A Biomimetic Study of Long Shaft Cellulose Hooks after Arctium minus (Burdock) Part III

Bruce Saunders

Abstract

Keywords:

1  Introduction

It is necessary to consolidate information before proceeding with the design. 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 []. A. minus is supposed to be the biological inspiration behind Velcro [] and it is interesting to compare their relative functionalities. It will become apparent that functionally, the Velcro hook resembles that of C. lutetiana more than it resembles the hook of A. minus. This shall lead to product description based upon long-shaft cellulose hooks and the opening elements of the design process for a product closely based upon the shape, functionality and material of these hooks.

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. By definition from Nachtigall [] a probablistic fastener is a random hooking mechanism that 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 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 [] his model specifically includes the interaction of neighbouring elements as contributing directly and not indirectly, to the attachment. All the hooks of the five species in this paper are a part 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 serves to arithmetically increase the overall attachment of the fruit to the host.

Further, it is stated by Gorb [] 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.

2  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 [] 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 [], a hollow base. The other two species derive from the surface of the mericarp.

Of the other species, A. minus  and G. urbanum, their hooks originate from the bract and carpel of the fruit and exhibit respectively 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 space charts of biological hook design criteria for cellulose hooks:

High Strength

Low Strength

Trichome                                               Sepal

Structure

High Strength

Low Strength

Small                                                      Large

Size

High Strength

Low Strength

Fixed base                             Single                                     Multiple

Degrees of Freedom

High Strength

Low Strength

Low                                                                        High

Elastic Modulus

All of these are based upon hooks made of cellulose. Introducing materials suitable for manufacture with their own properties will produce different relationships.

3  Functionality

3.1   Plant hooks

The following is compiled from both the research of Parts I and II and from the papers of Gorb et al [] [].

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 and less developed.

3.2   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 which 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

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.

4.1   Shape

‎Figure 1 shows the burdock hook shape that shall be used in the design. It shall be taken as prescribed. This image is repeated from Part I. This shape shall be central to the full design.

• 3-d reconstruction from SolidWorks of a burdock hook and shaft

4.2   Functionality and structural description

4.2.1    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.

4.3   Shaft

The structure of the burdock hook indicates shows that the shaft 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 Section ‎4.2.3 below.

A flexible base could be produced by mimicking the hook of the G. aperine fruit. This would rely upon introducing a variable material thickness in the shaft to allow buckling in different directions.

A solid inflexible base is the third possibility and will produce increased strength and directionality, perhaps at the cost of efficiency of attachment.

4.3.1    Substrate

The substrate shall be defined by testing for suitability and attachment strength and shall be dependent upon the finished size, shape and material of the hook. The natural substrate for cellulose hooks is fibrous. Similarly this could be replicated for a product but this is not a necessity. It will depend upon the selected material and the abilities and application of the finished design.

For instance, in considering biomedical applications such as sutures it would seem that a barbed spike is a better solution for piercing flesh than a piercing hook but this may not necessarily be the case since the success of such an implement must depend upon the amount of trauma induced, the recovery and the behaviour in situ post recovery. These effects cannot be assumed.

4.3.2    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, a hook with supporting “bract”, 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.

In fact modularising the hooks appears to offer many permutations which eventually will have to be modified during the process of material selection and manufacturing process selection and refined by application.

4.3.3    Scaling Effects

The ability to reproduce scaling effects shall be constrained by the mode of manufacture and material selection. It is clear that scaling effects are maximized when a material or structure is acting at its physical limits as occurs in optimized and very small structures. Since a burdock hook is made of cellulose, scaling effects combine with material properties to produce the resultant effect. It follows therefore that an artificial material, stronger than cellulose, will demonstrate reduced scaling effects.

4.4   Product Development

The image overleaf shows the result of extending the digitized burdock hook through a lofted feature into a flange similar to the flattened bract from which the natural bract originates. This image represents a modular hook from which the product design can be developed.