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Home » Biomimetics » 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

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

 

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