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Phd Transfer Paper – the Biomimetics of Hooks

Copyright B E Saunders 2016

 

PhD Transfer Report

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

 

 

Submitted by

Bruce Edward Saunders

 

July  2004

 

 

 

 

 

 

 

University of Bath

Centre for Biomimetic and Natural Technologies

Department of Mechanical Engineering

Faculty of Engineering and Design

BA2 7AY

 

Supervisor: Dr. A Bowyer

 

 

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

Project no. EN042

 

 

 

INTRODUCTION I – Introduction, Biological materials, Hypothesis. 6

Definition and Description. 14

Recording Shape. 15

Probablistic Fasteners. 19

The Operation of the Dragonfly Mechanism.. 19

Section I I –  Case Study 1: A Study of Bird Claws. 22

The Two Dimensional Digitising of Biological Structures. 23

Introduction. 23

Systematic Biology and Finding a Function Through the Digitised Profile. 23

Cladistics. 24

The Digitising of a Tiger’s Claw.. 25

Experiment 1.1 : Bird Claw Profiles. 25

Aim.. 25

Apparatus. 26

Method. 26

Results. 26

Discussion. 27

Conclusion. 28

References. 29

Bibliography. 29

 

 

Table of Figures

 

Figure 1 – SEM of a burdock (Arctium minus) hook at the tip of a modified bract. 7

Figure 2 – Plant cell structure. 12

Figure 3 – D(+) Glucose. 13

Figure 4 – b – D Glucose. 13

Figure 5 – Diagram showing prominent dimensions and sections of a manufactured hook  18

Figure 6 -Corresponding surfaces involved in the dragonfly head arresting mechanism. A and C are of the surface at the “front” of the thorax and B and D are of the surface at the back of the head (from Gorb p65) 20

Figure 7 – Dragonfly Head-arresting mechanism taken from [Error! Reference source not found.Error! Reference source not found.]) 21

Figure 8 A dimensionless plot of the attachment device design space from [Error! Reference source not found.] p170) 21

Figure 9 – Dragonfly head-arresting mechanism – detached. 21

Figure 10 – Dragonfly Head-arresting mechanism – attached. 21

Figure 48 – Result of digitising Robin Claw and exporting data to Excel 27

Figure 49 – Result of digitising Thrush Claw and exporting data to Excel 28

 

 

SECTION I – Introduction, Biological materials, Hypothesis

 

 

Figure 1 – SEM of a burdock (Arctium minus) hook at the tip of a modified bract.

 

 

 

 


 

Introduction

 

Learning about the background science and the biology from which the research proposal arose has occupied much time. The Museum of Natural History in London has been visited for viewing of the fossils of the Archeopterix as well as the Smithsonian Institute in Washington DC where fossils from the Burgess Shale in Canada have been observed. Some fundamental zoology was explored consisting of collecting insects and observing bird-life in South Africa.

 

These have all formed part of the research trail that originates from the author of the proposal, Dr Andrew Parker. Thus it is appropriate to introduce an early discussion of his book since it provides an evolutionary context as well as a model for this research.

 

Throughout this research project this researcher has been dogged by the suggestion that the end goal should have commercial application. From the hypothesis you, the reader, will see that indeed there is the possibility of developing a system for eventual commercial use. However it is not thought at this stage that some marvellous new form of hook will present itself for patenting. Instead the hypothesis will propose a method of using biological information to develop a design system to aid designers to manufacture light and efficient hooks from composite materials.

 

Biological materials are described in this report. They behave in an anisotropic manner similar to synthetic composite materials and this often accounts for some of the behaviour that we see in nature, for instance, the high strength to weight ratio of a spider’s spun web or of hair or the hardness of nacre (mother of pearl).

 

“In a Blink of an Eye: the Cause of the Most Dramatic Event in the History of Life” by Dr Andrew Parker [‎1]

 

Dr Parker’s book 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 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 unlocks the secret behind 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 the effects of 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 into different species at different times on the evolutionary time-scale. Some types of eyes occur in completely different species yet still obey the same physical principles, such as the eye of the octopus and the human eye.

 

Considering the grand set of all hooks in nature in this way, one is granted an insight into the development of a study of the vast number of occurrences of hooks in nature. The study of the mechanical properties of a hook is of biological interest since when placed in a functional ecological context the research should reveal information about the biological system in which it participated.

 

The interest in biological hook-shaped structures to engineers has two main commercial applications:

 

  1. Composite hooks imitating properties of those of biological materials, and
  2. The study of micro-fabrication methods.
  3. Biomedical/micro-surgical applications.

 

A study of a natural hook in its environment and an observation of its properties and performance can provide indicators for a design engineer when considering the design and manufacture of a hook.

 

Hooks constructed of composite materials have advantages. Composites are used for their high strength and reduced mass and research is well advanced into replacing parts that might ordinarily be made from dense metallic materials by composite parts (for example, in car engines).

 

The application to micro-fabrication techniques arises from scale effects that have been observed in structures as they decrease in size. To illustrate, if one takes a cube of material on a surface and reduces its size proportionally while observing the effects on mass (a function of gravity) and adhesion (a function of area), one finds that the gravitational force on the cube (its weight) reduces faster (of the order of 1/6th faster) than adhesive forces (friction between the cube and surface).

 

Combine this behaviour with current manufacturing research techniques into MEM’s (micro-electric mechanical devices) and surface texturing and there appears reason for studying small (micro) attachment mechanisms as they occur naturally in nature. Here we have an opportunity to study real-life models of systems whose behaviour becomes more difficult to imitate and predict as size decreases.

 

Compare the study of the forces on microstructures that are often designed to utilise friction and other small forces to the study of fluid mechanics.

 

In fluid mechanics, the flow field behaviour is artificially split into different realms for study, the fluid behaviour being dominated by different forms of the energy equation. Boundary layer flows (the study of fluid behaviour close to a surface) and thin, “squeezed” lubricant films are described by the same energy equation that is used to describe super-sonic flows, even although these different types of flows are different in terms of relative component energy exchanges.

 

High speed, high energy flows are dominated by large kinetic energy terms. Low speed flows have larger potential energy and friction terms relative to kinetic energy such that they cannot be ignored in the calculations of energy exchange.

 

Likewise with regard to mechanical structures but with reference to size, as the size of a structure reduces so the impact of forces that can normally be ignored increases (i.e. scaling effects) Small structures and their behaviour can provide a starting point for the design engineer and provide an insight into the behaviours of the structures at the order of size at which he wishes to design.

 

In the case of microstructures, biological structures and their behaviour can provide a starting point for the design engineer and provide an insight into the behaviours of the structures at the order of size with which he wishes to design.

 

The mechanical properties of a hook are therefore defined by its basic component materials and its size, while the function (i.e. purpose) and shape are a function of the material, size and environmental factors. The environmental factors are the substrate in which it engages and other “outside” influences. With regard to the manufacture of the micro-sized hook, this is a further interesting field. The science of micro-fabrication in its current state does not completely provide for the manufacture of biomimetic structures. The future of the science requires a greater understanding of self-assembly, the science of growing structures in bioreactors to mimic the behaviour of natural structures as closely as possible.

 

 

 

 

 

Biomaterials – A Brief Discussion

 

Julian Vincent in his text “Structural Biomaterials” [‎2] discusses the different materials found in nature. Not all of the materials he discusses are utilised in organisms to form hooks but some examples are listed below:

 

  • polysaccharides
  • insect cuticle
  • ceramics
  • keratins
  • bone

 

Some thought should be given to the full meaning of the descriptor “hook”. Is it a noun or is it a verb? Is it a hook or is it to hook? A hook at a nano-dimension is a molecular hook and an example of this is a chelate, a reactive benzene ring molecule that “hooks” an atom into its ring structure thereby rendering it inert. Chelates operate within the bounds molecular biology, associated with, amongst other things, a sense of smell. In this case hook is a verb since the organic molecule doesn’t look like a hook but it does hook a molecule via a chemical reaction.

 

At a larger micro-scale the hook starts to be hook-shaped in the sense being a noun and structures become a combination of fundamental structures like cells and cellulose micro-fibrils.

 

Teeth or fangs are formed from a bioceramic, namely of tooth enamel and dentine.

 

On an even larger scale, an example of a large biological hook in the human skeleton is the human hip – if one takes a section through the hip socket we obtain a hook-shaped profile and similarly for the ball that terminates the anterior end of the femur. In other words the hip socket and ball for matching rotated hook profiles.

 

Other biomaterials may not form hook-shapes themselves but they form the substrates to which hooks attach. And as such the behaviour of the material must be studied and understood since adverse reactions can affect the health of a patient (such as bone necrosis).

 

Biological materials (which are biological composites) are not necessarily homogenous. For example there may exist trace elements in the material or there may be differences in fibre alignment that in some way augment the strength or performance of the hook.

 

The field of biomaterials is large, far too large to be completely discussed in a transfer paper so the author will leave further discussion to a later paper.

 

A Discussion of Cellulose [‎3]

 

Plants, unlike animals, don’t possess supporting skeletons. Their strength comes from the cells where turgor pressure combines with the relatively rigid cell walls which are strengthened by microfibrils of cellulose.

Structure

 

Carbohydrates are a group of inorganic compounds containing the elements carbon, hydrogen and oxygen in the general ratio of 1:2:1.

 

Complex polysaccharides are composed of building blocks of monosaccharides.

 

Cellulose is a polysaccharide consisting of thousands of monosaccharide sugar molecules called b-d-glucose. b-d-glucose is a monosaccharide which is defined as the least complex of the carbohydrates. In other words a monosaccharide cannot be broken down into simpler carbohydrates by hydrolysis.

 

Seek definition of hydrolysis.

 

b-d-glucose is hexose (6 carbon) sugar which has a ring structure. The ring structure is formed when the C1 and C6 carbons come within close proximity of each other and an oxygen bridge forms which results in a hydroxyl group forming on the carbon 1.

 

Note that the carbons 2,3,4,5 in the straight chain glucose are called axes of asymmetry. When the ring structure forms, a new axis of asymmetry appears on carbon 1.

 

 

 

Polysaccharides are complex molecules of high molecular weight composed of a large number of repeated monosaccharides (monomers) joined through glycosidic linkages i.e. the hydroxyl molecule of adjoining rings react with the release of H2O to form an oxygen bridge.

 

 

[Insert figure p208]

 

 

Cellulose is a straight chain polymeric molecule of high molecular weight joined by b-1,4 links. It is a fundamental component of the cell wall and the most abundant natural product in the world. In new cells the wall has approximately 20% cellulose but as the cell matures and new wall material is deposited to form secondary walls, the cell wall becomes impregnated with non-carbohydrate materials such as lignin, suberin or cutin. Cellulose composes about 43% of the secondary wall.

 

Cellulose is insoluble in water and can only be completely broken down under strenuous chemical treatment such as when treated with concentrated sulphuric acid or hydrochloric acid or concentrated sodium hydroxide. Cellulose is the most abundant organic compound in the world and also one of the most valued compounds for its structural properties which have been utilised by humans for tools and shelters from the environment.

 

Synthesis

 

The bacterium Acetobacter acetigenum is a cellulose producing bacteria that is studied most, although according to the literature relatively little is known about the metabolism of cellulose. When radio-active labelled 14C glucose is fed to the bacterium cultures the carbon can eventually be found in cellulose.

 

For non-cellular production of cellulose, UDPG (uridine diphosphate glucose) which is a compound found in the yeast bacterium can be used to produce cellulose in the presence of enzyme preparations taken from A. xylinum or Lupinus albus. The addition of an acceptor molecule (cellodextrins) to the mixture enhances the process.

 

[insert image bottom p218]

 

[look for more information on synthesis]

 

 

The Hypothesis

Definition and Description

 

Hook Fundamental:

 

Consider the set of all hooks in nature. This set can be divided into subsets of similar hooks that I choose to describe as the hook fundamentals, F1-n. Each hook fundamental Fi is defined by a characteristic material and function. It is the presence of environmental factors such as the substrate to which the hook is to attached and other properties of the organism from which it arises (such as size) that the hook gains a characteristic shape.

 

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 tarsii (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 organisms of the same type as in the mating systems between male and female parts.

 

Establishing relationships between two hooks within a fundamental group:

 

Let there be types of hook f 1-n, from n different species, that are members of a fundamental group Fi, defined by the component material and function. 

 

Each hook fi in the set Fi will have evolved to its current shape through the properties of the component material and its function as well as external system factors to give a characteristic shape.

 

There are two valid methods of assessing hook fi’s performance:

 

  • 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. For instance, a burdock hook would be tested using natural fur as a substrate because this is the natural dispersal mechanism of the burdock seed pod.

 

Each form of test gives us data that can be interpreted in different ways, in the realm of engineering and the functional ecology realm.

 

Using both of the above methods on samples of a hook specimen f i and assessing the differences between the results gives an insight into the magnitude (and limitations) of forces that can only be measured by inference, such as those due to friction (a function of material and surface textures).

 

Comparing the data then provides us with a method of assessing the “perfection” of nature’s design.

 

We can then repeat similar tests on the hook specimen f j.

 

The performance of the n hooks can be plotted on the graph of size versus strength implying that function and material have thus been linearised. A line can then be drawn between them to represent a transition between their relative performances (See a later experiment on the fracture forces of a burdock hook).

 

This line should represent a continuous transition between the group of hooks and under normal conditions it should be predictable by taking into account the scaling relationship mentioned in the introduction and the performance of each hook that is now 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.

 

Expanding this to the set of n fundamentals F1 to Fn

 

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.

 

The purpose of this exercise

 

Once such a matrix has been established which shows relationships between performance and materials, 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.

Recording Shape

 

Instead of using 2-dimensional images of the profiles of hooks or launching into a mathematical definition of the shape of a hook using surface patches and non-uniform b-splines (NURBS), consider instead the use of a confocal microscope to obtain the 3-D voxel image of the shape.

 

Each voxel represents a volume element that can be considered as the fundamental building block of the shape and hence we automatically have a 3-D template for the hook.

 

Further, this 3-D voxel image can be converted into a .stl file using commercial software. This .stl file consists of a triangulated surface. Each triangle is made up of three (x,y,z) points and hence through triangulation the surface becomes defined in terms of a 3-D co-ordinate system. This new surface model is then scaleable.

 

And if each voxel image can be transformed to a surface model then the reverse must also be true. And so, once a hook has been studied through the two forms of tests described above and it has been established that it is, in fact, a “well designed hook”, it can be scaled to a size that renders it suitable for manufacturing from a suitable biomimetic composite.

 

Studying the substrate – a brief word

 

In his book Dr Andrew Parker describes how eyes or receptors of light of various wavelengths are the emitters of colour, through either reflection or emission. It should be noted that not all colours can be seen by man, for instance the budgerigar has two patches of ultra-violet emitting colour, one on each cheek, that are not visible to human eyes.

 

Now, in the place of colour, consider the substrate since a hook will interact with a substrate in order to achieve its evolutionary purpose, attachment. And there will be an ideal substrate that best suits the type of hook under consideration. For example in the case of burdock there should be an ideal relative hair thickness and density that best suits the hook and produces a maximum attachment force.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The mechanical design of hooks

 

The mechanical design of a hook uses well established engineering models with foundations in statics. There are fundamental design principles that relate cross-sectional area and other physical dimensions of the hook with its component material properties and the applied forces.

 

Figure 2 is a diagram taken from ASTM A668 that shows a typical, large load bearing hook with dominant geometric parameters indicated.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Prominent design parameters (related to the intended use of the hook) are:

 

  1. The degrees of freedom of the hook (does it swivel?)
  2. The material of manufacture and its properties
  3. Reduction in stress due to loading
  4. Reduction in damage to the hook itself
  5. The geometries of the hook such as cross-sectional area

 

B30.10 – 2000 Hooks is the relevant standard for the mechanical design of hooks.

 

The resolution of the stresses through the hook is a matter of relatively simple statics.

A complete analysis of the stresses through a hook would be a regurgitation from a second year Mechanics of Solids course and is trivial. Fenner [Error! Reference source not found.] gives a comprehensive analysis of structures, particularly chapters 5 and 6.

 

There is a great variation of hook designs currently available in the world, from prosthetics to crane hooks and many types of fasteners and attachment mechanisms in between. The best designs are all bespoke to the requirements of the application and the working environment. Designing a hook for a specific purpose using a biomimetic approach is like stepping into the evolutionary process by copying a design developed by nature to perform a similar task.

 

The stress model used to calculate stress in a hook under tension is simple:

 

Total stress = direct stress + stress due to bending

 

The direct stress is easy to calculate by hand and the bending stress the same, with some integration. But each calculation makes assumptions to simplify the model, particularly with respect to E, Young’s modulus, homogeneity and isotropy of material. It becomes more complicated when one considers the effects of composite material behaviour.


Probablistic Fasteners

 

The head arresting mechanism of the dragonfly has been studied by S N Gorb []. It is made up of two matching fields of flat-ish bristles or microtrichia that fit together and detach as the neck muscles of the dragonfly lift its head and replaces it in position during the course of everyday activities. This is thought to be because the neck of the dragonfly alone is not sufficiently strong to support the stresses of its activities, particularly eating in flight. The added support derived from the arrestor-mechanism is required as the dragonfly tears at the flesh of its prey.

 

The dragonfly head-arrestor mechanism is a probablistic fastener, as is burdock which is studied in Experiment 2.1.

The Operation of the Dragonfly Mechanism

 

The dragonfly, during its normal cycle of activities (flying, eating, mating etc) will detach and re-attach its head to its thorax in a manner that changes the head-thorax mechanism from weak to reinforced.

 

In his paper on the examination of this mechanism Gorb describes “the microtrichia-covered surfaces providing fixation due to high friction between the interlocking microstructures in the contact area” He also discusses this mechanism in his text “Attachment devices of insect cuticle” (which was referenced earlier in Section Error! Reference source not found..) An image is shown below (Figure 3) taken from this text, showing the 2 surfaces.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A figure from Gorb’s paper has been reproduced (Figure 4) and shows the different states of the attachment mechanism. In the figure the hatched blocks indicate when the attachment mechanism is engaged, the white blocks when it is disengaged. It can be seen that it is engaged when the dragonfly is eating, at rest and during mating in flight. It is disengaged in normal flight.

 

So, the head-arresting mechanism of the dragonfly is a multi-use, low strength friction joint of a field of structures.

 

 

 

 

A figure from the paper by Vincent and Mann that places biological attachment mechanisms in a “design space” is included below (see Error! Reference source not found. Figure 5 below).

 

 

 

Note that friction bonds are shown to be of high strength and low adaptability. This because in engineering systems, a friction weld is generally between 2 surfaces or edges and the separation of the surfaces irreparably destroys the joint.

 

To complete this description I have included two images below of two dragonfly specimens of the species Southern Hawker (Aeshna cyanea) that I collected in June 2003.

 

Figure 6 shows a specimen that was anaesthetised in a plastic container. In its struggle before succumbing to the ether fumes, the dragonfly continued flying, trying to escape. Hence at death its head was in the free-flight or detached position, resulting in the specimen having its head loose and sideways.  (see red arrow in the figure). If one looks closely one can see that the head is tilted sideways to the longitudinal axis of the body.

 

 

 

 

 

In comparison the second specimen was found dead on the stem of a vine two weeks later (see Figure 7 below). This specimen died naturally in a perched position with its head-arresting mechanism engaged as indicated by its strangely composed, prayer-like posture and with its head symmetrical about the longitudinal axis of the body.

 

 

 

 

It was my reading of Gorb’s paper on this dragonfly head arresting mechanism that drew me to collect these specimens. His book gave insight into the study of probabilistic fasteners and the parameters that were of importance during his study of the head-arrestor mechanism.

 

He counted hair density, length and thickness to be of importance to the effectiveness of the attachment. This is relevant to the future work that is discussed in the final sections of this report.


Section I I –  Case Study 1: A Study of Bird Claws

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The Two Dimensional Digitising of Biological Structures

Introduction

 

Experiment 1.1 (2-D digitising of bird claws) was inherited from my predecessor on this project. At that time the new biomimetics laboratory at Bath was not ready for occupation.

 

At the beginning of this project I inherited the following:

 

  1. A short write-up dealing with aspects of that student’s research.
  2. A collection of preserved specimens.
  3. An axioscope light microscope.
  4. Bespoke software “hookfit” for fitting a logarithmic curve through points (x,y).
  5. An Apple PowerMac with Nih Image software installed. Nih Image is a commercial software package used for 2 dimensional image analysis and manipulation.

 

I brought with me:

 

  1. A degree in mechanical engineering.
  2. Experience in a final year project on 3-D digitising and rapid prototyping.

 

Twenty years that had elapsed since I had had any formal study in the field of biology (1 A-level equivalent in 1982). This left me feeling the need to establish and understand the biology datum level required for the project study. It was important to me that I crossed over the barrier between the two disciplines, biology and engineering and that I understood why I was doing something in order to evoke enthusiasm.

 

Experiment 1.1 was conducted early in my research, before I correctly grasped the concept of functional ecology. The next sections include some background topics that I investigated whilst attempting to find out what it was that I was supposed to be doing. The Discussion (‎4.10) contextualises my results and proposes further research to develop a functional ecological hypothesis.

 

Systematic Biology and Finding a Function Through the Digitised Profile

 

For convenience I repeat the definition to be found in the glossary of the introductory section to this report:

 

Systematic Biology is the study of the organisation of biological information in a taxonomic or phylogenic manner.

 

I came across this term for the first time when considering an experiment that my predecessor started. He had done some work investigating the 2-dimensional digitising of hook profiles, asking an academic here at the University of Bath, Glen Mullineux, to write a program called “Hook-fit” that accepts a sequence of (x,y) co-ordinates and attempts to find a logarithmic function through them.

 

Experiment 1.1 presents the results of my investigations using 2-dimensional digitising. At the same time I was considering how finding a logarithmic function through the curve would be relevant to my research and engineering.

 

It was suggested that there might be some mechanical application for a law that would govern the design of a hook based on the fact that it’s curves formed part of the arc of a logarithmic spiral, but this failed to convince me that

 

  1. this was the correct application of functional ecology, and
  2. that there was much real practical use for such information.

 

Further, I had misgivings with regard to the technique of 2-dimensional digitising the claw profiles. This is discussed in Section ‎4.4 below.

 

The systematic biology paper “The Relative Success of Some Methods for Measuring and Describing the Shape of Complex Objects” [‎12]  by T McLellan and J A Endler describes their consideration of 2-dimensional leaf shapes and their attempt to find a correlation between nodes that labelled prominent, repeated features of different of leaves of similar species.

 

The authors concluded their paper by admitting that they had met with limited success in finding a useful correlation that could be used in classifying their leaves according to their nodes.

 

The paper provided me with reasons to conclude that the search for a function through the profile points fell into the realm of systematics. I concede that it may be true that finding a group of “like” functions that applied to functional groups of claws may provide information of taxonomic value and mathematical interest. However, even if this fact proved to be true, there would be limited application for such an approach to the field of engineering.

 

Cladistics

 

In his book on insect attachment mechanisms S N Gorb devoted a section to insect tarsii, providing a breakdown of the tarsi structures of various organisms, in particular, the number of claws or hooks per tarsus, which are generally used for gripping the irregularities of a surface (anchorage). This form of study is useful for developing a taxonomic understanding of the evolution of the insect system. It is termed cladistics [‎13] and grouping the insects in this way provides an indicator of their evolutionary development. However it would seem to be of little importance to the field of engineering.

 

The Digitising of a Tiger’s Claw

 

In the paper by Mattheuk and ReussThe Claw of the Tiger: An Assessment of its Mechanical Shape Optimisation” [‎14] they came to two conclusions:

 

  • the upper and lower curves of the silhouette of a tiger’s claw could be fitted to sections of the curve of a logarithmic spiral.
  • by exporting this silhouette to an FEA package and applying finite element analysis to the 2-dimensional silhouette of the claw they concluded that the tiger claw has an optimum shape with no excess, non-load bearing material.

 

Since the finite element analysis was carried out on a longitudinal section of the claw without reference to the axial section varying throughout the length of the claw, it appeared to me that the results regarding material shape optimisation, while perhaps correct, are inconclusively substantiated.

 

I visited the Science Museum in London recently and while looking at the huge variety of stuffed birds there, it struck me that there was a large variation in claw cross-sections. Large ground-living birds have claws that are triangular in section with the point at the apex and a flat, highly-stressed bottom face. Other birds had graceful scimitar-like claws with an ovoid cross-section. I suggest that these different forms relate to the functions that they are required to perform, such as scratching at and running on the ground and defence in the case of the ground-living birds, while the grasping of branches was the function of the scimitar claws.

 

My final year project was in 3-D digitising and my undergraduate training in mechanical engineering included 3-D finite element analysis using ANSYS. This affected my approach to Experiment 1.1. It did not seem satisfactory to persist with two dimensional digitising when there were possibilities for capturing the three dimensional data so that that an eventual 3-D FEA analysis could be made. I have since revised that opinion somewhat and this is discussed further in the experiment discussion, ‎4.10.

 

After referring to the paper on the confocal microscopy of a monkey’s tooth by Sanson et-al, I moved on to an attempt to image a selection of specimens using the confocal microscope in the Biology laboratory (see Experiment 2.1). Sanson et-al’s paper described a method of casting and moulding the jawbone of a small bat in a resin with a suspension of fluorescent material. I am certain that the same technique could be used for bird claws as they are of the same order of magnitude in size. This could be used to research shape optimisation further, or, in the purist application of biomimetics, to record the exact shape of a small (~100 micron) sized biological structure.

 

Experiment 1.1 : Bird Claw Profiles

Aim

 

To experiment with the software package Nih Image

To use Nih Image to record profiles of bird claws.

 

Apparatus

 

Axioscope microscope

Powermac pc with installed Nih Image software

 

Method

 

The step-by-step method of finding the profile of a claw using Nih image is described in the APPENDIX 1. The resulting data points were exported to Microsoft Excel and a simple 2-D plot was produced.

 

My specimens were scavenged from the carcasses of birds found in the vicinity of the university. The whole claws were separated just below the feather level on the bird’s legs.

 

It was decided to image the corresponding first toe-claws of each specimen. The claws were too large to be placed on a microscope slide and instead they were placed by hand directly beneath the microscope objective.

 

The image was captured in the Powermac, and put through thresholding to separate the claw shape from background noise. This silhouette was then digitised manually moving the screen cursor over the image and selecting points.

Results

Robin Claw

 

Thrush Claw

 

Discussion

 

The moment I began positioning the claws under the microscope I became aware that there was an opportunity for the introduction of error; the possibility that the hook shape would twist as it curved or begin to spiral, thereby introducing a z-co-ordinate.

 

This disturbed my commitment to the experiment and led me to explore other methods of capturing the three dimensional shape of a hook (and many of the examples I was seeing, reading and hearing about were small, less than 5 millimetres in size going down to hundreds of microns). This led to Experiment 2.1.

 

In the last two years I have been doing some reading on biological topics. This has altered my perception as to the results of the experiment. This has happened as the functional ecology aspect came alive for me. It is only recently that I have felt confident enough in the subject to continue this discussion as follows.

 

The thrush and the robin are 2 common birds of the English countryside songbirds. They live in the same environments and have similar habits – they are not ground-dwelling although they land to forage for food. They have similar body morphologies and they land in trees i.e. they use their feet for grasping onto branches and they also “flatten out” their feet when they land the ground.

 

From Figure 48 and Figure 49, it can be seen from comparing the overall dimensional span of the claws, that is, the length and amplitude of the curves, that they are dimensionally similar. In other words, the thrush claw is approximately twice the size of the robin’s claw.

 

The obvious reason for this is because the thrush is a bigger bird than the robin and the thrush’s foot is scaled up to accommodate this.

 

But from a functional ecology perspective, we must consider the system in which the claw exists and functions. This system includes the whole foot of the bird with toes and muscles and the substrate (twig/branch) that the foot grasps. The claw operates in conjunction with these to perform its grasping function.

 

Therefore, with regard to the two specimens, we have the design for two grippers of different sizes, for the purpose of carrying two different loads. And because the robin’s foot is smaller than that of the thrush it seems reasonable to hypothesise that each foot is ideally suited for grasping twigs of different diameters, that correspond to some minimum strength in order to support the mass of the bird.

 

Conclusion

 

The 2-dimensional digitising of the robin’s claw is only one part of a study of the functional ecological system of a bird’s claw. It would be necessary to study the full system within which the claw operates, from the dimensions of the complete foot to the dimensions of typical branches that it would grasp, in order to prove a hypothesis.

 

Such a hypothesis would take this form:

 

“There is an optimum claw/foot relationship for holding branches of a certain diameter, or a range of diameters”

 

This would have a robotics application with regard to the design of micro-manipulators.

 

This is discussed further in the conclusions of this report: Further work.


References

Bibliography

 

  1. “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
  2. “Structural biomaterials”, J F V Vincent, Macmillan Press Ltd, ISBN 0-333-26125
  3. “Plant Physiology”, Fourth Edition, Devlin and Witham, ISBN 0-87150-765-X

 


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