Appendix 4 – Studies of Attachment Mechanisms and Probablistic Fasteners in Nature

Summary

This appendix is concerned with plant and insect attachment mechanisms and their testing. Papers by Gorb et al describe the testing and assessment of plant hooks from five species and the development of a study/design procedure for miniature attachment devices. There is an assessment of the attachment mechanisms in nature and their insertion into the design space for engineered hooks and thereafter papers on insect tarsal/plant surface interactions.

Table of Contents

1Introduction

This appendix contains the detailed description of eight papers, all of direct relevance to the work in the main body of the report.

2 to 6 contain a review of papers from S N Gorb et al concerning the study of hooked and parabolic fasteners and the development of and design methodology for biological fasteners.

Section 7 contains reference to a paper by Vincent and Mann, an overview of the concept of transferring biological information to the engineering sphere including specifically the design space of attachment mechanisms.

Sections 89 describe studies of insect tarsi performance and insect tarsi/surface interaction and their parameters.

It is principally those problems that engineering has yet to overcome for which biologically inspired solutions are of the greatest interest to engineers. In engineering today manufacturing and design challenges are miniaturization and MEMS. Since so many biological systems function at a molecular level and many biological structures are of a size that is impossible for mankind, as yet, to manufacture, this area provokes a lot of interest.

The paper by Vincent and Mann includes reference to TRIZ, a Russian design algorithm/patent database that provides a framework for systematically mapping all solutions to a centre of design knowledge. It also is an indicator for invention optimization, the second opportunity for generalized biologically inspired solutions to provide inspirations.

2“Contact Separation Force of the Fruit Burrs in Four Plant Species Adapted to Dispersal by Mechanical Interlocking”, (2002) E Gorb, S Gorb [1]

2.1Description

The fruit of four plant species (Agrimonia eupatoria, Circaea lutetiana, Galium aparine and Geum urbanum), all of which support burrs as a structure for interlocking attachment to animals (a property termed Zoochory), were studied and the separation forces of each type of burr was measured and compared. The dispersal by animal fur and feathers is known as epizoochory.

These detachment values were then related to physical dimensions that could be compared in the structure of the burrs. In other words, morphological variance of the burrs was examined and estimated (burr length and burr diameter at the basal part, see Figure 1) and the dependence of the force on the size and morphology of the burrs was examined for each species and then compared between species. The number of burrs to hold the fruit in place was counted and compared as well.

Three questions were asked:

1. Does the contact separation force differ between the species studied?

2. Which morphological variables of the burrs influence this force?

3. Are there some scale effects on the number of burrs per fruit, the force of the single burr and the total force of all burrs?

2.2Materials and methods

The burr morphologies are all noted in detail in the paper. The process of force application is described as well as the nature of the fracture. Variables used to describe the hooks are as per Figure 1 below:

Figure 1 – Scheme of morphological burr variables from Gorb et al [1]

Figure 2 – SEM’s of fruits and burrs of G. aparine and G. urbanum from Gorb et al [1]

Figure 2 above shows the fine detail of the surfaces of each burr as has been described in the text for each of the burr species. Such close examination is necessary in order to note microscopic structures that might supply additional anchorage to the burr.

Figure 3 – Graphs of results of tests from Gorb et al [1]

With reference to Figure 3, the top graph is the separation force of a single burr relative to fruit weight. The second graph shows the interrelationship between the minimal number of burrs to hold the fruit in place, the separation force of a single burr and the fruit weight. The final graph shows the summation of the force of all the burrs covering the fruit versus the fruit weight. Figure 4 below shows the contact separation force for each of the species of burrs.

Figure 4 – The contact separation of the burrs from Gorb et al [1]

Figure 4 above shows the actual distance moved by the lower test platform. This test was copied in the laboratory (see experiment 3 in the main body of this report) using an Instron tensile testing machine. The second shows the mean values and standard deviations of the contact separation force values.

Consideration of Figure 5 would seem to show that tests A, B and C all were conducted using hooks in situ on the supporting fruit. In D this is not so clear.

Figure 5 – Video sequences of burr separation for each of the four species from Gorb et al [1]

Figure 5 above shows hooks from each of the four types of plant being tested. Note the loop of the micro-force tester beneath each of the hooks (as per the schematic diagram in Figure 6 below) and the horizontal dark lines on each if the images that indicates the level of the hook at commencement of the test.

2.3Force measurements

Figure 6 – Micro-force Tester as used from Gorb et al [1]

In Figure 6 the components of the micro-force tester are an upper platform (P) to which the sample is glued, a steel wire loop (LP), a glass spring (G). FOS is a fibre optic sensor that detects deflections in the spring via the mirror (M).

The force tester was a Tetra Gmbh manufactured by Ilmenau, Germany.

2.4Data analysis

In the data analysis, the Kruskal-Wallis test of one-way ANOVA on ranks was used followed by Dunn’s method of pairwise multiple comparison between series (SigmaStat 2.0 for Windows)[3]. To calculate dependence between different morphological burr variables measured, linear and exponential regressions were applied. The ANOVA statistic (F) was estimated for the regressions. The F-test statistic gauges the contribution of the independent variable in predicting the dependent variable. It is the ratio between the regression variation from the dependent variable mean and the residual variation about the regression line.

The P-value is the probability of being wrong in concluding that there is an association between the dependent and independent variables. The smaller the P-value, the greater the probability that there is an association between the dependent and independent variables. It was concluded in this paper that P<0.05 could be used to predict the dependent variable from the independent variable.

The paper concludes with asserting that the separation force depends primarily on the span of the diameter of the hook.

2.5Further papers of interest

These are papers have not been read by the author as of yet are on order.

1. “Biological microtribology: anisotropy in frictional forces of orthopteran attachment pads reflects the ultra-structure of a highly deformable material”, S Gorb, M Scherge, Procedures of the Royal Society of London. B 267 (2000) 1239-1244

2. “A study of adhesive seed dispersal of three species under natural conditions”, K Kiviniemi, Acta Botany, Neerl. 45 (1996) 73-83

3. “Plant dispersal by Hares (Lepus capensis) in Kenya”, Ecology 58 (1977) 681-686.

4. “Seed production and predispersal predation in the biennial composite species Arctium minus” (Hill) Bernh. And A. lappa L. Oecol. 34 (1978) 283-295

5. “Ecology of Seed Dispersal”, Annual Review of Ecological Systems. 13 (1982) 201-228

3“Natural hook-and-loop fasteners: Anatomy, Mechanical Properties and Attachment Force of the Jointed Hooks of the Galium aparine Fruit”, (2002) E V Gorb, V L Popov, S N Gorb [2]

3.1Description

This is a study of the jointed hook of Galium aparine, this form of jointed hook not being found elsewhere in nature. The hook is described to exist in two parts, a hooked cone and joint-like base. The joint is actually a zone of “hollowness” at the base which allows the hook to flex. Force testing is carried out using a micro-force tester and, using a mathematical model describing hook geometry, it is found that hooks with and without a base had different elastic moduli. Further experimentation showed that hooks with joints are better able to adapt to forces in different directions, in other words the bent more easily and resisted damage due to the hinge at the base of the shaft. Semi-thin sections were embedded in resin and stained with safranin and fast green, showing that the hook walls contain cellulose and lignin.

Artificial hooks (N3 Original Velcro Hook-Band and Velcro Fastening Systems) were tested for comparison. They are described as being “rather large, solid and lacking joints”.

3.2Materials and methods

The fruit and hooks are briefly described in the paper, but in detail.

3.3Microscopy and morphometry

A combination of light and scanning electron microscopy was used. There is detailed description of the methods of fixing the specimens for examination. A 3-D model was obtained of the fruit using digital images of longitudinal and cross sections. Wall thickness was measured by cross-sectioning at different levels and using light microscopy to digitize the images. The previous paper was used to supply the data for contact separation forces (see Figure 7 below).

Figure 7 – Contact separation forces (hooks have high variability in shaft length) from Gorb et al [2]

3.4Force measurements

The same force tester used in the previous paper was used here. There is a description of how to derive the material properties using the same force tester. This consisted of applying a transverse force slowly to the specimen, in the region where the specimen begins to curve to form the hook (see Figure 11). The shaft is deflected by the transverse loading. The loading head is then halted and held in place. Over time the loading on the shaft decreases indicating the material exhibits visco-elastic properties because the elastic force relaxed over time.

The elastic modulus was calculated during the approaching process by modeling the hook as a tapered shaft and measuring the displacement with reference to the applied force to yield E for the material (see 3.6).

An experiment was conducted by creating a false joint to see how it affected the result. The results can be seen in Figure 8 and Figure 9. It was concluded that

“…joints provide a higher chance of initial interlocking of fruits. Even if only the apical part of the hook is attached, an initial interaction force may lead to proper interlocking.” Further, this joint effect is simulated in nature by hooks not found on the side of the fruit facing the contact surface because the flexible base allows other hooks to become engaged and contribute to the attachment. It is stated that this joint effect is unknown in industrial hook-and-loop fasteners.

It does not suggest an explanation for the reduction in contact separation force for the artificially jointed hooks compared to those that had been glued to the test support.

Figure 8 – Testing for elastic modulus from Gorb et al [2]

Figure 9 – Multi-directional tests and with tests with artificial basal joint from Gorb et al [2]

Figure 10 shows an SEM, a drawing and the product of the sectioning of the hook, digitized and reproduced in a computer graphics package. Figure 11 shows the equation derivation for the hook displacement as a function of the applied force, from which Young’s modulus is calculated from the experiments illustrated in Figure 9. The bending moment equation is applied considering the shaft of the hook to be a cone with walls inclined at a constant angle  to the vertical with wall thickness h, shaft length L, deflection y measured and force F being the applied transverse force (see Equation 7 in Figure 11 – The calculation of the displacement of a hook at the point of the force application as a function of the applied force (F) from Gorb et al [Error: Reference source not found]).

Figure 10 – A specimen hook from Gorb et al [2]

Figure 11 – The calculation of the displacement of a hook at the point of the force application as a function of the applied force (F) from Gorb et al [2]

3.5Data analysis

As in the previous paper Kruskal-Wallis one-way ANOVA on ranks was used with P<0.001 and Dunn’s Method of pairwise multiple comparison (see [3].

3.6The calculation of the displacement of a hook

Here follows the calculation of the displacement of a hook at the point of the application as a function of the applied force (F) as it appears in Gorb, with some additional explanatory notes. This was used for the determination of Young’s modulus of the hook (that is, the shaft of the hook to the point where it begins to curve see Figure 8 to see the point of force application in the diagram). The hook is considered as a beam with a changing cross-section similar to a tapered shaft, with point of the shaft bent over into a hook. The equation of a beam from the base to the point of initial curvature reads

M – EI 

whereis the force moment

E is the Young’s modulus of the material

I is the moment of inertia of the beam cross-section

 is the beam curvature

For small deflections

M = F(L-x) (2)

Where L is the length of the beam, and x is the co-ordinate of a current point of the beam measured from a solid support. For the curvature we have:

 = d²y/dx² (3)

where y is the transversal deflection of the beam at the point x.

3.7Further papers of interest

These papers have not been read by the author as of yet and some of them are on order.

1. “Seed Dispersal by Adhesion” Sorenson, A.E., Annual Review of ecology and Systematics, 17, pp. 443-463, 1986

2. “Fruits: morphology, ecology, practical significance” Levina, R.E., Privolzhskoje knizhnoje izdatelstvo: Saratov, 1967

3. “Plant biomechanics: an engineering approach to plant form and function”, The University of Chicago Press: Chicago and London, 1992

4“Miniature Attachment Systems: Exploring Biological Design Principles” S N Gorb [4]

4.1Description

This paper does not contain any experimental work. It is a descriptive summation of previous work and much of it appears in Gorb’s book “Attachment devices of Insect cuticle” [5] (see Appendix 1). The paper gives an overview of the functional design of attachment devices occurring in insects and how nature’s design may be used as a basis for biomimetics in various technological areas.

It presents a case for exploring biological attachment mechanisms to solve some of the problems of miniaturization. Gorb says:

“There are three main areas, in which nature’s solutions of attachment mechanisms may be applied: (1) precise mechanics, (2) gluing and joining technology, and (3) material science of surface-active composite materials.”

In particular he advocates nature’s use of surface patterns that form friction-based probabilistic fasteners that “provide precise reversible coupling surfaces with a minimum expenditure of force”. For prototyping micro-scale surface patterns the engineering approach is to use low viscosity wax to produce surface casts and copy the surface profiles using existing techniques. But first it requires a biologist’s knowledge of systems and a material scientist’s techniques to measure their properties.

“An engineering approach is to copy the surface profile using available techniques”.

4.2Biological attachment systems

Figure 12 – Attachment microstructures of insect body from Gorb [4]

Figure 12 above shows the eight fundamental classes of attachment principles, and below:

1. hooks

2. lock or snap

3. clamp

4. spacer

5. sucker

6. expansion anchor

7. glue

8. friction

In nature, studying with a reverse engineering analysis, it is recognized that different combinations of these can exist in any one attachment mechanism.

Living creatures possess specialized surfaces enabling the minimization of contact forces (anti-friction systems) or their maximization (friction systems) (see).

In all systems friction is required to overcome friction. Optimization consists of minimizing friction at one end of the system while maximizing it at the other, for instance low friction in joints but high friction between surfaces and contact with the limbs in locomotion.

In biology, contact pairs of surfaces are considered. They may be

1. anti-friction, or

2. friction pairs.

Anti-friction surfaces are always pre-defined pairs of surfaces. Such systems have merit for study in the field of tribology, that is, the study of friction, wear and lubrication.

Friction surfaces may deal with predefined surfaces known as probabilistic fasteners such as wing-locking devices or head-arresting systems.

Alternatively, a friction system may have one surface which is unpredictable such as between the feet of and organism and the variety of surfaces that exist. Insect attachment pads are represented by two designs, hairy and smooth.

These two types of friction devices represent two main working principles of frictional devices; mechanical interlocking and maximization of surface area.

The paper also says the following, which is important when considering the mimicking of a biological attachment mechanism:

“Since biological surfaces are a part of the physical world, most of the friction and adhesion phenomena in biomechanical systems can be explained by mechanical interlocking and/or area of contact between surfaces, independent of the basic physical forces involved in the particular attachment mechanism. This indicates that the geometry of the surface, load forces at which the system operates, and mechanical properties of material will play essential roles in the design of the actual system. In addition, chemistry of surfaces, the presence and nature of secretory fluids additionally mediate surface forces. Since friction and adhesion are very complex physical phenomena, the biggest challenge in studying them in biological systems is to collect maximum information about gross morphology, ultrastructure, chemistry, and mechanics of surfaces to explain the functional principles of particular attachment systems.” (see Figure 13)

Figure 13 – Functional significance and Working Principles of Contacting Surfaces from Gorb [4]

Figure 14 shows the nature of the study of attachment mechanisms. For application to MEM technology, Gorb says that nature is full of micro-scale surface patterns which have yet to be studied. Continental® tyres is cited as a biomimetic example since it has developed a “honey-comb” tread.

Figure 14 – Interdisciplinary character of studies of bilogical attachment mechanisms from Gorb [4]

When considering designing from natural systems, the paper suggest that the material currently most appropriate for mimicking the range of properties of biomaterials is polyurethane foam because local foaming presents an opportunity for varying material properties in the same piece of material. It says that this suggests that polyurethane foams can be used to mimic biological attachment devices with visco-elastic properties.

Figure 15 – Dental wax method for surface replicas from Gorb [4]

With reference to Figure 15 above, it shows different patterns that can be copied by taking simple casts. A two-part silicon wax is poured over the surface and an impression is taken. This impression can then be filled with “Spurr’s resin” or another low viscosity resin which becomes relatively stiff and can be removed from the negative without damage.

Figure 16 – Anti-attachment plant substrata from Gorb [4]

This form of casting is viewed as the first step towards studying a biological surface, studying the surface alone, without the influence of other biological properties. This has application in the field of pest control. Figure 16 – Anti-attachment plant substrata from Gorb [Error: Reference source not found] shows the variation of insect attachment to plant surfaces. Gorb says:

“Knowledge about the structural properties of insect leg attachment devices and plant surfaces together with experimental data on attachment devices and plant surfaces together with experimental data on attachment abilities of insect pests on a variety of structured substrata might be useful for pest control. Directional changes of plant sorts, using genetic technology or a selective process by man, may result in plant surfaces preventing or reducing attachment of particular insect pests.”

This is an important comment. It would appear that there are other possibilities for imaging and studying the relationship between insect tarsi and leaf surfaces and this is discussed in Experiment 3 in the main body of the report.

4.3Further papers of interest

These papers have been read by the author as of yet. Some of them are on order.

These papers have not been read by the author as of yet. Some are on order.

1. “Microtribology of biological materials” Scherge, M. & Gorb, S.N., Tribology letters, 8, pp. 1-7, 2000

2. “Using biological principles to design MEMS” Scherge, M & Gorb, S N., Journal of Micromechanics and Microengineering, 10, pp. 359-364, 2000

3. “Biological micro- and nanotribology” Scherge, M & Gorb, S N., Springer: Berlin et al., 2001

4. “Biological microtribology: anisotropy in frictional surfaces of orthopteran attachment pads reflects the ultrastructure of a highly deformable material” Proceedings of the Royal Society of London B, 267, pp. 1239-1244, 2000

5“Probabilistic Fasteners with Parabolic Elements: Biological System, Artificial Model and Theoretical Considerations” S N Gorb, V L Popov [6]

5.1Description

This paper is based upon [4], “Miniature Attachment Systems: Exploring Biological Design Principles” S N Gorb, Design and Nature, 2002, following a design path described there from the biologist’s identification of the structure to the material scientist’s assessment of properties of the materials and the properties of the mechanism, and then onwards to the mathematical modeling of the behaviour.

Gorb asserts in the previous paper [4] that as one considers smaller and smaller attachment mechanisms, hooks disappear from the mechanisms and it is parabolic fasteners that become the structures that form the mechanical interlock.

This paper deals only with such parabolic fasteners. There is description of the fastener structures with regards to the properties and structures of insect cuticle. The attachment mechanism is then modeled mathematically and subjected to mechanical testing using a plastic imitation produced from resin moulds.

There is a final discussion of the relative merits of hook-and-loop fasteners such as Velcro to parabolic probabilistic fasteners.

Figure 17 – velcro, from [7] Figure 18 – SEM of burdock hook, Saunders 2002

5.2The work of the biologist – identifying the structure

The paper defines probabilistic fasteners as having surfaces with outgrowths that do not correspond exactly to each other and the interlocking takes place without precise positioning of both surfaces. Probabilistic fasteners, it says, demonstrate high frictional forces when the surfaces come into contact. Attachment is based on the use of the surface profile and the mechanical properties of the materials, and is fast, precise and reversible.

The paper says that these types of attachment occur mostly in arthropods, such as head arresting mechanisms in dragonflies (discussed in the next paper) and the elements that lock the elytra of beetles together.

Examples of arthropods with elytra locking mechanisms that are probabilistic fasteners meriting study and presented in the text are:

Hymenoptera (wasps, bees, ants), Heteroptera (bugs), Coleoptera (beetles), Dermaptera (earwigs), Diptera (flies) and some Lepidoptera that have developed a mechanism for attaching their wings to their bodies when at rest. There are co-opted fields of cuticular outgrowths present on two separate parts of the body. They differ in shape, density and directionality (see Appendix 1).

For wing fixation when not in flight, the beetle wing locking system contains five surfaces covered by outgrowths and eight on the wings. The location of the surfaces and the directionality of the outgrowths prevents movement of the wings in different directions.

Figure 19 – The left column of images is the corresponding protruberances of the elytra of a tenebrionid beetle. The right column of images is the opposing protruberances of the dragonfly head arresting mechanism from Gorb et al [4]. Note that single elements of this structure or 0.5 – 50 m in length.

The head arrestor mechanism of the dragonfly immobilizes the head during feeding or when the dragonfly is in tandem flight. The fields of outgrowths are on the rear surfaces of the head and neck.

Figure 20 shows different types of modified outgrowths that have been identified in functionally corresponding fields.

Figure 20 – Different outgrowths that have been identified in head arrestor mechanisms from Gorb et al 4]

5.3Force testing the structure

Because of the nature and size of the biological structures, an artificial plastic model was used. It consists of two surfaces covered by process of different lengths and size.

The study was undertaken to combine experimental data of force measurements, obtained on a large scale model system, and theoretical considerations based on the simple model of behaviour of probabilistic fasteners with parabolic elements.

The parabolic elements were modeled on those appearing in with different geometric proportions and different materials with different frictional properties to see how they would affect the loading-attachment behaviour of the system (see Figure 21).

Figure 21 – The set-up for force measurement showing the load cell which moves only in a vertical direction, i.e. down to measure the engagement force of the surfaces and upwards to measure the force to disengage the elements from Gorb et al [4]

The elements were tested in a dry state and when wet with water and then oil. The load force was defined as the force to push the surfaces together and the attachment force as the force to separate them.

Figure 22 shows the geometry of the teeth. The profile was modeled as a simple quadratic and later, the elastic deformation of the plastic teeth in a horizontal direction due to the interaction is modeled as linear (see Figure 23, where F_el is the lateral deforming force). The dimension D is the distance between the two teeth at the point of interaction.

5.4An analytical model for a parabolic probabilistic fastener

Figure 22 – The geometry and dimensions used in the analysis below from Gorb et al [6]

The mathematical model presented in the paper is repeated here as Figure 22 and Figure 23, for reference with only some additional explanatory comments added.

1. Geometric Relationships

From Figure 22, using ordinary Cartesian Co-ordinates and from the simple geometries of the system, the following is derived. R₁ and R₂ are the tip radii for the lower and upper element respectively.

Let y₁(x) = h₁ – x²/2R₁ (lower element), (1)

And y₂(x) = H – h₂ + (x – D)²/2R₂ (upper element) (2)

Where D is the horizontal distance between teeth at any time and can be expressed as the sum of the initial distance plus the displacement d due to their interaction:

D = D₀ + d (3)

And considering the point of contact as being denoted by y₁ = y₂

Then from (1), (2) and (3)

y₁ = y₂ = h₁ – x²/2R₁ = H – h₂ + (x – D)²/2R₂ (4)

Which gives: –x/R₁ = (x – D)/R₂ (5)

and x, the point of contact can be obtained as;

x = D*R₁/(R₁ + R₂) (6)

(4) and (6) combined give:

h₁ + h₂ – H = ½ D²(R₁ + R₂) (7)

Now denote

h₁ + h₂ = H₀ (8)

R₁ + R₂ = R₀ (9)

From (6 and (7):

D = sqrt(2R₀(H₀ – H) (10)

X = R₁*sqrt(2(H₀ – H)/R₀) (11)

And note from the geometry of the system

Tanx/R₁ = sqrt((2*H₀ – H)/R₀) (12)

The paper proceeds with the analysis, producing an expression for the attachment and detachment forces in terms of the loading force applied by the load cell, the friction coefficient  and the angle of contact .

2. Modelling of Loading Force

Figure 23 – A free body diagram of the forces at the contact surfaces and their components from Gorb et al [6]

For loading, the force is pushing the teeth together. So four forces act upon the element under loading:

F₁ the vertical force generated by the applied load

F_el a horizontal force occurring because of elastic displacement of the tooth

F_n the normal component of the interaction between the teeth

F_f the friction force (tangential force) between the teeth

Consider the left diagram of Figure 23. In equilibrium conditions the sum of the forces in the horizontal and vertical directions is zero.

F₁ = F_f sin + F_n cos 

F_el = F_n sin – F_f cos 

The friction force F_f can be written as

F_f = F_n where  is the coefficient of friction. (15)

Considering the deformation of the elements and assuming linear elasticity:

F_el = _d₁ = ₂d₂ (16)

Where d₁ and d₂ are the horizontal components of the teeth, and ₁ and ₂ are their elastic coefficients. The whole relative displacement of both teeth d₁ and d₂ is

d = (1/₁ + 1/₂)F_el (17)

Now denoting

(1/₁ + 1/₂)^-1 =  (18)

then

F_el = d (19)

Now, from (13), (14, (15), (19)

F₁ = F_n(sin + cos) the loading/attachment force (20)

F_el = d =F_n(sin – cos) the elastic deformation force (21)

3. Modeling of Detachment Force

Consider now the right hand drawing in Figure 23. Note that due to the change in direction the freebody diagram has changed where the friction force and the applied force have reversed directions. In equilibrium conditions:

F_A = F_f^*sin – F_n^*cos (22)

F_el = F_n^*cos + F_f^*sin (23)

Where F_A is the maximum adhesion force (or detachment force).

From (15) and (19) it follows that

F_A = F_f^*(sin – cos (24)

d = F_n^*(cos + sin) (25)

4. There is a further relation, the interrelation between loading and detachment forces. Normal and frictional forces will be different during the compression and detachment phases but the geometries (including  and F_el (the force related to the elastic deformation of the teeth) will be the same.

Then combining (20), (21), (24) and (25) the relationship between the applied compressive force and the resulting attachment force is:

F_A = F₁(sin – cos sin – cos)/(coscossin + cos)

= F_l(tan – tan – )/(stan + tan + ) (26)

F_A = Force of attachment

F_l = Force of compression

The paper continues with a calculation for the relationship between the attachment force and the load force.

This case applies for a case of ideal, cone-shaped teeth.

For parabolic teeth, the angle depends on the applied compressive force and the equation (26) determines implicitly the dependence of the detachment force on the applied compressive force.

Considering the relations (3) (7) (10) (12) (20) (21) this relationship will be

(tan – D₀/R₀)(tan + 1) = F_L/R₀(tan – ) (27)

This equation determines the dependence of tan on the applied force F_L.

Denoting

F = F_L/R₀, and (28)

 = D₀/R₀ (29)

equation (27) can be written as follows:

tan = [sqrt{(1 + d – f)² + 4fm(d – )} – (1 –  – f)]/2 (30)

Minimum loading force resulting in a positive adhesion can be determined from the condition,

tan = 1 (31)

from (24) where we set F_A = 0

Solving equations andwe obtain

f_min = [2(1 – ^^ 

or, taking into account definition (28)

F_L,min = R0[2*(1 – ^^ 

The characteristic scale of the attachment force is R₀.

Figure 24 – Graph of model results for attachment force on the load force from Gorb et al [6]

5.5Conclusions

This paper needs to be regarded as illustrating a design methodology for extracting biological information, modeling and testing.

There are salient points to be highlighted;

• There is always a critical compressive force required to interlock frictional fasteners.

• After overcoming this critical value the attachment force increases with loading force.

• The attachment force is of the same order of magnitude as the elastic force needed to deflect the fastener elastically in the horizontal direction by a distance equal to the diameter of the teeth tip.

• The dependence of the loading force on the detachment force is sensitive to the form of the teeth.

• The model does not take into account teeth density.

• It is asserted that in biological systems, the longer and wider the teeth, the less densely they are distributed. Further, in biological systems the larger the body mass the lower the density of teeth. It is suggested that a study that investigates the relationship between tooth density, absolute size and periodicity of teeth of both contacting sheets would be of interest.

There are two commercial forms of probabilistic fasteners currently marketed:

1. Velcro which is hook and loops, and

2. Dual-lock which has both surfaces covered in mushroom shaped structures.

These two fasteners have an on/off functionality.

Biological fasteners have a more sensitive functionality:

1. They have to be able to be engaged by a critical force depending on the geometry of the outgrowths, mechanical and frictional properties of the material and the load forces generated by the material.

2. They have to be detached by muscular force quickly.

3. They have to withstand external forces from disrupting the attachment.

Advantages of probabilistic fasteners with parabolic elements over Velcro include the following:

1. It provides more structural possibilities for tuning of the load-attachment relationship.

2. The attachment force can be scaled easily and precisely according to the loading force.

3. The system is less noisy.

4. Fabrication of surfaces at the microscopic scale is possible (useful for MEMS applications).

5. Multiple attachment-detachment performance does not destroy surfaces as fast as Velcro.

5.6Further papers of interest

These papers have not bee read by the author as of yet. Some are on order.

1. “Functional Morphology of the head-arrester system in Odonata”, Gorb S N 1998b, Zoologica 148, 1-132

2. “The Cuticular Protruberances of Insects”, Richards, A G & Richards P A 1979, Int. J Insect Morphology and Embryology, 8, 143-157

3. “Biological Micro- and nanotribology” Scherge, M & Gorb S N. 2001

4. “Design of insect unguitractor apparatus” Journal of Insect Morphology 230, 219-230

6“Evolution of the Dragonfly head-arresting system” S N Gorb [8]

6.1Description

This fixation system (the paper says) of the head of the adult Odonata is unique amongst arthropods. It involves the organs of two body segments, the head and the neck.

The parts comprise formations of complicated microstructures – fields of micro-trichia on the rear surface of the head and post-cervical sclerites of the neck. The skeleton-muscular apparatus sets the arrester parts in motion.

The paper concentrates on structural evolution. A total of 227 species from 26 odonate families were studied by Gorb using scanning electron microscopy.

6.2The head arrestor mechanism

The head arrestor mechanism 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, rather like the brushes used to polish shoes (see )

Figure 25 -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 [8]

It is suggested that the reason for this action in a dragonfly is 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 and during its normal cycle of activities (flying, eating, mating etc) it 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” [5].

The figure from Gorb’s paper shows the different states of the attachment mechanism at different phases of the dragonfly’s activities. 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. It is disengaged in normal flight and at rest but engages prior to take off and again while landing. One can follow the pattern of arrows through the diagram to follow the progress of attachment and detachment during its activities.

Figure 26 – Dragonfly head-arresting mechanism taken from Gorb [8]

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

6.3Schemes of corresponding frictional surfaces occurring in odonate head-arrestor mechanisms

Figure 27 – Schemes of corresponding frictional surfaces occurring in odonate head-arrester mechanisms from Gorb [8]

Figure 27 – Schemes of corresponding frictional surfaces occurring in odonate head-arrester mechanisms from Gorb [Error: Reference source not found] shows some of the configurations found by Gorb.

For the purposes of illustration two images have been included below of two dragonfly specimens of the species Southern Hawker (Aeshna cyanea), collected in June 2003.

Figure 28 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 it seems 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.

Figure 28 – Dragonfly head-arresting mechanism – detached. The wingspan is approximately 80 mm from wingtip to wingtip.

In comparison the second specimen was found dead on the stem of a vine two weeks later (see Figure 29 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.

Figure 29 – Dragonfly Head-arresting mechanism – attached. The wingspan is approximately the same as that of the previous specimen, 80 mm.

Gorb count hair density, length and thickness to be of importance to the effectiveness of the attachment. It is suggested that material qualities such as surface texture also contribute significantly, reflected in the frictional characteristics.

6.4Further papers of interest

These papers have not bee read by the author as of yet. Some are on order.

1. “A comparison of the neck and prothoracic sclerites throughout the orders of insects from the standpoint” G C Crampton (1926) Trans. of the American Entomological Society 52, 192-248

2. “Microstructure of the head fixation system of dragonflies in scanning electron microscopy” S N Gorb, (1990) Zool. Zh. 69, 148-154 (In Russian)

3. “Inner morphology of the arrestor-system in the damselfly Erythromma najas Hansemann (Zygoptera, Coenagrionidae)” Gorb S N (1990) Vestnik Zool. N6, 61-68 (In Russian)

4. “Morphology of the head fixation system in calopterygoid damselflies (Odonata, Zygoptera, Calopterygiodea), Gorb S N (1990), Zool. Zh. 69, 37-45 (In Russian)

5. “Design of insect unguitractor apparatus” Gorb S N (1996), Journal of Morphology, 230, 219-230

6. “Ultrastructural architecture of the microtrichia of the insect cuticle” Gorb S N (1997) Journal of Morphology 234, 1-10

7“Systematic Technology Transfer from Biology to Engineering” (2002) J F V Vincent, D Mann [8]

7.1Description

This paper is included here as a background paper to research into biological systems for the purposes of engineering innovation. It makes use of a Russian design algorithm called TRIZ which, researchers say, identifies a “systematic means of transferring knowledge between different scientific and engineering disciplines”.

The contents of this paper have been addressed here with reference to biological attachment mechanisms to demonstrate how attachment mechanisms can fit into the TRIZ framework.

7.2Ideality

TRIZ makes great use of the term ideality and descriptions of what makes a solution ideal. It is concluded that the use of an external system of any kind is not ideal and that ultimately “the system should evolve to be self-serving or self-actuating”.

The TRIZ database itself provides an objective framework for accessing solutions from other technologies and sciences by using functionality as the key.

Refer to Figure 30 – The technology of joining – note that biological attachment mechanisms fit into the areas distinguished by relatively high adaptability and low strength where some biological fasteners, including Velcro, gecko feet and octopus suckers, have been placed into the design space of all fasteners. It should be noted that the space denoted “friction bond” refers to a form of permanent welding using friction, commonly used for welding/joining plastics.

The attachment mechanisms researched in the preceding papers, particularly those of parabolic structures, have not yet been classified and included into this chart. With reference to Sections 4.2 and 6.1 previously, it can be suggested that these fasteners would share a space with gecko feet, being of high adaptability and relatively low strength.

Figure 30 – The technology of joining – note that biological attachment mechanisms fit into the areas distinguished by relatively high adaptability and low strength from Vincent, Mann [9]

7.3TRIZ and trends of technical evolution

TRIZ illustrates technological progress through a series of formulae that are supposed to demonstrate a pattern of thinking and/or evolution and also to map a direction in which inventive solutions arise.

In particular with reference to attachment mechanisms, Figure 31 – TRIZ series for jointed parts below shows the evolutionary series. In considering the meaning of the word “field” with reference to attachment mechanisms in a general form, TRIZ infers that an inventive solution of ideality would be one that integrates the use of fields from within the system.

There are to obvious solutions arising from this. The first is the use of a field of structures as per probabilistic fasteners, friction-based, re-usable and none specifically aligned to increase the opportunity for attachment.

Figure 31 – TRIZ series for jointed parts from Vincent, Mann [9]

The second approach suggests that using a field in attachment mechanisms could indicate internal stress fields, in other words a self-actuating attachment mechanism of a material that was able to change shape in a controlled manner. This clearly shows where, with reference to Gorb’s work on Miniature Attachment Systems (Section 4), the material scientists steps in to both analyse the biological material and to work upon analogues in other materials such as shape memory materials and polymers to reproduce the desired qualities.

7.4Further papers of interest

These papers have not bee read by the author as of yet. Some are on order.

1. “Life’s lessons in design” Ball P (2001) Nature 409, 413-416

2. “A physical model of nacre” Jackson A P, Vincent J F V, Turner R M (1989) Composites Science and Technology 36, 255-266

3. “Improvements in or relating to a method and a device for producing a velvet type fabric” Velcro S A (1955) Swiss patent no. 721338

8“Performance and Adaptive Value of Tarsal Morphology in Rove Beetles of the Genus Stenus (Coleoptera, Staphylinidae)” (2002) O Betz [10]

8.1Description

This paper describes how the tarsi of these beetles have adapted to use on different surfaces.

The tarsal claws have tenent setae or hairs on their underside which, it is suggested, act with the hooking action of the claws to aid attachment to surfaces in a functional synergism. Closely related species of this genus can walk upon the surface of water and climb vertical plant surfaces. There is an observed difference in the morphologies of related species in that those that can only walk upon water surfaces but not climb vertical surfaces have narrower claws than those that can climb vertical surfaces.

It is further suggested that “the main selective demands driving the widening of the tarsi in several lineages have come from their firm attachment to smooth plant surfaces.”

The stated hypotheses for these experiments is as follows:

1. That widened tarsi allow better adhesion to smooth plant surfaces and thus more effective climbing in the (reed) vegetation and

2. That widened tarsi allow better support on the water surface.

8.2Method

8.2.1Climbing vertical surfaces

Each beetle had a stiff hair glued to the surface of the pronotum (the anterior or upper surface of the beetle). They were then weighed because the experimental procedure includes placing the entire beetle upon a microbalance and then measuring the change in reading. The hair was used to fix the beetle to a mount such that the beetle was in a vertical position without contact to any surfaces.

Four surfaces of different roughness values (R_a) were brought into contact with the legs of the beetle. The surface roughness was determined using an optical profiler (Veeco Instruments Inc., type NT3300) run in the VSI mode and calibrated according to an NIST-certified step height standard (10.10 m step height).

It is said that as soon as the surfaces were brought into contact with the legs, the beetles began trying to climb, producing a reading on the micrometer. If the beetles didn’t respond they were brushed with a light brush to stimulate “escape” behaviour.

Tests were conducted on the beetles with claws and setae intact, with the setae contribution suppressed by coating and fixing them with superglue and with amputated claws.

8.2.2Walking on water

Each beetle was filmed walking on the surface of a small basin of water. Since the mechanical principles associated with this form of attachment include surface tension and not the mechanical interaction of structures, the aspects of this paper associated with this part of the experiment are not included here.

It is sufficient to include that the paper describes an assessment of the wettability of the tarsi and the surface tension of typical pond water.

8.3Statistical analysis

The number of setae per tarsus was obtained from a previous paper on the species.

“The square root of the number of setae and the cube root of body mass was calculated. Simple linear regression analysis was used to test for the dependence of the maximal exerted pulling force on the number of tenant setae. To correct for body size, two separate linear regression analyses of both these log-transformed variables against log-transformed body mass were performed. The non-standardised residuals of this analysis (i.e. the difference between the data and the linear regression fitted to them) were then used to test for the final relationship between the two variables. The Tukey test was used to test for differences between slopes of the different regression lines. Mann-Whitney U-tests were performed with the non-standardized residuals to test for overall differences in maximum pulling force between the group of species with wide tarsi on each of the various surfaces. To test for differences between the climbing performance of the same individuals on different test surfaces, a Friedman test was performed, followed by the Wilcoxon test for paired comparisons. The Wilcoxon test was also used to perform within-species comparisons of the climbing performance of individuals before and after manipulation of the claws and the tenent setae. Interspecific comparisons of pulling forces were performed with pairwise Mann-Whitney U-tests. The significance levels of all the non-parametric tests that included more than one comparison were corrected according to the sequential Bonferroni procedure (Sokal and Rohlf, 1995)”,

8.4Results

It was found that species with wide tarsi on average exhibited significantly higher forces than species with slender tarsi. This clear distinction between the two groups was observed only on glass and photographic paper, i.e. the smoothest surfaces. Therefore the importance of the number of ventral tarsal tenent setae for the attained pulling forces is greatest on glass and decreases in the order of increasing surface roughness.

Tests were made on the leaves of Phragmites communis and Glyceria maxima, both fresh and dried.

The experimental results of the study demonstrate the importance of wide tarsi, accommodating a large number of tarsal setae, for climbing on vertical plant surfaces. On rough surfaces the maximally attainable pulling forces should be limited only by (i) the leverage and maximum power output of the leg muscles and (ii) the yielding strength of the pretarsus and the surface projections of the substratum. It is suggested that the shape of the claws in relation to the surface roughness may have a special significance but this is not investigated further.

There is also mention of the tarsal secretion of insects, sandwiched between the ventral tarsal surface and the substratum, considered to be a vital component of attachment in both hairy and smooth systems. The underlying attachment forces acting parallel to the substratum are generally considered to be a combination of capillary, viscous, friction and molecular forces.

8.5Natural plant surfaces

Natural plant surfaces usually combine the surface characteristics of both rough and smooth substrata. The smooth plant epidermis might be disrupted by cuticular folds, leaf veins, trichomes or wax crystalloids (see Appendix 3). Because wax can contribute towards reducing traction by exfoliating and clogging the setae it is thought that the structure of a single setae is of less importance.

Figure 32 – A mechanical analogue of of tarsul and setae on leaf surface from Betz [10]

Consider Figure 32 – A mechanical analogue of of tarsul and setae on leaf surface from Betz [Error: Reference source not found] and note how, during the pulling action, the metatarsal rotates about the fulcrum of the surface irregularity. This has the effect of pressing the setae to the plant surface which increases both the surface area and the reaction force from the surface and therefore the adhesive and frictional forces respectively due to the setae.

8.6Further papers of interest

These papers have not bee read by the author as of yet. Some are on order.

1. “Structure of the tarsi in some Stenus species (Coleoptera, Staphylinidae), External morphology, ultrastructure and tarsal secretion.” Betz O (2002) Journal of Morphology

2. “Plant surface waxes and insect behaviour”. Eigenbrode S D (1996), In “Plant Cuticle” (Ed. G Kersteins), pp 201-22. Oxford: BIOS Scientific Publishers

3. “Attachment forces of ants measured with a centrifuge: better “wax runners” have a poorer attachment to a smooth surface” Federle W, Rohrseitz K, Holldobler B, (2000) Journal of Experimental Biology, 203, 505-512

4. “Scale effects on the attachment pads and friction forces in syrphid flies (Diptera, Syrphidae). (2001) Gorb S, Gorb E, Kastener V, Journal of Experimental Biology 204, 1421-1431

5. “Adhesion of a leaf feeding ladybird Epilacha vigintioctomaculata (Coleoptera: Coccinellidae) on a vertically smooth surface.” Ishii S (1987) Applied Ent. Zoology 22, 222-228

6. “How pitcher plants trap insects” Juniper B E, Burras J K (1962), New Scientist 13, 75-77

7. “Plant Surfaces” Juniper B E, Jeffree C E (1983), London: Edward Arnold. pp93

8. “Tarsal structure and climbing ability of cockroaches” Roth L M, Willis E R (1952) Journal of Experimental Zoology 119, 483-517

9. “Role of waxblooms in preventing attachment to brassicas by the mustard beetle Phaedon cochleariae” Stork N E (1980c) Etymology Experimental Applications 28, 100-107

10. “Polar and non-polar interactions in adhesion” Wu S (1973) Journal of Adhesion 5, 39-55

9“Roughness-dependent Friction Force of the Tarsal Claw System in the Beetle Pachnoda marginata (Coleoptera, Scarabaeidae)” (2002) Z Dai, S N Gorb, U Schwarz [11]

9.1Description

This paper examines the force relationships between the tarsal claw of a single species of beetle and surfaces of varying surface roughness. It adopts a mechanistic approach, examining the structure of the claw and the dimensions of the claw tip as well as the surface roughness R_a and examines their interactions. It considers the attachment force to have two component forces, namely interlocking and friction.

This paper studies the attachment forces generated by claws in a “free walking” beetle, emphasizing the relationship the relationship between the dimension of the claw tip and the substrate texture. The species Pachnoda marginata was selected for experimentation because it does not possess any specialized attachment devices for smooth substrata.

9.2Materials and method

See Figure 33 – Measuring the thrust of a beetle from Dai et al [Error: Reference source not found] and note the comments included from the original paper. The forces generated by a moving beetle were measured to assess the force range with which the tarsal claw interacts with the substrate. The mechanical properties were then evaluated by testing the individual claws in a fracture test.

Figure 33 – Measuring the thrust of a beetle from Dai et al [11]

Then the internal structure was studied using a scanning electron microscope after being air-dried for 4 weeks and sputter-coated with gold-palladium (10nm). The claw material was studied using a freshly fixed, dehydrated and critical-point dried claw. Sandpaper of six different roughnesses was used, the surface profile being measured using the perthometer M1 (manufacturer Mahr GmbH, Dusseldorf, Germany).

R_a was defined as the square root value of the difference between heights to its average height.

Figure 34 – Claw Goemetry shows the method used to describe the shape of the claw. The claw is described using a set of radii. Five arcs are used to describe the curves. Drawing “C” shows how the claw was split up into component shapes for stress calculations.

Figure 34 – Claw Goemetry from Dai et al 11]

The internal structure of the claw is shown in Figure 35 – SEMs of the claw interior structure below.

Figure 35 – SEMs of the claw interior structure from Dai et al [11]

Figure 36 below shows the force measurements of the claw over the various surfaces.

Figure 37 – Force generation on different surfaces from Dai et al [11]

Figure 38 below show the idealized geometry used to calculate the interactions between claw tip and a surface irregularity.

Figure 38 – Claw tip interaction with surface irregularities from Dai et al [11]

9.3Further papers of interest

These papers have not bee read by the author as of yet. Some are on order.

1. “Scanning electron microscopy of the epidermal surface in plants.” In ”Scanning Microscopy in Taxonomy and Functional Morphology” Barthlott W (1998) (ed. D Claugher) pp 69-94 Oxford: Clarendon Press

2. “Classification and terminology of pant epicuticular waxes” Barthlott W, Neinhuis C, Cutler D, Ditsch F, Meusel I, Theisen I, Wilhelmi H (1998) Botannical Journal of the Linnaues Society 126 pp 237-260

3. “Defence by foot adhesion in a beetle (Hemisphaerota cyanea)” Eisner T, Aneshansley D J, (2000) Procedures of the National Academy of Science USA 97, pp 6568-6573

4. “Biomechanics of the movable pretarsal adhesive organ in ants and bees” Federle W, Brainerd E L, McMahon T A, Holldobler B (2001) Procedures of the National Academy of Science USA 98, 6215-6220

5. “Elasticity and movements of the cockroach tarsus in walking” Frazier S F, Larsen G S, Neff D, Quimby L, Carney M, DiCaprio R A, Zill S N, (1999) Journal of Comparative Physiology A, 185, 157-172

6. “The climbing organ of an insect Rhodnius prolixus (Hemiptera, Reduviidae).” Gillet J D, Wigglesworth V B (1993) Procedures of the Royal Society of London B 111, 364-376

7. “Design of the insect unguitractor apparatus” Gorb S N (1996) Journal of Morphology 230, 219-230

8. “The role of trichomes in plant defence” Levin D A (1973) Quarterly Review of Biology 48, 3-15

9. “The cuticle, epicuticular waxes and trichomes of plants, with references to their structure, functions and evolution.” Jeffree C E. In “Insects and the Plant Surface” (ed Juniper B E and Southwood T R E) pp 23-64 London: Edward Arnold

10. “Mechanical, sensory and glandular structures in the tarsal unguitractor apparatus of Chironomus riparius (Diptera, Chironomidae)” Seifert P, Heinzeller T (1989) Journal of Zoomorphology 109, 71-78

11. “Anatomy of the honey bee” Snodgrass R E (1956) New York: Comstock Publishing Associates

10References

1. “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

2. “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

3. “Practical Statistics for Field Biology” Fowler, Cohen, Jarvis, 1998 John Wiley and Sons, ISBN 0-471-98295-4

4. “Miniature Attachment Systems: Exploring Biological Design Principles” S N Gorb, Design and Nature, 2002

5. “Attachment Devices of Insect Cuticle”, S Gorb, 2001. Kluwer Academic Publishers. ISBN 0-7923-7153-4

6. “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

7. “Really Useful: the origin of everyday things”, J Levy, New Burlington Books, ISBN 1-86155-337-4

8. “Evolution of the Dragonfly head-arresting system” S N Gorb, Proc. R. Soc. Lond. B (1999) 266, 525-535

9. “Systematic Technology Transfer from Biology to Engineering” J F V Vincent and D L Mann, Phil. Trans. R Soc. Lond. A(2002) 360, pp 159-173

10. “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)

11. “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