcro as patented by George de Mestral (made of polyester resin) could be described as a releasable, reusable, probablistic hooked mechanical interlocking fastener. 

The term “Velcro” is also loosely applied to describe the form of metallic joining method that was recently developed to replace tacking when welding metallic plates together, which is a permanent join.

So the word “Velcro” has come to mean a manner of joining two opposing surfaces together without adhesive using matching surface structures that generally speaking can be separated again without damage to the surfaces although this is not the case with the metallic Velcro described above.

Further, it would seem that the term Velcro is no longer limited to hooked structures.  On the contrary, fastener structures have developed and a new kind of fastener using mushroom shaped structures with a matching receiving surface is now commonly seen on the packets of rolling tobacco for example, but this is not a probabilistic fastener because the matching surfaces require alignment.

In functional terms, silent Velcro could be defined to mean:

  1. Reusable
  2. No audible energy upon release.
  3. Probablistic
  4. Number of parts (two – structure and matching substrate)

And by:

  1. Attachment structure morphology
  2. Strength to attach
  3. Strength to release
  4. Frictional component and other scaling factors that contribute to attachment

Each of these points should be expanded upon as the absence or misinterpretation of any of them changes the resulting attachment mechanism.

7.1.1    Reusable

A reusable attachment mechanism can be static such as a Velcro strap on a bag or it can be moveable.  A foot is a reusable attachment mechanism.  A shoe is a reusable attachment mechanism. Reusable implies that the principles or structures that form the attachment are either undamaged by separation or are replenished or repaired.  Appendix 1 – Library of Zoological Examples of Attachment Mechanisms Classified According to Shape and Function of the authors transfer report details the various relationships and types of attachment. 

A Velcro strap has a corresponding predefined surface. According to Nachtigall [ REF _Ref128744680 \r \h ‎3 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003100320038003700340034003600380030000000 ] it is a releasable attachment device by two structures.  A shoe does not need a predefined surface.  According to Nachtigall it is a releasable attachment device by one structure.

In the case of insect tarsi, Appendix 4 Sections 10 and 11, “Performance and Adaptive Value of Tarsal Morphology in Rove Beetles of the Genus Stenus (Coleoptera, Staphylinidae)” by O Betz [ REF _Ref111098415 \r \h ‎4 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003100310031003000390038003400310035000000 ] as described in Appendix 4 Section 8 and “Roughness-dependent friction force of the tarsal claw system in the beetle Pachnoda marginata (Coleoptera, Scarabaeidae)” by Z Dai, S N Gorb, U Schwarz [ REF _Ref111113328 \r \h ‎5 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003100310031003100310033003300320038000000 ] as described in Appendix 4 Section 9, provides a sufficient insight into the relative performance of the tarsal structures, the claws and the setae.

The structure of the insect attachment mechanism generally consists of a number of claws, commonly two, and setae or hairs that can vary in length, density and number.  Scaling effects when copying these structures means that the significance of each and their contribution to attachment will vary. The setae can also secrete an adhesive that contributes to the attachment strength.

Equally and as important is the substrate.  For instance, in the case of the pitcher plant, directional hairs help to guide the insect in the direction of the pitcher. In the case of a manufactured attachment mechanism this effect can correspond to patterned surfaces corresponding to the claw configurations.

All the structures consist of insect cuticle and are shaped accordingly.  To make use of their shape optimization properties it must be born in mind that the final material chosen for manufacture must have similar properties or the shape must be adjusted according to the new material properties.

7.1.2    Attachment type and strength

Attachment can be permanent or temporary. The strength depends upon material and shape.  This proposal is set within the bounds of hook-shaped attachment mechanisms and the possibility of looking at parabolic fasteners is therefore artificially restricted.  Hooks are modeled by Gorb as tapered shafts and material qualities are studied in his paper “Natural Hook and Loop Fasteners: Anatomy, Mechanical properties and Attachment Force of the Jointed Hooks of the Galium Aparine Fruit” E V Gorb, V L Popov, S N Gorb [ REF _Ref128744789 \r \h ‎6 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003100320038003700340034003700380039000000 ] as described in Appendix 4 Section 3.

This work can be adapted to model a dual hook combination.  Further Gorb defines attachment mechanism characteristics such as the ratio between attachment and detachment forces and their variation.

For the purpose of this research it is suggested that it is possible to produce a variable detachment force based upon the angle of the attachment device.  This would mean a low force of attachment with a resulting high detachment force which decreases with rotation to a low detachment force, much like the placement of a foot during walking.  Heel-down produces attachment, toe-down provides release.

7.1.3    Friction

Gorb discusses probabilistic fasteners and he states that it is parabolic fasteners and not hooked fasteners that yield the best possibilities for investigation in nature. (See “Probablistic Fasteners with Parabolic Elements: Biological System, Artificial Model and Theoretical Considerations” S N Gorb, V L Popov, [ REF _Ref128744846 \r \h ‎7 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003100320038003700340034003800340036000000 ] as described in Appendix 4 Section 6) In this case what is being discussed is the interface between mechanical interlocking and friction. The interface is the dependence of the mechanical interlocking upon the frictional force between surfaces.

Hooks are shape optimized for an optimum angle of force application. The relationship between the hook tip and the substrate will defined the strength of attachment depending on the degree of mechanical interlock and the frictional force.  Appendix 3 details typical organs of plant surfaces that are the natural substrates of insect tarsi.  Modeling the surfaces as a matching substrate to tarsi configurations would optimize the attachment.

7.1.4    No driven moving parts

In this proposal it is being considered to study a mechanism that has no external forces other than those derived indirectly from the placement of the mechanism. S N Gorb has done work on the definition of attachment mechanisms including static analysis and the mathematical modeling of the relationships between attachment and detachment forces that define the effectiveness of an attachment mechanism (See “Miniature Attachment Systems: Exploring Biological Design Principles” by S N Gorb  [ REF _Ref75939057 \r \h ‎8 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F00520065006600370035003900330039003000350037000000 ] as described in Appendix 4 Section 4).  Also see Experiment 3 in the main body of the report.

This means that an assembly of hooks and structures needs to be designed that is hinged and reactive to positioning.

This mechanism need not be limited to simply two hooks neither need it be limited to hooks that directly resemble insect claws.  For instance a tarsal mechanism using hooks that are the shape of burdock hooks would equally be valid.

7.1.5    No audible energy upon release

As mentioned previously there are variations as to the interpretation of the word noise. The environmental agencies will have one version in terms of suburban noise, for instance.  There is also the relationship of audible noise to audible frequencies.  What is certain is that any vestige of attaching force that is present will imply a loss of energy when it is released.

7.1.6    Probablistic

This describes the ability to attach randomly without precise matching of surfaces. Velcro is a probabilistic fastener as is a robot foot that can attach to different surfaces and release with the minimum of noise and hence energy release.

7.2    The design process

The steps to record and reproduce the morphology of a specimen tarsus using Solid Modeling are as follows:

1)                  Digitize structure profiles to obtain the sweep path. (see Experiment 1 and 2 in the main body of the report and Appendix 5.)

2)                  Section the structures with a microtome and digitize the sections to gain the shapes.

3)                  Preserve the sectioned material for analysis for signs of trace materials and other non-homogeneities in the material.

4)                  Reconstruct the structures in Solid Modeling and assemble them together. Also see Appendix 6.

7.3    Finite element analysis

Using Solid Modelling the direction of optimum force application can be found by looking for the optimum stress profiles.  This must be done after first assembling the component structures into their composite structure and examining the freedom of movement and the angles of engagement with a substrate.

Thereafter a static force model can be developed which can be done in terms of physical variables for the range of movement of the attachment structure.

7.4    Rapid prototyping

The data file for the assembly can be saved in a .stl format and exported to a rapid prototyping device.  As is discussed above, scaling effects will influence the significance of the setae, their length and number and whether they should even be included in the design.

7.5    Sizes

The size of the prototype device should be judged according the form of test to be conducted:

A larger device can be used to measure and test the range of movement and test the engaging and disengaging action.  Thereafter a range of sizes should be produced and the relative attachment forces measured.

7.6    Gait

The gait of the insect will naturally play an important part as the activating and deactivating action of the tarsus.  The details of this will have to be drawn from standard texts.  For instance, in terms of the human gait a foot can placed down heel to toe and at different angles. But this forms only a portion of the full leg motion.  Similarly with the gait of an insect only a portion of the gait needs to be considered. This is helpful since clearly the control systems for the accurate mimicking of motion are difficult to reproduce. But the essence of the idea should be clear and it is the fundamental mechanism of attachment and detachment that shall be studied.

7.7    Steps in the mechanism development shall include

Apart from the steps already described above, further development shall include:

  1. Establishing the locus of motion of critical points on the mechanism.
  2. Cross correlation of material properties of the biomaterial versus some suitable artificial material.
  3. Establishing some relation between mechanical interlock/frictional force and angle of attack between mechanism and substrate.

7.8    Substrate

The design of the substrate probably rivals the importance of the development of the mechanism itself.

Patterns, textures and roughness could all play a part.  Descriptions of some natural substrates can be found in Appendix 2 of the transfer report.

7.9    Final comment

It is quite likely that a biomimetic attachment device based upon a tarsal mechanism could require properties beyond simple structural detail.  For instance, scaling effects will reduce the effect of the setae.  It may be possible to introduce analogues to this to increase the effectiveness of attachment.  One idea that springs to mind is to secrete an adhesive that could be left behind when the attachment device is lifted from the substrate using capillary action to draw fresh fluid down a hollow structure from a artificial gland within the device.  This would act to replenish the adhesive ready for the replacement of the next step.

8      References

  1. “Evolution of the Dragonfly Head Arresting System” S N Gorb, Proc. R. Soc. Lond. B (1999) 266, p525-535
  1. “Attachment Devices of Insect Cuticle” S Gorb, 2001, Kluiwer Academic Publishers, ISBN 0-7923-7153-4
  2. “Biological Mechanisms of Attachment, The Comparative Morphology and Bioengineering of Organs for Linkage, Suction and Adhesion”, W Nachtigall, 1974translated by M A Biederman-Thorson, Springer-Verlag, ISBN 3-540-06550-4
  3. “Performance and Adaptive Value of Tarsal Morphology in Rove Beetles of the Genus Stenus (Coleoptera, Staphylinidae)” (2002) O Betz, Journal of Experimental Biology, 205, 1097 – 1113 (2002)
  4. “Roughness-dependent friction force of the tarsal claw system in the beetle Pachnoda marginata (Coleoptera, Scarabaeidae)” (2002) Z Dai, S N Gorb, U Schwarz, Journal of Experimental Biology, 205, 2479-2488
  5. “Natural Hook and Loop Fasteners: Anatomy, Mechanical properties and Attachment Force of the Jointed Hooks of the Galium Aparine Fruit” E V Gorb, V L Popov, S N Gorb, Design and Nature 2002
  6. Probablistic Fasteners with Parabolic Elements: Biological System, Artificial Model and Theoretical Considerations” S N Gorb, V L Popov, Phil. Trans. R. Soc. London A(2002) 360, 211-225
  7. “Miniature Attachment Systems: Exploring Biological Design Principles” S N Gorb, Design and Nature, 2002
  8.  

A Biomimetic Study of the Long Shaft Cellulose Hooks of Arctium minus (Burdock) Product Development – Part III

A Biomimetic Study of the Long Shaft Cellulose Hooks of Arctium minus (Burdock) Product Development – Part III

Bruce Saunders

 

Abstract

This paper details the development of a family of parts using the functional ecology, field testing and morphological recording of Parts I and II in this sequence of papers. A. minus is used to form a kernel to the family of parts, all of which are hook shaped attachments manufactured from a plastic.  There are essential differences between the biological species and the manufactured analogue not least the choice of component material since cellulose, the component anisotropic biomaterial, does not have an artificial equivalent. Scaling effects are once more introduced into the discussion in terms of future work and field testing.

Keywords:  modular, stress, miniature, plastic, hook

1  Introduction

Parts I and II have been aimed at demonstrating S N Gorb’s model biomimetic approach for the generation of a product. In the previous two papers the basic ecology of the species has been described and the reasons for the choice of structure for study based upon the hypothesis of Nicklaus ‎[1], an engineer. Three methods of morphological study have been described which can be used for any small structure, one of which is relatively new when applied to these structures (see ‎[2]). These three methods vary in terms of hardware requirements which has implications on cost, versatility and memory storage. The mathematical analysis of the hook under static loading was demonstrated in Part I indicating that these cellulose hooks are prone to failure due to induced shear. In tadem with this family of attachment devices is a family of substrates which permit probabilistic attachment of varying qualities and properties.

       

2  Functionality

The morphology of the A. minus hook has been accurately recorded and its performance under tension has been tested and compared with those of four other species ‎[3]. A. minus is supposed to be the biological inspiration behind Velcro ‎[4] and it is interesting to note that functionally, the Velcro hook resembles that of C. lutetiana more than it resembles the hook of A. minus.  

     In considering the hooks of A. minus, C. lutetiana, A. eupatoria, G aperine, and G. urbanum, the hooks of each of these plant species is associated with plant dispersal, for attaching the plant fruit to passing hosts but each has a different hook arrangement in terms of number of hooks per fruit and their arrangement on the fruit. Gorb’s purpose in studying C. lutetiana, A. eupatoria, G aperine, and G. urbanum was to find an optimum hook (or burr) morphology, investigate scale effects of the burrs per fruit and to assess the contact force of a single burr compared to the mass of the fruit. By adding a study of A. minus to his work and concentrating on burr morphology and material properties and assessing the structural information available it will be shown that the biological indicators do indeed supply information that can lead to the generation of a product or a family of products that is different from conventional Velcro, by following a biomimetic process. (Note: At no stage in this work has a patent database been consulted. This was a purposeful omission so as not to influence the biomimetic process.)

     In all five species the burrs in their various formations and numbers form probabilistic fasteners. From Nachtigal ‎[5] and Gorb ‎[6] a probablistic fastener is a random hooking mechanism. A reusable attachment device is a releasable attachment mechanism by one structure, i.e. there is no single matching structure required for attachment to take place. This definition does not specify that the structure (the hook) should be part of a field of structures nor that interaction between component structures is a necessary part of attachment. Considering Gorb’s work on frictional parabolic fasteners [7] his model specifically includes the interaction of neighbouring elements as contributing directly to the attachment force. The hooks of all five species in this paper form parts of fields of structures of different numbers but the hooks do not interact to increase their individual attachment force. They all act individually and their collective action taken to serve to arithmetically increase the overall attachment of the fruit to the host.

     Further, it is stated by Gorb ‎[3] that he has an interest in measuring the scaling effects of the detachment force of the fruit from their supporting structure on the parent plant. If one considers that the burrs have a direct purpose of hooking the fruit to a host then it would seem that with respect to his study of morphological variables and their respective influence on burr strength there are finite possible responses when a hook comes into contact with a host. They are:

 

  1. Fruit detachment from the parent plant.
  2. Hook flexure if fruit detachment does not take place, to release the host and keep the hook intact for the next host.
  3. Removal of host fibres.

    

     Any other response such as hook fracture and shaft fracture would result from the fruit being held in place on the parent plant and would render the hook useless for its intended purpose which would be contrary to an evolutionary strategy. Only C. lutetiana has a curve which flexes to release the substrate and only G. aperine has a hollow base at the bottom of its shaft which allows a multi-degree of freedom flexure.

 

2.1   Summary

The following is compiled from the research of Parts I and II.

 

  1. In the plant kingdom, with regards to plant growth and evolution, only energy efficiency can be assumed with regards to structure. All structures are governed by the same basic physical and chemical laws.  This implies a direct link between material composition, morphology and function but does not necessarily indicate a best overall solution to a prescribed problem from an engineering perspective since engineers have a wide variety of materials at their disposal.
  2. The tensile testing upon Arctium minus confirmed that S N Gorb’s conclusion with regards to hook strength, that shaft strength and then hook radius was of primary importance morphologically speaking, were true to a degree, but that the material resistance to shear induced by bending was more important than the influence of bending moment due to the length of the lever arm.
  3. It was noted that functionally burdock hooks are single use only and that the originating bracts, from which the hooks form act as a single degree of freedom hinges thereby aiding attachment.
  4. It was noted that the diameter range of known natural host hair fell between 20 and 100 microns in diameter, all consisting of the material a-keratin.
  5. It was observed that burdock hooks have a radius or curvature of between 50 and 150 microns and a thickness of approximately 200 microns and that cellulose microfibril alignment is all parallel to the direction of the hook.
  6. It was observed that unlike Velcro, burdock hooks have a pointed tip and their hooks are thin enough in silhouette to combine a hooking function with an action of piercing the fibres.
  7. It was noted that hooks originating from trichomes (plant hairs) appear to be weaker that hooks originating from carpels or bracts. This could be due to the fact that trichomes are simpler structures consisting of fewer cells.

 

3  Hook structure

Three of the species (C. lutetiana, G. aperine, A. eupatoria) are the weakest in tension and they originate from trichomal structures. From Devlin ‎[8] trichome is a collective noun for all types of outgrowths supported by the cell wall of the epidermal layer. The epidermis is the outermost layer of cells in a plant and its functions include manufacturing the structural material of the plant. A trichome is a plant hair and can be glandular and non-glandular, cellular, multi-cellular, branched or unbranched. Of these three species, G. aperine exhibits a multi-degree of freedom due to, from Gorb ‎[9], a hollow base. The other two species arise from the surface of the mericarp.

     A. minus  and G. urbanum, have hooks that originate from the bract and carpel of the fruit respectively and exhibit the strongest contact separation forces. Both have a single degree of freedom due to their origination from a flattened structure.

     From this information it is possible to derive dominant parameters for the strength of these hooks that are different from S N Gorb’s, namely

 

Structure (stomatal, bract, carpel)

Size (small, large)

Degrees of Freedom (none, many)

Elastic Modulus and degree of anisotropy (cellulose)

 

3.1   The functionality of Velcro

As a product, Velcro is purported to derive from burdock. It is of interest therefore to make a comparison between the two before attempting to develop a further product biomimetically from these plant hooks.

 

  1. It was noted that the nylon from which Velcro is manufactured is flexible and resilient enough to withstand multiple attachments and re-attachments.  The artificial substrate however can be damaged over time.
  2. It was observed Velcro hooks are assembled in parallel fields which is similar to the spherical fields of both the A. minus and the G. urbanum.
  3. It was observed that confocal microscopy, although memory intensive, was a viable means of non-destructive indirect measurement of a micron-sized cellulose hook with natural fluorescent properties.  Further it is surmised that the product of a confocal microscope, a stack of .tif images, could be converted directly for virtual reality applications, rapid prototyping devices and could have application in the field of producing nano- and micro-structures.

 

4  Design brief

(The following work draws heavily upon the capabilities of CosmosWorks.) Unlike conventional design briefs where a required function is specified with parameters to place constraints on the design, here it is the shape and functionality that is specified for which a suitable material and application is sought (see ‎Figure 1). The shape and functionality are described and not prescribed but prescriptive tools are used to enhance the description for the purposes of manufacture.

 

 

 

Figure 1:       3-d reconstruction from SolidWorks of a burdock hook and shaft. The length of the green section is 120mm in CosmosWorks. (See note below on scale).

 

[Note on scale in drawings: 8mm = 100mm. Therefore 120mm = 100×15 = 1500mm = 1.5mm in actual length]

 

4.1   Functionality and structural description

4.1.1    Hook

 

In considering the range of attachment types shown in the five species considered, they indicate that a certain range of hooks could be considered (see ‎Figure 1 to ‎Figure 4) varying in structure, flexibility, size and strength. If structure and size are considered to be “given” constraints, flexibility and strength are material and manufacturing properties. Because of the asymptotic approach to the design all possibilities can be explored and confirmed or eliminated as the design progresses. Considering the reproduction of a hook as shown in ‎Figure 5 the following functions can be defined:

 

  1. To hook and to flex to release substrate or not to flex and not release.
  2. To pierce such that the hook can be inserted with a forward action like a barbed spike or simply to thread between a fibrous substrate.
  3. To flex in a single plane to aid attachment through a flexible base, not to flex in any plane or to flex in multiple planes.

 

4.2   Shaft

The structure of the burdock hook consists of a shaft that emerges from a flattened supporting bract. The burdock bract itself is rectangular with the hook emerging from one of the narrow edges. This bract has its own permanent attachment to the fruit pedicle at the base. Replicating this bract opens a number of possibilities in terms of hook configurations. See ‎Figure 2: below.

 

 

          

 

Figure 2:               Front and side views of hook with tapered shaft

 

     Every step that follows in the development of this design must be hand-in-hand with a manufacturing process. This in turn is heavily dependent upon the choice of material and the forming and shaping processes that can be used upon it.

 

         

 

Figure 3:               Front and side view of hook with added hexagonal flange

 

 

4.2.1    Stress Analysis

 

The stress analysis was performed using an add-in of SolidWorks 2004 called CosmosXpress 2000. This package only accommodates isotropic materials and doesn’t contain full details of properties of plastics and composites materials.  For the purposes of the exercise the material was chosen to be Acrylic (medium to high impact) with the following properties:

Table 1:               Properties of low to medium impact acrylic (from CosmoXpress 2000)

 

Property Name

Value

Elastic modulus

2.4e+009 N/m^2

Poisson’s ratio

0.35

Yield strength

2.0681e+008 N/m^2

Mass density

1200 kg/m^3

 

     It was noted from Part I that, in the fractured hooks, the cellulose microfibrils are all parallel and in alignment with the curvature of the hook. This means that the microfibrils are all subjected to direct stress, either compression or tension. Cellulose is anisotropic in behaviour, absorbing greater tensile stress than compressive stresses. This information can be related to the behaviour of the substitute acrylic shown in ‎Figures 4: to 6 below. The hook is anchored in a manner that mimics its constraints whilst attached to the fruit of the burdock. It is loaded at the tip to deliver the maximum bending moment.

 

 

Figure 4:               The applied loading to the tip of the hook (from CosmosXpress 2000)

 

 

Figure 5:               The applied restraints include the tapered bract (from CosmosXpress 2000)

 

 

Figure 6:               The maximum deformation under loading

 

     The hook shows highest stresses in the internal and external fibres of the shaft and in the underside of the hook which experimentation has shown to be the region of failure. Relating the behaviour of anisotropic cellulose to isotropic acrylic it is concluded that the Neutral Axis of the deformation will shift in the direction of the tensile loading in order to maintain the product of stress/unit area x area about the Neutral Axis (from bending theory). The build-up of material on the shoulder of the hook absorbs additional compressive stresses and so prevents buckling at the hook. The alignment of parallel fibres through the arc of the hook means that there are differing overall lengths in fibres – those on the inner curvature are shorter than those on the outer curvature by a distance approximately equal to the product of thickness x theta, theta being the angle of curvature. As the hook straightens under load these fibres move relative to each other leading to a disruption in the hemi-cellulose and lignin matrix. This prevents crack propagation in accordance with the Cook-Gordon model and leads to fibre pullout as the shorter fibres fracture in tension.

4.2.2    Hook field structure

 

It has been noted that hooks in nature are assembled in different configurations and numbers. Gorb compared the mass of the fruit with the contact separation force of single hooks in order to assess the hook performance for each species and the number of hooks required to support the fruit which could be viewed as a measure of design efficiency.

     With the design progressing with a development of a modular hook with a supporting “bract” anaogue, the opportunity exists to experiment with:

 

  1. Field configurations, densities and numbers.
  2. Bract shapes i.e. square, rectangular, circular, octagonal etc.
  3. Bract attachment mechanisms for both attaching bracts to each other to form composite fields as well as for attachment to a structure needing an attachment mechanism.
  4. Bract shapes also offer the opportunity to manufacture the hooks in flattened rows.

 

     Modularizing the hooks offers many permutations which eventually will have to be modified during the process of material selection and manufacturing process selection and refined by application.

 

 

Figure 7:               A zipper-like configuration of sixteen adjoining hooks

 

     In ‎Figure 8: note the hexagonal basal flange is only a single permutation of those available.

 

 

Figure 8:               The zipper of Figure 8 in profile

 

‎Figure 8: above and ‎Figure 9: below show the profile and isometric views of the zipper mechanism. Note that both rows of hooks face in the same direction. A simple application of this form of plastic attachment could be the application of a name tag to a garment without thread, replacing the use of a safety pin.

 

Figure 9:               The zipper configuration in isometric view

 

 

Figure 10:           A Rabbit-Ear configuration

 

 

Figure 11:           The Rabbit-Ear configuration in profile

 

‎Figure 10:‎and Figure 11: above show a two pronged configuration utilizing the geometry of the hexagonal basal plate. Clearly this could be expanded to up to six radial hooks, illustrating why the choice was made to develop the modular single hook as a basis.

 

5  Discussion

It has been concluded that there are no overt scaling effects associated with Arctium minus hooks (see Part I). Further it was decided that there were design indicators associated with the shape and the freedom of movement of the Arctium minus hooks.

     These have been utilised in the designs of this paper, having been obtained through the processes described n Part II. It is now appropriate to move to a rapid prototyping device for the purposes of testing performance and functionality.

     The modular design makes possible a number of designs and configurations all of which will have properties of their own.

 

 

6  Conclusion

The chosen material analogue has a high impact upon design properties in particular its formability and its behaviours under different forms of stress. By reducing the flexibility of the hook under tension, a hook has been produced that closely approximates that of A. minus in both shape and functionality to produce a product that is not Velcro. It will be strong in tension, probabilistic and multi-use although it can be predicted that either the substrate or the hook supports could incur damage during detachment. If used in conjunction with a material weak in shear such as acrylic it could be possible to design for failure, creating a supporting flange that will yield and tear under certain conditions of stress thereby making the attachment device single use and reducing damage to the underlying substrate when energy is absorbed by the tearing acrylic. It will not require a bespoke substrate although it may be possible to optimize attachment performance by comparing performance for different types of substrate.

 

References

[1]    Nicklaus, K. J. Plant Biomechanics – An Engineering Approach to Plant Form and Function (Chapter 10), Biomechanics and Plant Evolution, University of Chicago Press, pp. 474-530, 1992.

[2]    Evans A. R, Harper I S, Sanson G D,Confocal imaging, visualisation and 3-D surface measurement of small mammalian teeth. Journal of Microscopy, 204, Pt 2 pp. 108-119 2001

[3]    Gorb E., Gorb S. N., Contact Separation Force of the Fruit Burrs in Four Plant Species Adapted to Dispersal by Mechanical Interlocking, Plant Physiology and Biochemistry, 40, pp. 373-381, 2002

[4]    Popov E. V., Popov V. L., Gorb S. N.,Natural hook-and-loop fasteners: anatomy, mechanical properties, and attachment force of the jointed hooks of the Galium aparine fruit, Design and Nature Review Paper DN02/40800, 2002

[5]    Nachtigall W., Biological Mechanisms of Attachment, The Comparative Morphology and Bioengineering of  Organs of Linkage, Suction and Adhesion, Springer-Verlag, pp        ,1974

[6]    Gorb S. N., Attachment Devices of Insect Cuticle, Kluwer Academic Publishers, pp       , 2001

[7]    Gorb S. N., Popov V. L., Probablistic Fasteners with Parabolic Elements: Biological System, Artificial Model and Theoretical Considerations,

[8]    Devlin R. M., Witham F. H., Plant Physiology, Fourth Ed., Devlin and Witham, PWS, 1983

[9]    Popov E. V., Popov V. L., Gorb S. N.,Natural hook-and-loop fasteners: anatomy, mechanical properties, and attachment force of the jointed hooks of the Galium aparine fruit. Design and Nature Review Paper DN02/40800 2002

 

A Biomimetic Study of Arctium minus (Burdock) Part II – Imaging Small (~mm) Hooks of Cellulose and Insect Chitin

A Biomimetic Study of Arctium minus (Burdock) Part II – Imaging Small (~mm) Hooks of Cellulose and Insect Chitin

Bruce Saunders

Abstract

As part of a project in producing a novel product from the burdock hook after biomimetic methodology developed by S N Gorb, this paper describes an investigation into the most appropriate method of shape acquisition for the purposes of reproduction and product development. This morphological study investigates confocal microscopy, 2-D digitising and the use of a microtome and digitising software. Small structures of cellulose and insect cuticle are imaged using confocal microscopy and the benefits and disadvantages of this approach are noted. A 3-D image of the burdock hook is produced from a 2-D digitised profile using SolidWorks 2004.  

Keywords:  Reverse engineering, shape acquisition, confocal microscopy, 2-D digitising, finite element analysis, rapid prototyping, Solid Works, cellulose, insect chitin, miniaturisation

 

1  Morphological Studies

This phase of the study concerns itself with recording shapes for the purposes of engineering analysis and reproduction.

1.1   Predictive and descriptive engineering

Predictive engineering is conventional engineering. A part is described with technical drawings and then analyzed to predict its behaviour and then constructed. Descriptive engineering is reverse engineering. An existing structure or mechanism is described and analyzed as it exists. Building restoration is a form of reverse engineering, particularly if the building is old and forgotten techniques are used to restore a building to its original condition. Engineered parts for which technical drawings have been lost or gone missing are reproduced using reverse engineering. Seeking to manufacture a product from a biological structure for which there never were any drawings, equally, is a form of reverse engineering.

     Attempting to manufacture a structure that precisely mimics a biological structure is an attempt to unite both the prescriptive and descriptive, i.e.  to use the prescriptive language of engineering to describe and analyze that which already exists, for the purposes of reproduction.

1.2   Shape Acquisition

Shape acquisition has a history in biological studies. From the first cave drawings man has endeavored to reproduce that which he observes in nature. Today, shape is used to provide clues as to internal composition of a biological structure when considered in the context of biomaterial strengths and behaviour and the use of the principle of shape optimization.

     Dai, Gorb and Schwarz [1]used methods of analyzing 2-D radii of curvature in insect tarsii to identify structural anomalies which superficially would seem to indicate zones of weakness or stress concentration but in reality identify zones of localized hardening/strengthening due to the presence of zinc or other trace minerals in the insect cuticle. When a structure does not break under loading when the shape of the structure would seem to indicate that it should, there is an indication that some material discontinuity is responsible.

     Beraldin et al [‎2] in their paper on the virtual reality applications of scanning technology discuss the use of data transfer for layered manufacture and rapid prototyping. Confocal microscopy makes use of light intensities provided by fluorescing molecules to form images of minute structures and their internal components. Evans et al [‎3] used this physical phenomenon and technology, by casting the external morphologies of bat’s teeth to generate 3-D images of teeth to study wear patterns.

     Finite element analysis comprises the precise division of a 3-D morphology into vertices and edges in order to compute stresses at a distance from an applied load in a structure. Surface modeling using constructs such as the Canny edge detection method to create order out of data clouds, transforming them into a triangulated form for the purposes of creating 3-D surfaces.

2  Aim

The above introduction prompted the following questions:

  1. Can a mesh formed from random points of light intensities be used to form a finite element analysis mesh?
  2. Can a mesh formed from random points of light intensities be used to form a mesh for conversion to .stl format and sent to a rapid prototyping device?
  3. Can small structures be imaged using a confocal microscope without the use of the casting methods of Evans et al?

2.1   Microscopy Techniques

The following techniques were the focus of preliminary investigation, through the lectures of Dr I Jones, then of the Neuroscience Department at the University of Bath [‎4]:

  1. The principles of fluorescence microscopy
  2. Epi-fluorescence microscopy
  3. Confocal microscopy
  4. 2-photon microscopy
  5. Near field scanning optical microscopy

     The fluorescence effect is produced by irradiating atoms with a high energy light source (laser) which causes excitation of orbiting electrons. These electrons jump “outwards” to high energy orbitals before returning to their normal state, releasing energy at a specific wavelength which is detected via an emission filter.

     Confocal microscopy makes use of a laser light source whereas epi-fluorescence microscopy makes use of a normal bright light source and two filters, an excitation filter and an emission filter. Samples are viewed through an eye-piece.

     The advantages of confocal microscopy using a laser light are:

  • Reduced blurring
  • Increased effective resolution
  • Improved signal to noise ratio
  • z-axis scanning
  • depth perception
  • magnification is electronically adjusted
  • there is clear examination of thick specimens

The following procedure is described by Evans et al for the production of cubic voxels and virtual reality applications from his paper on the imaging of mammalian teeth [‎3].  It essentially notes how to take a suitable image of a small object (~mm) for the purposes of digitizing, reproduction and study in virtual reality.

     In capturing an image it must be born in mind that the goal was an accurate 3-D model for both virtual reality applications. It is important to set the slice thickness accordingly to arrive at an undistorted image i.e. cubic voxels.  The paper by Evans et al details a method of taking a cast of a tooth which is more technically cumbersome than simply putting a microscope slide with specimen under the objective and so some of his paper is not relevant here (the details concerning the casting of the teeth).

     Optical slices were taken through the x, y plane where each slice was square (e. g. 256 x 256) pixel 8-bit image at medium scanning speed.

     Slices must be taken at the same distance as the interval between pixels to make cubic voxels.

     Software such as Zeiss is used to generate a 3-D image from the stack of slices, where pixel intensity represents height and the z-height is found by comparing the intensities for each x, y point (in fact, a column of pixels all with co-ordinates (x, y)). In most of the tests run by Evans et al, the cubic voxels (and z-interval) were 7.8 mm long, generated in one of two methods:

  1. For the x 5mm lens – a 256 x 256 pixel image was scanned at zoom 1 (field of view (FOV) of 2 x 2 mm), or a 128 x 128 pixel image was scanned at zoom 2 (FOV 1 x 1 mm)
  1. For the x 10mm lens, a 128 x 128 pixel image was scanned at zoom 1 (FOV 1 x 1mm)

     Therefore using a lens with a field of view (FOV) of 2 x 2 mm at a setting of zoom 2 reduces the field of view to 1 x 1.

     Surface noise can affect the image and give a false indication of where the true surface lies.  Evans et al did experiments with the x 5 and x 10 lens to see how best to obtain the most accurate surface image. They used two techniques to try to reduce surface noise; accumulation and averaging. Accumulation is to accumulate and average several images at each z height and then create an image from the accumulated image slices.  On the microscope, for example, an “Accumulation 2” scan stands for the number of slices that are averaged (two).

The second method was to take the average of a number of reconstructed 3-D images of the same area. This was tested using a specially prepared and dimensionally precise standard glass specimen and comparing resultant images. The specimen was cubic and so without any undercuts but with a 45o fillet.  Inner width was 1.3mm and outer width 1.7mm.

     It was found that averaging produces better results than accumulation.     Sanson et al used a resin casting of their teeth specimens which was coated with eosin, a fluorescent dye. 

2.2   Confocal Microscopy: Apparatus and method

It was decided that small biological specimens could possibly be translucent enough to laser light such that it might not be necessary to use the casting method of Evans et al.  Instead it was decided to attempt to image plain untreated specimens of cellulose and insect chitin.

     A specimen burdock bract was mounted upon a “well” microscope slide in distilled water (it is a feature of both confocal and atomic force microscopy that specimens may be mounted without treatment) and placed under the objective of a confocal microscope. (Sincere thanks are due to Dr Ian Jones, post-doctoral researcher in Neuroscience in the Biology Department, University of Bath for his curiosity, assistance and instruction on operating the microscope.). 

     Confocal microscope and scanner:

  • A Zeiss Axiovert single photon confocal microscope (inverted microscope with the objectives underneath the platform).
  • Zeiss LSM 510 module (laser scanning microscope) with 2 lasers
    • 1 x Argon (488nm)
    • 2 x HeNe (543nm & 633nm)

     Objectives:

  • all x 10, 40(oil), 63(oil) & 63(water)
  • digital zoom up to x 200
  • differential interference contrast.

     The field of view: 1 x 1 mm.

     Pinhole setting: 1 optical unit.

     Scanning slice thickness: 19nm

     Also:

  • Well slides which are microscope slides with a bowl ground out in the centre to receive specimens that are not flat.
  • Distilled water as a medium for slide mounting.
  • It is important to get the hooked specimen in the right orientation on the slide to avoid displaying an undercut surface to the laser light. 
  • It is important to optimise the strength of the laser and reduce the required depth of penetration to prevent excess bleaching. 
  • The same specimen can be remounted a number of times in different orientations in the slide to fully expose the complete detail of the structure. 

3  Results

When suffused with the laser light at three different frequencies it was found that the burdock hook fluoresced well under the green laser light.  Under the red and blue light the resulting image was less distinct but these colours worked well for the insect tarsii. The stacked image is then output to file and stored as a sequence of .tif files that are viewed in .avi format (see below for the full range of .tif images).

3.1   Burdock hook stereograms

Stereogram images of the hook follow (‎Figure 1, ‎Figure 2‎, Figure 3). The data from the confocal microscope is a sequence of image slices that are then automatically reassembled (stacked). Evidence of the stacking can be observed in the images from the stepped outline of each image. The glow that surrounds the stereogram images derives from the fact that this view of the hook is assembled using standard confocal software and the viewer is looking through preceding and following images which are a result of the perspective of looking at angled images.  Only in a profile image does a stark outline of the hook show.  There is an artefact on the microscope slide that shows to the side of the hook.

 

Figure 1:Stereogram 1 of the burdock hook specimen

 

Figure 2:Stereogram 2 of the burdock hook specimen

 

Figure 3:Stereogram 3 of the burdock hook specimen

(Dr I Jones, October 2002)

3.1.1    Burdock  .tif images

     The individual .tif images that make up the above stereogram are below (see ‎Figure 8) imaged under the green light. The specimen was lying upon its side for the z-axis scan to minimise the number of scans required to scan the entire specimen, with the hook in profile to take into account undercut of the hook.

1.    2. 3.

 4.  5.  6.

 7. 8.  9. 

10.11.12.

13.14.15.

16.17.18.

19.20.

 

Figure 4:1 – 20 The individual z-axis scan .tif files that make up the stereogram of the burdock hook (the scale bar defines 200 microns)  (Dr I Jones October 2002).

     Note that the images from the confocal microscope show some internal structure of the hook, particularly the cellulose microfibrils.  These microfibrils are visible in the next experiment which fractures the hooks in a tensile tester. The hooks are made up of cellulose fibres bound together with hemi-cellulose to form microfibrils [‎5]. The curves of the hook are smooth suggesting that the material is homogenous.

     Figures 5 and 6 show the tarsii of two insects, a common grasshopper and a common bee, both composed of insect chitin. Tarsi and setae are clearly visible.

3.2   Grasshopper .tif images

1   2  3  4

5   6   7  8   

9  101112

13141516

17181920

21222324

2526    2728

2930  

Figure 5:1 – 30 The individual z-axis scan .tif files of the scan through the tarsus of a common grasshopper (the scale bar defines 200 microns)  (Dr I Jones October 2002).

3.3   Bee .tif images

1   2  3  4

5   6   7   8  

9  101112

13141516

17181920

21222324

25262728

2930

Figure 6:1 – 30 The individual z-axis scan .tif files of the scan through the tarsus of a bee (the scale bar defines 200 microns)  (B Saunders October 2002).

3.4   Discussion

     Can a mesh formed from random points of light intensities be used to form a finite element analysis mesh? No, because finite element analysis requires discrete points to form a continuous scaffold for the purposes of calculation. Only carefully constructed shapes in finite element software can be meshed for the purposes of structural analysis. Edge detection and data clouds of light intensities do not yield the ordered data sets required to form a finite element scaffold.

      Can a mesh formed from random points of light intensities be used to form a mesh for conversion to .stl format and sent to a rapid prototyping device? Yes, as is indicated by Beraldin et al above. There is software available on the market that allows for file conversion to .stl format required for a rapid prototyping device. There needs to be some consideration as to the purpose of the imaging.  There are limitations to the capabilities of a rapid prototyping device which means that any reproduction would lose its scaling effects. Sanson et al [‎3] used confocal microscopy combined with taking casts of bat’s teeth to produce images of tooth wear patterns to be studied using virtual reality. Beraldin et al described a variation of the technique which could be applied to any stack of data points to produce a resin model from a rapid prototyping device or a model in virtual reality applying it to works of sculpture but the question needs to be asked: of what practical use would a large scale resin model of a biological structure be apart from fulfilling some educational role? The virtual reality applications particularly with respect to the medical field would seem more important.

     Can small structures be imaged using a confocal microscope without the use of casting methods? Yes. The first method of shape recording selected was the use of confocal microscopy. Confocal microscopy has a particular attraction due to the fact that specimens need only be mounted in a distilled water solution and the examination is non-destructive. The ambition of this experiment was to seek a method of direct data transfer without recourse to curve-fitting for moving directly to a prototyping device.

     Finite Element Analysis cannot be abandoned for the purposes of product design therefore confocal microscopy and the random mesh arising from its imaging loses its attraction. Instead a more ordered form of image acquisition is used. Why? Because the purpose is to manufacture a product out of a standard material and there is a need to predict behaviour.

3.5   Conclusion

     Confocal microscopy is commonly used in the field of neuroscience. Its application to the field of biomimetic study could be controversial since it is expensive hardware and memory intensive. This notwithstanding, memory capacities are increasing and technology advancing at a speed which may make its use more frequent in the future.

     In reality a confocal microscope and its output is a laser scanner like many others on the market, engineered for microscopic applications. The random nature of measurement of light intensities is suitable for conversion to .stl files and this was shown by Dr Dylan Evans who used an MRI scan, also an output of image sections, to construct a model of the human heart using a rapid prototyping device. But it is not suitable for the ordered nature of Finite Elelment Analysis.    

     There is not yet a unifying and truly descriptive and prescriptive method of shape acquisition. The compromise is creating a mesh for the purpose of surface modelling and a second mesh for the purpose of finite element analysis, each mesh deriving from a different data set. And because commercial design packages include .stl compatibility the following method was adopted.

4  Alternative Morphological Recording: Sectioning and 2-D digitizing

It is appropriate to consider an alternative means of collecting morphological data on the hooks.  This comprises of using a microtome and a digitizer with a finite element package such as Solid Modeling. One begins by taking into account that one shall be using a Solid Modeling feature known as “loft”. This requires what is known as a “path” which is a digitized spine along which a number of cross-sections shall be distributed prior to rendering of the object in 3D. Digitizing the upper and lower profiles provides for a smoother model by providing two paths to support the intervening profiles. Thereafter, using the microtome to section at predefined and measured intervals along the profile, a number of cross-sections are taken perpendicular to the inner spline and each digitized.  Each section is preserved so that the sectioned material can be inspected. This method would seem to be particularly applicable to the biomimetic study of insect tarsi.

     The data is transferred to the Solid Modeling package to reconstruct the hook in 3 dimensions.  The advantage to this form of morphological recording is that it is cheaper and mobile compared to a confocal microscope – the digitizer, microtome and software are relatively commonplace, the digitized sections are distinct and internal detail is revealed by the sectioning and this can be included in the reconstruction.

     Alternatively a simple silhouette can be used, measured and reconstructed. It was assumed each profile was circular which is clearly not entirely true but is a close enough approximation for the purposes of illustration.

Figure 7:Figure 1 – Electron micrograph with grid superimposed. Each bar represents an interval of 100 microns.

     Using ‎Figure 7 it was possible to digitise two splines for the inner and outer profiles. Diameters were measured perpendicular to the inner spline and used to reconstruct the hook using the loft feature, the result of which is shown below.

Figure 8:3-D image of reconstructed burdock hook. For scale compare with scale bar of Figure 7.

5  Conclusions

The generation of a product from a biological structure combines prescriptive and descriptive processes. At present technology does not allow us to make the transition smoothly. Finite element analysis and graphical representation utilise the 3-D meshing of data points for differing purposes.

     Small biological structures of cellulose and insect chitin are translucent to laser light and therefore can be scanned with non-destructive results. This may also be true of other biomaterials. Commercially available software can be utilised to convert the resultant dataclouds to 3-D models but this does not mean that the model is suitable for finite element analysis.

     In terms of efficiency based upon cost and computational effectiveness including memory storage, confocal microscopy is more expensive than conventional methods of sectioning and digitising. However in terms of operator time it is by far the cheapest.

     It could be possible to use the confocal microscope to perform data capture and export the product to a finite element package, thereafter to re-mesh to perform finite element analysis. This is not so simple as it might seem, however, since finite element analysis has its own demands in terms of discrete vertices and lengths that must be fulfilled via the act of drawing construction by the user. These needs are not fulfilled by appointing relatively random vertices of light intensities that arise through the act of laser scanning a biological structure.

     It has been established in Part I that the burdock hook consists of a uniform biomaterial which is known to be anisotropic. It is sensitive to shear due to the bending moment of loading and resistant to flexing. It is formed to shear under heavy loading and to be receptive to many different substrates. The burdock hook, through its flattened bract support, has a single degree freedom which increases its propensity to attach.

References

[1]    Dai Z, Gorb S N, Schwarz U,Roughness-dependent friction force of the tarsal claw system in the beetle Pachnoda marginata (Coleoptera, Scarabaeidae), Journal of Experimental Biology, 205, pp. 2479-2488, 2002

[2]    Beraldin J. A., Blais F., Boulanger P., Cournoyer L., Domey J, El-Hakim S. F., Godin G., Rioux M., Taylor J., Real world modelling through high resolution digital 3D imaging of objects and structures. ISPRS Journal of Photogrammetry and Remote Sensing, 55, pp. 230-250, 2000

[3]    Evans A. R, Harper I S, Sanson G D,Confocal imaging, visualisation and 3-D surface measurement of small mammalian teeth. Journal of Microscopy, 204, Pt 2 pp. 108-119 2001

[4]    Jones  I., Personal Communication, November 2002, Research Officer, Neuroscience, Department of Biology, University of Bath, Bath, UK

[5]    Vincent J. F. V., Structural Biomaterials, The Macmillan Press, 1982

[6]    Sellinger A, Weiss P. M., Nguyen A., Lu Y., Assink R. A., Gong W., Gong C., Brinker C. J., Continuous self-assembly of organic-inorganic nanocomposite coatings that mimic nacre. Nature, 394, pp. 256-260 (1998)

[7]    Devlin R. M., Witham F. H., Plant Physiology, Fourth Ed., Devlin and Witham, PWS, 1983

A Biomimetic Study of the Long Shaft Cellulose Hooks of Arctium minus (Burdock) Part I – Functional Ecology and Field Testing

A Biomimetic Study of the Long Shaft Cellulose Hooks of Arctium minus (Burdock) Part I – Functional Ecology and Field Testing

Bruce Saunders

 

Abstract

Hooks associated with plant seed and fruit dispersal, with relatively long-shafts and short spans have been identified in five species by S N Gorb. Arctium minus (or Burdock as it is commonly known) is reputed to have already been the source of engineering design inspiration for George de Mestral (see Velcro). There are marked differences in the shape and functionality of natural hooks and the probabilistic fastener that he designed and developed. This paper presents Part I of a formal biomimetic study of A. minus after the methodology outlined by S N Gorb on biomimetic fasteners. The variety of long-shaft cellulose hooks supports its potential for design applications for attachment to material substrates. From study of Gorb’s data it is concluded that there are indicators for structural behaviour apart from the morphological variables indicated by Gorb and these are flexible versus fixed bases to the shafts and degrees of resilience of the component material. The natural substrate properties are presented as being indicative of the receptiveness of the hooks to a range of substrates. Field testing consisted of tensile testing mounted A. minus hooks in an Instron tensile tester in a laboratory to note the fracture strength (contact separation force) and mode of failure which was characteristic of a composite biomaterial.  

Keywords:  Fibre dimensions, tensile testing, fracture, composites, bending and axial loading, biological design indicators, scaling effects

1  Introduction

This series of papers draws heavily upon the work of S N Gorb and his colleagues.  A. minus is a species of plant that supports hooks for the purposes of seed dispersal that was omitted in his study of scaling effects ‎[1] in biological hooks and it is studied here in order to investigate if the omission was warranted. Further, after his study of the G. aperine hook ‎[2], the hook of the A minus is studied to identify any salient biological design indicators that could give rise to the development of a new product.

     The question of intelligent design and perfection in plant hooks associated with plant reproduction is taken to have been addressed by the work of Allmon and Ross as cited by Nicklaus ‎[3], Howe and Smallwood‎[4] and by S H Bullock ‎[5] and it is therefore sufficient to merely state here that for the purposes of structural biomimetic study, plant biological structures must be treated as they are without regard to their origins or reason for being and examined for design indicators that can be utilised for the purposes of modern design and manufacture. To assume perfection in Nature’s design is a fallacy. All that can be assumed about Nature’s designs is energy efficiency with available materials. However in seeking a design indicator, successful structures that are present in more than one species are a point of departure for study from Nicklaus’ analysis of the evolutionary process (i.e. the structures have passed through the “evolutionary sieve” in more than one species – an indicator of success.).

     Hooks with a long shaft and a small diameter hooked tip have been studied by S N Gorb in a number of papers and he specifically states‎[4] that at the time of his writing, there were no commercial lightweight attachment mechanisms that exhibited a flexible base as he found in the case of G. aperine (multiple-degrees of freedom). Species he studied that support hooks were A. eupatoria, C. lutetiana, G. aperine and G. urbanum ‎[5]. These hooks are not formed through the process of adaptive growth since they are single-use. They therefore must be genetically defined to occur in the required shape. Interaction with the environment changes their qualities in a genetically predefined manner. The distinct difference between these hooks is the structures from which they arise; G. aperine hooks are stomatal in origin as are those of A. eupatoria and C. lutetiana while the hooks of G. urbanum arise from carpels. Of the five hooked species only the hooks of A. minus arise from modified bracts encasing the ovary.

 

 

Figure 1:               Arctium minus with mm scale bar, showing the single order of freedom arrangement of hooked bracts overlaying each other.

 

2  Scale

D’Arcy Wentworth Thomson’s book “On Growth and Form” ‎[6], devotes a chapter to scale effects. The entire Chapter 2 is entitled “Magnitude” where he describes the “The Principle of Similitude”. By the Principle of Similitude forces such as inertia become small enough to ignore whilst others are magnified in their effect.  For the purposes of hooked biological structures attention is drawn to his discussions on size, cell size, gravity, body-size, surface tension, viscosity and Brownian motion in the case of extremely small structures in a liquid medium.

     In the case of natural hooked structures, many of the examples in Nature are  so small (~100mm in thickness) that scaling factors become significant in the action of attachment. It is common to find that it is a combination of properties that act coincidentally that produce an effect ‎[7].

     Adhesive secretions, other fluid properties such as surface energy and capillarity and even applied pressure gradients combine with mechanical interlock to produce a resultant attachment force. Gorb notes ‎[8] that biological systems present the material scientist with goals for new materials that can model the behaviour of biomaterials.

     The burdock hook (radius of curvature ~ 250mm, shaft diameter ~ 200mm) is desiccated when mature, without any secretory organs. The full action of mechanical interlock can take place in both a wet and dry environment thus the scaling effects are limited to those of size, friction, moisture, inertia and gravity.

     When attempting to reproduce these assets for a commercial product one is faced with the problem of overcoming the very same problems that give these attachment mechanisms their special qualities. It can be predicted that there will be a problem using conventional rapid prototyping devices to judge their performance due to their ability, or rather, their inability to reproduce resin models in the order of size of less than 100 microns in thickness which is necessary in order to reproduce any scaling effects observed in the biological sample. A typical deposition prototyper deposits nylon resin in layers of 100 microns, about half the burdock shaft thickness and further the material lacks properties analogous to biological materials ‎[9].

 

The Functional Ecology of Arctium minus

Higher plants use a variety of dispersal agents such as wind, water, animals and people ‎[1].  Dispersal by animals is known as zoochory. The dispersal of seeds or fruit (known as diaspores, more often fruit than seeds) by attachment to animal fur or feathers is known as epizoochory.  Diaspores of this kind do not provide valuable nutrition to the animal to which they attach themselves nor do they actively attract animals to parent plants.  Instead they have special structures such as hooks, barbs, burrs and spines or sticky secretions and they detach easily from the parent plant.

     In fur and feathers the diaspores may remain attached for a long period of time until animals groom them off or until the animal dies. Arctium minus has natural symbiotic partners in seed dispersal that are wild animals and birds indigenous to the UK, such as rabbits, badgers, foxes, sheep and deer.  The diaspores of Arctium minus are adapted for dispersal by mechanical interlocking.

     Arctium minus is commonly known as burdock and it is found throughout the UK and is a member of the Thistle family.  It is common knowledge that it is an annual noxious weed commonly found by the side of pathways and riverbanks.  It grows approximately to 2 meters in height and generally features single or multiple primary stems off which arise secondary and tertiary branches.      

     In terms of the plant’s life cycle, the hooks become operational early in the year, acting as a defense mechanism while the immature seeds develop.  From observation, at this stage the tensile force required to remove the fruit from its supporting stem is at its highest. The corolla or flowers are in evidence at the apex of the fruit, protruding from the basal cup comprising of the ovary and surrounding bracts.  This fruit is green and the hooks are already developed but pliant. As the fruit matures the corolla withers and then disappears. The seeds are present in the ovary and these are freed by the total disintegration of the fruit which begins immediately the fruit is separated from its host plant.

     Each of the bracts is flattened at the base where it originates, becoming narrower to form the shaft of the hook.  Therefore each hook has a single degree of freedom which, according to Gorb ‎[1] has implications for its attachment ability, decreasing the contact separation force and increasing the propensity of the fruit to attach because the ability to bend implies weaker and flexible cell structures yet a greater ability to become attached in a probabilistic manner. As the plant and its seeds mature the entire plant desiccates and becomes brittle.  The detachment force required from its supporting stem for the now brown fruits and the mature seeds they contain reduces to a load far below that of the fracture force of the hooks and the fruit freely attaches itself to passing host. This is generally a one-off attachment. Once the fruit makes contact with the ground it is ready to await germination.

    Due to its narrow profile, the burdock hook has a further function, namely an insertion effect. It enables the hook to pierce fibrous surfaces like a blunt needle and this could be an important indicator in later design.

     The behaviour of the Artium minus hook under loading is studied here. The hook is composed of the bio-composite cellulose which is comprised of cellulose fibrils bound together in a matrix of hemi-cellulose and lignin. Full descriptions of the chemical composition and formation of these can be found in appropriate texts such as ‎[10] and ‎[11].

   This paper forms part of the biomimetic process as described by Gorb ‎[12], namely material study and mathematical analysis of loading. Note that Gorb includes duties for chemists in attachment structures that include secretions but this is not applicable in the case of burdock due to its dessicated state during the season of diaspore dispersal and lack of evident secretions.

4  The substrate

The substrate, because it forms one half of the attachment system for these types of hooks, must be accounted for in a study for the purposes of producing a product. The question that needs to be answered is the overall effect the substrate fulfills. In terms of the host substrate being fur or feathers, the qualities of these substrates have been studied elsewhere for other purposes. ‎Table 1: the diameters of some common natural fibres below).

 

Table 1:               Natural fibre diameters‎[13]

 

Type of hair

Diameter (microns)

Human

90-100

Llama

20-40

Fine wool

19.5

Mohair  

25-45

Merino wool

12-20

 

 

     Hair is made of keratin. Keratins form a group of varied proteins which contain significant amounts of sulphur cross-linking and stabilizing in the material. It is found in horn, hair, hoof, feather, skin, claws etc. The types of keratin include mammalian, avian and others such as reptilian ‎[10].

     In mammals, keratin occurs in hair, hoof and horn.  Human hair is a composite consisting of a fibre/matrix mix. In a relaxed state the hair is mainly a-form and when heated and pulled straight it turns into a b-form.  The a-form is the a-helix and the b-form is the anti-parallel b-sheet which results from pulling the a-helices beyond their yield point. Bird feathers are also made of keratins as is silk.

     This can be related to the inner radius of the hook in order to seek design indicators of an optimum ratio. Such experimentation can be left until later in the product design but for the moment it should be mentioned that the inner diameter of the burdock hook, from outer tip to inner shaft surface, is approximately 250 microns and this can be compared to the above figures (see ‎Table 1: .

     Perhaps the most important aspect to note with reference to the functionality of A. minus is not a critical geometrical relationship between the hook and a particular fibre but the fact that the hook accepts all fibre diameters for the purposes of mechanical interlock i.e. it is non-specific.

 

5  Tensile Testing of the A. minus Hook

The testing of the burdock hooks occurred in laboratory conditions. The hooks of burdock fruit were harvested a month prior to testing and stored in a dry condition. The purposes of this experiment were to study the material behaviour for the purpose of designing a product. Certain aspects of the bract’s behaviour were isolated for the purpose of the experiment whilst others were suppressed. The detachment force of the fruit from the stem, the extension of the hook prior to fracture and the force to remove the hook from the fruit; these were all suppressed for the purposes of the experiment. The first and third because they were irrelevant to a product study and the second because the hooks were all naturally curved prior to tension being applied making it difficult to isolate true extension due to material deformation from extension due to the taking up of slack. Further, standard values of Young’s modulus for cellulose (7-15 GPa from ‎[10]) were used. This was not an experiment to determine the Young’s modulus and measured strain was not relevant to the test.

5.1   Aim

To investigate the fracture force and mode of fracture of hooks from the plant genus Arctium minus or common burdock using an Instron tensile testing machine to observe any telling differences that could be observed from the conclusion of Gorb that the span of the hook was the significant factor in contact separation force by testing specimens of different radius of hook collected from burdock pods of varying diameters. Further, to observe the nature of fracture of the composite biomaterial and to use this information in developing a design for an attachment mechanism based upon the burdock hook and its functionality.

     This experiment draws from the methods and is compared with the results of the following two papers:

 

  1. “Natural hook-and-loop fasteners: Anatomy, Mechanical Properties and Attachment Force of the Jointed Hooks of the Galium aparine Fruit” E V Gorb, V L Popov, S N Gorb ‎‎[2], and
  2. “Contact Separation Force of the Fruit Burrs in Four Plant Species Adapted to Dispersal by Mechanical Interlocking” E V Gorb, S Gorb ‎[1].

 

     These two papers yield fundamental descriptions and conclusions upon which the following experiment is based. Their investigation into scaling effects in small hooks led to the following assertions: the four main attributes that influence burr performance are span, structure, size and material flexibility. All four species tested were found to exhibit behaviour within the known bounds of cellulose performance. (E = 7 – 15GPa). The significant difference detected was an unforeseen weakness in strength displayed by C. lutetiana. This was associated with an increase in material flexibility; the hooks didn’t fracture, they flexed to release the loop and the hooks remained intact. This form of response is very similar to that of commercial Velcro and would indicate that Velcro better approximates the behaviour of C. lutetiana than A. minus as is commonly asserted.

     The four main attributes described are repeated here:

 

  1. Structure: stomatal structures are smaller, rely upon the thickness of the cell wall and have stress concentrations at their base.
  2. Size: the longer the shaft length the greater the strength. This is probably due to a shaft diameter to length ratio, the longer the shaft the thicker the shaft.
  3. Span: the smaller the span of the hook the greater the strength due to a reduction in lever arm and hence bending moment.
  4. Flexibility: the greater the material flexibility the greater the chance of the test loop slipping from the hook and the hook surviving. Gorb’s tests indicate that there is an associated decrease in attachment strength.

 

     Gorb suggests that it would be of interest to investigate the required force for detachment of the fruit from the stems but this was not considered relevant to this method for designing a biomimetic fastener.

5.2   Method and Apparatus

  1. Specimens were collected from four separate burdock plants that grow behind the University of Bath accommodation blocks. The plants all stand in a line next to a sandy path that passes between the University grounds and the golf course.
  2. Note was maintained of the conditions of collection and the regions of the individual plants from which specimens were collected. These specimens were collected late in October 2003 and tested in December. It was observed that the plants themselves were brown and dry with the leafy vegetation of early season growth disappeared and the seedpod fully developed.
  3. It was judged that the effect of the delay between the collection and testing of the hooks would have little effect on the relative performance of the hooks and probably little effect on the absolute performance of the individual hooks given that they were collected in a naturally desiccated state and maintained in a dry condition until ready for testing, thereby preventing/inhibiting decomposition. Their desiccated state also made them ready for SEM work.
  4. Five individual fruit specimens (each consisting of an array of approximately 100 hooked bracts) were collected from each plant giving 20 specimens in total. A selection of these specimens was then tested.
  5. The Instron tensile tester was equipped with a 1N loadcell.

5.3   Specimen Preparation

Each fruit was sectioned into halves under a dissecting microscope. One of these halves was returned to the specimen packet in case more hooks from the same specimen would be required. The other hemisphere of bracts/ovary/seeds was separated to yield individual hooked bracts for experimentation.

     Ten individual hooks were taken from the dispersed hemisphere. These were mounted in preparation for testing in the Instron machine by gluing each separate bract to a plastic mounting. The bract shaft with its hook extended was exposed for interaction with a testing substrate analogue, a loop of silk thread. The Instron tensile tester applies extension and measures the resultant reaction in the specimen through the loadcell and the rate of extension was set at 1mm/sec using a 1N load cell.

     Gorb states that the shaft length is the principle main morphological variable influencing a hook’s strength. Thereafter, hook span and material flexibility are most important, his theory being that the larger the span the greater the lever arm of the bending moment and the stress at the shaft. In this case material composition is constant for all the hooks.

 

 

 

 

 

 

 

 

 

 

 

 

Figure 14:   A rack of 5 hooks ready for testing

 

 

Figure 15:               Hook testing in the Instron Tensile tester. Arrow indicates looped thread.

5.4   Results

The results of the tensile testing are tabulated below. Up to nine sample hooks were taken off of six fruit. The mean value of these results for each specimen is plotted versus the diameter of the fruit.

 

Table 2:               Results of tensile testing

 

Fruit number

 

1

2

3

4

5

6

1

0.00101

0.00114

0.00057

0.00135

0.00059

0.00139

2

0.00104

0.00121

0.00108

0.00093

0.0011

0.00114

3

0.00107

0.00099

0.0011

0.00112

0.0012

0.00112

4

0.00103

0.00095

0.00083

0.00124

0.00088

0.00106

5

0.00087

0.00098

0.00092

0.00114

0.00109

0.00105

6

 

0.00085

0.00091

0.001

0.00118

0.00131

7

 

0.0009

0.00092

0.00086

0.00127

0.00127

8

 

0.00093

0.00107

0.00113

 

0.00109

9

 

0.0009

0.00115

 

 

0.0012

Ave (N)

0.001

0.000983

0.00095

0.001096

0.001044

0.001181

Std Dev

7.8E-05

0.000118

0.000179

0.000161

0.000235

0.000119

Diameter (mm)

23.5

15

14

26

25

23

 

The results of this tensile test were directly compared with the values obtained by Gorb in his paper on contact separation forces. In his experiments the species with the lowest contact separation force isC. lutetiana, the species whose hook functionality most closely matches the flexible hooks of Velcro which are flexible in order to meet the demand of multiple usage in the product with the minimal of damage to hook and fibre substrate (for clarity note that there is a difference between flexible bases and flexible hooks – in the first instance the whole structure moves with the flexing of the base, in the second only the arch of  the hook flexes).

     Comparing the force results obtained for A. minus with Gorb’s results shows that the magnitude of the results for A. minus fall between those of A. eupatoria and G. urbanum but are significantly higher than the other species with a flexible base, G. aperine. Certainly in terms of order of magnitude the tests would seem to reflect a fair result.

     Therefore the order of magnitude in fracture strength, from lowest to highest, is as follows:

C. lutetiana, G. aperine, A. eupatoria,             A. minus,               G. urbanum

Stomatal,                                                              bract,                      carpel

     That is, in increasing cellular complexity and thickness. Gorb’s investigation into his four hooked species was to investigate the correlations between contact separation force and various morphological variables, seeking a negative correlation that would oppose intuitive reasoning. If, for instance, it was found that in a species the contact separation force varied with the inverse of hook span this would be an indicator of a scaling indicator that would be of interest for further investigation. The G. aperine hook was of interest to Gorb since these hooks were distinguished by their hollow base and high degree of flexibility in all directions. The same can be said of the A. minus with the flattened bract at the base of the hook.

     In terms of statistical analysis, Gorb used ANOVA based upon ranks to compare the variables of the four species and investigate the correlations. In the case of this experiment where a single species is investigated it is suited to use a direct comparison between the load values of his paper. A simple form of scale measurement is used, that those hooks that originate from a large fruit would be proportionately larger than those from a small fruit. This is in fact obviously true from visual inspection of the specimens.

 

 

Figure 16:           Results of tensile testing

 

5.4.1    Images of fracture

 

The SEM images of the fractured hooks in ‎Figure 5: overleaf clearly show the fibrous nature of the hook material. The fracture surfaces are of interest. As will be seen in Part II, the hooks all have a thickening of the outer surface in the early curvature of the hook which will resist bending and compression, inducing fracture instead of bending. This effect is visible in the images.

     The composite nature of the material is clear and it should be noted how the fracture surface fractures unevenly and there is fibre “pull-out”. From Prof J F V Vincent’s notes on the mode of fracture of fibrous composites ‎[10], fibre “pull-out” indicates that the fibre/matrix interface of the plant material consisting of cellulose microfibrils, hemi-cellulose and lignin is tightly bound. It can be seen from ‎Figure 5: that all 4 specimens (taken to be typical examples of fracture in the specimen set) experienced failure on the inner curvature of the hook as would be expected for a hook of material experiencing a bending moment with the inner fibres under tension while the external fibres are in a state of relative compression about a point of rotation. More importantly for a hook shape the inner fibres will be shorter than the outermost fibres therefore strain will be highest in the inner fibres. This means that the tensile forces in the inner curvature and therefore induced shear will be higher than the fibres in the outer curvature. 

     The surface is typical of a fibrous composite break in bending.All hooks fractured at the region of the join between hook and shaft which is the region of the entire hook structure (both shaft and arced tip) that experiences the largest stress when the hook is placed in tension, noting that the bract itself is secured by glue. At no single instance did any of the test hooks fail at the bract.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 17:                     SEM’s showing sample fracture surfaces of cellulose microfibrils

 

 

5.4.2    Discussion

 

The specimen fruit size ranged from 14mm to 26mm in diameter. It was reasonably assumed that the sizes of hooks increased proportionally from fruit to fruit, including shaft length and span. Sample hooks were taken from different positions on the spherical fruit.

     With reference to ‎Figure 4: (the graph of fracture forces) it can be seen that the hook fracture forces are all of the same order of magnitude but that there is a levelling of the slope in the region of the diameter equalling 20mm.   

     The separation force levels out at 1.2 mN which can be taken to indicate the ultimate tensile strength of the cellulose microfibrils and the point at which the crack accelerates across the fracture plane. More on this follows in the next section.

     All hooks fractured in the region just beneath or at the commencement of curvature.  This is in line with bending theory since the material at this point will experience the highest bending moment and the maximum distortion, particularly at the innermost fibres which will be in tension.  These fibres will experience the highest strain as the hook tries to straighten under loading.  The outermost fibres will be in compression as the hook distorts and “straightens” under loading. Once the inner fibres have failed the full load is then transferred to the outer fibres which immediately fail in tension under the significantly higher stress.

     The inner fibres strain at differing rates. This causes a disruption in the binding matrix. Once the matrix has been disrupted crack propagation is disrupted and the individual fibres that are now unsupported by the matrix rupture in shear and fibre pullout occurs. The crack face moves as the hook bends and then separates because the region of highest stress intensity moves with the hook deformation, staying in the region where the bending moment is the highest.

 

5.5   Analysis

 

It was noted that there was a difference between the diameter of wire used by Gorb and the silk thread of this experiment (of the order of x10). Both the wire loop and the silk thread represent an artificial substrate, replacing natural fibre. Silk thread is a composite of natural silk of which each fibre is much finer than fur fibres. The wire loop appears much finer than a natural fibre and the question should be asked if it contributed to severing the hook tips.

     The analysis that follows derives from undergraduate engineering structural analysis. Note that although cellulose is a biocomposite, the density of the fibres in the fibre/matrix composite is such that for the purposes of analysis the hook material shall be treated as an isotropic solid. This is because the hook fibres are loaded in direct stress only. The basic morphology of the hook shall follow the sketch in ‎Figure 7:. Dimensions for the hook are taken from the SEM below (‎Figure 6:). An SEM of a fractured hook has been placed alongside.

 

 

 

 

 

Figure 18:                     An SEM of an A. minus hook reproduced from Part I and an SEM of a fractured hook which appears again later in the Results.

 

     Let the hook be placed under tension. The stresses in the material will comprise two components due to the tensile loading:

 

 

 

Figure 19:                     Free Body Diagram and stress diagrams for the bending stress and axial stress characteristic of a hook under tensile load from Fenner ‎[15]

 

     It has been noted previously that the A. minus hook does not taper in diameter from the top of the shaft. There is an increase in material on the shoulder of the hook before it tapers to a point. This influences the hook’s behaviour in tension, increasing its resistance to flexing, increasing its attachment to its host and its disposition to fracture.

     The analysis of a hook under loading is completely presented in Fenner ‎[15].

Vincent has presented standard figures for the elastic modulus of cellulose as 7-15 Gpa and notes that for biomaterials the Poisson ratio is generally taken to be 0.5 (though not always).

     By using these figures as a maximum and minimum value and calculating the stress due the loading it should be possible to evaluate the percentage strain during the test. All dimensions are taken from ‎Figure 6:. Calculations are based upon the sketches in ‎Figure 7:. The values for direct strain and shear strain can be calculated and compared. This specimen calculation is based upon the average fracture force of specimen 3 i. e.

 

f = 0.001168 N (from Table 5)

E = elastic modulus = s/e = stress/strain                                                         (1)

 

st = tensile stress = force/area = f/A                                                                 (2)

where the area is the cross-section of the hook.

 

A = (p *d**2)/4                                                                                                   (3)

Where d = 200 x 10-6

 

L = lever arm = d/2 + span/2                                                                             (4)

Span = 100 microns, therefore

L = 200 microns

d = 0.000120m

 

st = f/A = f*4/(p*d2)                                                                                           (5)

 

st = (1.17 x 10-3 x 4)/(p x (120 x 10-6)2) = 1.035MPa

 

sbm = f*L*yNA/Iyy                                                                                                                                                 (6)

 

where Iyy = the second moment of area of a circle about a neutral axis y-y and yNA is the distance from the neutral axis to the edge of the section.

 

sbm = (100 x 10-6 x 200 x 10-6 x 1.17 x 10-3 x 4)/(p x (1202 x 10-6)2)

                = 2.069 x 10-3 Pa

 

stotal = 1.035MPa

 

Now by substituting each of the range values of E = (7-15GPa) for cellulose we find emn and emax.

 

emax = 0.000148, emin = 0.000069

 

     These results suggest that:

  1. Since the longitudinal strains are so low, there must be some other reason for failure.
  2. The bending moment has a negligible impact upon the failure in direct stress.

 

If we consider shear stress, ss = Fs/A

Where A is the angled shear plane at angle q and Fs is the shear component of the applied load, then

 

                Fcosq /Asecq = ts                                                                                                                         (7)

 

Let q = 30o

 

Then ts =  ((1.17 x 10-3)cos q)/((p  x d**2) x secq/4)

 

                = 32MPa

 

If G = E/(2 x (1 + u))                                                                                           (8)

 

Then G = E/3 = (2.33Mpa, 7.5Mpa)

 

And g, the shear strain, where g = t/G                                                              (9)

 

                = (13.7, 4.23)

 

This suggests that the hooks fail in shear induced due to the bending moment, seeming to confirm the hypothesis that cellular complexity and strength could be of higher consequence upon contact separation force than the relative lever arms and other mechanical morphological variables.

 

5.5.1    Conclusion

 

This experiment confirms that the separation force of a natural hooked structure is directly dependent upon the span or radius of a hook and directly dependent upon the component material’s resistance to shear. It shows that the A. minus hook behaves in the same manner as the hooks studied by S N Gorb previously in that there is a positive correlation between hook span and contact separation force i.e. no inverse scaling effects.

       It could be assumed in mechanical design of a hook that the smaller the span of the hook the higher the separation force since this would reduce the tensile stress due to the bending moment. But in composite biomaterials this is not the full story. The bending moment does not add substantially to the direct stress the hook experiences. The true weakness can be found in the cellulose microfibril’s relatively low resistance to failure in shear.

     From Vincent ‎[10] biomaterials have two types of natural resistance to crack retardation, the Cook-Gordon model where a weak matrix/fibre interface intercepts the crack propagation and absorbs energy of crack propagation and the second is a toughening coating on the exterior of a material. In this test which was performed on an Instron tensile tester which applies load through displacement, the load is not removed or eased after the first crack appears. Loading continues at the same rate (1 mm/sec in this case).

     There can be reasonable argument put that using a Poisson’s ratio of 0.5 is not accurate.  However even of this were so, the results for strain (e) are very low.

     This experiment helps illustrate the types of properties that shall be important in the specification of a product.  It demonstrates (as a biological indicator) that there is a possibility for designing a single degree of freedom hook that mimics A. minus in shape and functionality which would be different from commercial Velcro. It must be born in mind that all the hooks in this experiment as well as in Gorb’s will demonstrate energy efficiency and therefore material and stress optimization in their structure. Further it demonstrates that as a form of biological mimicry, the introduction of vesicles or spaces into the biomaterial matrix could be a valid approach to strengthening a composite hook and that cracks introduced during the process of extension can contribute to the retardation of crack growth.

 

References

 

[1]    Gorb E., Gorb S. N., Contact Separation Force of the Fruit Burrs in Four Plant Species Adapted to Dispersal by Mechanical Interlocking, Plant Physiology and Biochemistry, 40, pp. 373-381, 2002

[2]    Popov E. V., Popov V. L., Gorb S. N.,Natural hook-and-loop fasteners: anatomy, mechanical properties, and attachment force of the jointed hooks of the Galium aparine fruit, Design and Nature Review Paper DN02/40800, 2002

[3]    Nicklaus, K. J. Plant Biomechanics – An Engineering Approach to Plant Form and Function (Chapter 10), Biomechanics and Plant Evolution, University of Chicago Press, pp. 474-530, 1992.

[4]    Howe H. J., Smallwood J., The Ecology of Seed Dispersal. Annual Review of Ecological Systems 13, pp. 201-228, 1982

[5]    Bullock S. H., Comparative Experimental Study of Seed Dispersal on Animals. Ecology 58, pp. 681-686, 1997

[6]    Thomson D., On Magnitude (Chapter 2), On Growth and Form, Cambridge University Press, pp. 15-48, 1961

[7]    Scherge M., Gorb S. N.Biological Micro- and Nano-tribology Nature’s Solutions, NanoScience and Technology m01/18085, Springer, pp. 231-239 and pp197, 2001

[8]    Scherge M., Gorb S. N.,Microtribology of Biological Materials. Tribology Letters 8, pp. 1-7, 2000

[9]    Ashby M, Johnson K, Materials and Design, The Art and Science of Materials Selection in Product Design, Butterworth Heinemann, pp. 256-257, 2002

[10]Vincent J. F. V., Structural Biomaterials, The Macmillan Press, 1982

[11]Devlin R. M., Witham F. H., Plant Physiology, Fourth Ed., Devlin and Witham, PWS, 1983

[12]Gorb S. N., Miniature attachment systems: Exploring biological design principles. Design and Nature, DN02/40799, 2002

[13]Stamburg G., Wilson D., Veterinary Medicine http://www.llamapaedia.com/wool/

[14]Popov E. V., Popov V. L., Gorb S. N.,Natural hook-and-loop fasteners: anatomy, mechanical properties, and attachment force of the jointed hooks of the Galium aparine fruit. Design and Nature Review Paper DN02/40800 2002

[15]Fenner R. T., Mechanics of Solids, Blackwell Scientific Publications, pp. 296-297, 1993