Roughness-dependent friction force of the tarsal claw system in the beetle Pachnoda marginata (Coleoptera, Scarabaeidae)

Beetles (Coleoptera) are the largest group of insects and inhabit nearly every biological niche. During evolution, to enable walking and attachment on the variety of substrata, beetles developed various leg adaptations (Stork, 1987). To generate propulsive forces, a locomotory mechanism must be able to generate sufficient grip or friction with the substrate. Specialized adhesive tarsal setae of representatives of some beetle families provide a mechanism of attachment of plant surfaces, because such natural substrata can be very smooth indeed (Stork, 1983a,b). Claws are structures adapted to diverse rough textures(Nachtigall, 1974). Attachment mechanisms of specialized adhesive devices, such as arolium, pulvilli,euplantulae, tarsal hairs etc., have been studied experimentally in a variety of insect taxa such as flies (Bauchhenss,1979; Walker et al.,1985; Gorb, 1998),bugs (Gillett and Wigglesworth,1932), ants (Federle et al.,2000), orthopterans (Gorb et al., 2000; Jiao et al.,2000), and beetles (Stork,1980; Ishii, 1987; Eisner and Aneshansley,2000).

The mechanism of claw action on rough textures in various animals seems at first glance to be trivial (Cartmill,1985). However, it is still not clear what substrate roughness is critical for this attachment system, and how attachment force is related to claw dimension and substrate texture. It is known that friction forces,generated by claws, are part of the autonomous action of the bee pretarsus. During the tarsus placement on the substrate, claws contact with the surface. If the grip is sufficient to prevent sliding, claws become the driving mechanism for generation of propulsive forces. If the claws slide along the substrate, arolium, which is responsible for attachment on smooth substrata,will be mechanically activated (Snodgrass,1956; Federle et al.,2001). The insect unguitactor apparatus, which is connected to the claws on one side and to the tendon of the claw flexor muscle on the other side, plays an important role in claw kinematics(Heinzeller et al., 1989; Seifert and Heinzeller, 1989; Radnikow and Bässler,1991). It has been hypothesized that claws, interlocked with the surface, cause interlocking of the unguitractor plate when the claw flexor muscle is contracted (Gorb,1996). This mechanism allows stable claw holding in a bent position for a long time with a minimum of muscular force expenditure.

This paper studies the attachment forces generated by claws in the free-walking beetle with an emphasis on the relationship between the dimension of the claw tip and the substrate texture. Pachnoda marginata(Coleoptera, Scarabaeidae) was selected for experiments because this species does not possess any specialized attachment devices for smooth substrata. To evaluate the force range by which the claw can interact with substrate, forces generated by the freely moving legs were measured using the load cell force transducer. To obtain information about material properties of the claw, its mechanical strength was tested in a fracture experiment, and the internal structure of the claw material was studied by scanning electron microscopy. Data obtained by these different approaches led us to propose a model explaining saturation of attachment force with an increased texture roughness.

Beetles (Pachnoda marginata Drury, Scarabaeoidea) were obtained in the larval stage from a supplier. After pupation and hatching, adults were kept under normal room conditions (20-24 °C). Beetles were individually weighted prior to the experiments (mass=1.002±0.233 g, mean ±S.D., N=9). Intact and broken claws were air-dried for 4 weeks,sputter-coated with gold-palladium (10 nm) and examined in a Hitachi S-800 scanning electron microscope (SEM) at 20 kV. A SEM study of the claw material was also carried out with a freshly fixed, dehydrated and critical-point-dried claw. There was no significant difference in the structure of this stiff material from claws that had been air-dried or critical-point-dried.

The sandpaper used for the experiments is covered by Al₂O₃ particles (Wirtz-Buehler GmbH, Düsseldorf,Germany). The grit number, particle diameter and surface roughness(R_a) are listed in Table 1. Surface profile was measured using the perthometer M1 (Mahr GmbH, Göttingen, Germany). R_a was defined as the square root value of the difference between heights to its average height (see Appendix A). R_awas not measured for the sandpaper types P60 and P100, because their roughness was beyond the measuring range of the perthometer.

To measure forces generated by walking beetles on different textures, a force sensor (load cell force transducer, 10 g) was used (Biopac System Inc. USA), mounted on a stand connected to the platform(Fig. 1). A metallic cross beam was used to transmit the beetle force to the sensor. One side of the crossbeam was connected to the sensor and another supported by the platform. The height of the beam was adjustable in a vertical direction. The distance between the beam and the sandpaper surface was adjusted to a suitable height (D)corresponding to the beetle's height (5-7 mm) plus 1-3 mm. The force sensor was attached to an amplifier and computer-based data-acquisition and processing system. The beetle's position was monitored by a video camera mounted on a binocular microscope. Experiments were video-recorded, and geometrical parameters were obtained from single video-frames.

The sensor was calibrated at the point where the crossbeam was connected before and after an experiment (sensitivity 10 μN). 3-5 beetles with three repetitions per individual were used for the experiment with each sandpaper.

To evaluate forces generated by a freely moving single leg, the beetle was fixed to a micromanipulator (World Precision Instruments Inc.), enabling adjustment of the beetle position relative to the sensor. Whenever the beetle grasped and pulled the sensor tip, the force was monitored and recorded. Five repetitions each for the forelegs, midlegs and hindlegs were done in three individual beetles.

The mechanical properties of the claw were tested on a Biotester Basalt-01(Tetra GmbH, Ilmenau, Germany) (for details, see Gorb et al., 2000). The claw of a freshly killed beetle was glued with cyanacrylat glue (5925 Universal, S. Kisling & Cie AG; Zürich, Switzerland) to the platform. The metal spring was moved downwards, pressing with its tip against the claw tip until the claw was broken (Fig. 4A). The deflection of the spring tip was monitored by the fiber-optical sensor. Knowing the spring constant, the deflection was recalculated in the force. The maximum force of force—distance curves was used for calculations of braking stress. Since claw geometry of the fore-, mid- and hindlegs is constant (Fig. 2A), seven claws from different legs were tested.

While walking on a sandpaper surface, the beetle contacts the surface with its claw tips and, depending on the friction force in the contact area,generates propulsive movements. Fore- and midlegs pull themselves posteriorly or medioposteriorly towards the body, whereas hindlegs push themselves posteriorly from the body (Fig. 2A-C). Typical claw lengths are 1.33, 1.20 and 1.21 mm for rear,middle and front claws, respectively. The claw shape of the fore-, mid- and hindlegs is very constant (Fig. 2A). The shape can be described as a set of five arcs(Fig. 2B, Table 2). At a high magnification the claw tip resembles a hemisphere(Fig. 3D).

The inner structure of a claw consists of three parts: (1) the outer,exocuticle part, 16.2±4.33 μm thick (N=2, n=11,where N is the number of individuals used and n is the number of claws measured), (2) the inner, endocuticle part, 26.2±3.5μm thick (N=2, n=8) and (3) the central lumen (25.0-30.0μm) (N=2, n=8) (Fig. 3E,F). The exocuticle is a very dense layer composed of thin lamella. The endocuticle consists of thicker lamellae, which seem to be not densely packed. Data on inner structure of lamellae(Fig. 3E) were used in the geometrical model of the claw (Fig. 2C).

Claw lumen contains fluid that might influence the results of calculations,if it were in a closed volume; however, the lumen is connected to the body volume, so the water content of the lumen was not considered to be an important factor influencing the breaking stress of the claw.

The effect of surface roughness on the friction force of beetles was experimentally tested on a variety of sandpapers(Fig. 5A,B; Table 1). A typical force curve obtained in the experiments is shown in Fig. 5C. Maximum peaks and corresponding time were processed together with the beetle's position relative to the crossbeam (X). The force output by the beetle was calculated according to Equation 1.

Saturation of friction force was observed with increasing particle diameter of the substrate. Friction force rapidly increases with increased of particle diameter of the sandpaper in the range 12-50 μm(Fig. 5D). At particle diameters of 50-270 μm, only a very slight force increase was revealed. On rough textures, the forces were about 38 times higher than the average beetle weight. On relatively smooth textures the forces were comparable to the average weight of the beetle.

Recordings were obtained separately for the fore- (n=62), mid-(n=45) and hindlegs (n=94). Only the maximum values from each recording were taken into account. Maximal force of a single leg ranged from 100 to 200 mN, which is about 10-20 times higher than the average weight of an animal (Fig. 6). However,during the test, 7.5 % of maximal values out of 94 hindleg recordings exceeded the upper measurement limit of the force sensor. Thus, the forces generated by hindlegs should be slightly higher than given in Fig. 6.

Comparison of force data obtained for single leg measurements with the data of the friction force at high particle diameters(Fig. 6) revealed that the average force output by six legs is higher than the friction force on very rough textures (Fig. 5D). The summarized force of six legs is about 550 mN, and a maximal value of the friction force is about 380 mN. The explanation of this fact is that beetles usually have 3-4 legs in the stance phase during walking. This means that the total force generated by the legs must be summarized not for 6 but for 3 legs.

In insects, claws are controlled by the action of a single muscle, the retractor unguis (Snodgrass,1956; Gorb, 1996). Muscle contraction results in contact to the substrate during the stance phase of walking (Radnikow and Bässler,1991). In the cockroach, previous kinematic and ablation studies demonstrated that, during walking, the multi-segmental structure of the tarsus, together with the elasticity of resilin-bearing elements of tarsal joints, aid in disengaging the contact of the claws with the substrate when the claw retractor muscle relaxes, and lift the tarsus together with the claws away from the substrate (Frazier et al.,1999). Such a design can facilitate the rapid and efficient use of the tarsus in walking while under active control by a single muscle. It may also be advantageous when an insect walks on a wavy substrate(Frazier et al., 1999).

Breaking stress of the cuticle was previously measured in insect arthrodial membranes and solid cuticle of sclerites(Hepburn and Chandler, 1976). It is about five times higher in the solid (78.5±11.7 N mm^-2) than in the membranous cuticle (15.6 N mm^-2). In our experiment, breaking stress of the claw was evaluated to be 143.4 N mm^-2, if both exocuticle and endocuticle layers were taken into account. It is twofold higher than that of the solid cuticle of the locust. Presumably, a combination of the dense-layered exocuticle and loosely packed endocuticle plays a crucial role in the high strength of the claw material. The breaking stress of claw material is similar to that of vertebrate bones(88-174 N mm^-2) (Fung,1993). Taking only the exocuticle part into account, the calculated breaking stress value (684.2 N mm^-2) was comparable to that of some types of steel (320-720 N mm^-2)(Pisarenko et al., 1988). In addition to the claw, high-strength properties can be expected in the cuticle of chewing and cutting mouthparts and in joint cuticle.

Friction force depends on the relationship between the dimensions of the claw tip and surface irregularities. When the surface roughness is lower than the radius of the claw tip, the claw slides over the substrate irregularities. Such a geometrical relationship results in low friction force. When the roughness is remarkably larger than the tip radius, claws tend to interlock with the substrate irregularities. Below we present a model which describes friction force of the claw on rough substrata.

According to the morphology of the claw, we can assume that the tip of the claw is part of a sphere (Figs 3D, 7A). Three assumptions were made about the substrate: (1) substrate irregularities are hemispherical; (2)all particles have the same diameter, corresponding to the mean diameter of the sandpaper particles; (3) each hemisphere is partly immersed in the glue at a depth of h (Fig. 7A). To reach a maximum force, the weight of the beetle has to be balanced by the horizontal force F, assuming that the contact force between tip and glue surface is zero. An initial contact geometry of the model assumes two areas of claw contact: with the horizontal part of the substrate and with the particle. Two forces are acting on the claw tip: (1) the force generated by leg muscles and directed along the substrate surface (F);(2) animal weight, directed perpendicularly to the substrate surface(W). In this situation, the friction force will depend on the maximum frictional force when the claw slips on the particle surface. This is possible only when the angle α, describing the relationship between claw tip radius and particle size, is large enough. At a certain minimal α,sliding of the claw tip is prevented by the substrate particle, which results in the mechanical interlocking between the claw tip and the particle. In this case, the friction force entirely depends on the forces generated by the beetle.

From Equation 5, the limit of the horizontal force F for a certain weight W can be obtained, when the angle α is big enough(tanα-f>0). If the force generated by the beetle is greater than the limit, sliding will take place. In our experiment, such a situation was obtained at relatively low force (Fig. 5D). The force generated by the beetle on different surfaces can be predicted from Equation 5. For example, for sandpaper with particles of an average radius of 9.15 μm, the minimum contact angle is 28.81°, the predicted generated forces at h=0 are 46.18, 9.51, 3.38 and 2.46 mN for friction coefficients of 0.5, 0.4, 0.3 and 0.2, respectively. The predicted value at the friction coefficient of 0.5 corresponds well to the value of 30.4 mN measured in our experiments (Fig. 7B,C).

When particle radius is greater than that of the claw tip, Equation 5 results in a small contact angle α. This leads to a negative left part of equation 5 (tanα-f<0), so that the claw interlocks itself with surface particles. The tip can remain stable and weight has no influence on the measured force. In this case, the measured force corresponds to the force generated by the beetle's leg muscles only. According to the model, a maximal horizontal force of 67.9 mN can be obtained on a surface with particles of an average radius of 26.1 μm at the friction coefficient 0.2,but this value is much lower than the value of 255 mN obtained in the experiment. The prediction seems to be reasonable, because the frictional coefficient of the beetle cuticle on the glass is about 0.35 (Z.D. and S.N.G.,unpublished data). Claw interlocking (self-locking) takes place if the friction coefficient is not lower than 0.3. The h/R ratio has different limitations for various friction coefficients (h/R should be 0.04, 0.15 or 0.26 if the friction coefficients are 0.3, 0.4 or 0.5). The model explains why the force generated on surfaces with a particle diameter of 12-50 μm is low, and why it is high and varies slightly at a particle diameter of 50-270μm.

Insect attachment systems evolved as adaptations for efficient locomotion on a variety of surfaces. Insects usually walk on plant substrata, and,therefore, many aspects of insect—plant relationships deal with mechanical surface interactions. Presumably, such interactions are different in a variety of ecological groups of insects, such as herbivores and parasites, or specialist and generalist phytophages. From the plant perspective, completely different functions of the surface profile and coverage, such as insect trapping function and selective defense against herbivores, may involve similar general mechanisms.

Plant surfaces have a wide range of textures. They may be smooth, hairy or covered with waxes or moist secretions. The wax layer widely varies in thickness and has a crystalline structure. It is usually an extremely thin layer on the cuticles of aquatic plants, whereas substantial crusts appear as pruinescence on fruits, stems and leaves. The most common types of crystal shapes are tubes, solid rodlets, filaments, plates, ribbons and granules(Barthlott and Ehler, 1977; Barthlott and Wollenweber,1981; Barthlott,1998). Current classification of plant epicuticular waxes, based on high resolution scanning electron microscopy of 13,000 plant species,distinguishes 23 types of wax (Barthlott et al., 1998). Trichomes are hair-like protuberances extending from the epidermis of aerial plant tissues(Levin, 1973). They may be unicellular or multicellular, glandular or non-glandular, straight,spiral-shaped, hooked, unbranched or stellate. There are some examples of trichomes responsible for trapping insects and small animals in carnivorous plants, such as Sarracenia purpurea, Genlisea spp. and Darlingtonia spp. (Jeffree,1986). Presumably, felted trichome layers provide a physical barrier against insect predators, protecting young leaves(Curtis and Lersten, 1978).

Adult Pachnoda marginata feed on diverse fruits and flowers but they can also burrow into the soil and walk on litter surface. That is why potential surface roughness in nature remains unpredictable for this species. Our work shows that surface roughness strongly influences the attachment abilities of the insect claw system. Insect tarsi equipped only with claws can attach to a vertical surface only at a substrate roughness comparable to or bigger than the diameter of the claw tips. Thus, it can be concluded that by the mediation of the surface roughness, plants may change insect—plant interaction. Our work is a step towards understanding which type of attachment device is optimized for a plant surface with particular properties. The scaling effects and the role of mechanical properties of substrate material,however, remain poorly understood. Further comparative studies on the texture of plant surfaces and dimensions of insect claw tips may complete the proposed model.

Presumably, the exocuticle and endocuticle layers have different material properties. Since the differences are not known, the breaking stress of the claw was calculated in two ways. In the first one, only the geometry of the exocuticle layer was taken into account. In this case, calculated stress is higher than the real stress. In the second one, both layers (exocuticle and endocuticle) were taken into account, assuming that both of them have the same material properties. In this case, calculated stress is lower than the real stress. The real stress probably has an intermediate value somewhere between the results of these approaches.

List of symbols
 
• B, b

  Widths of the bending squares

 
• D

  Height of crossbeam from sandpaper surface

 
• D, d

  Diameters of the outer and inner circles, respectively, of the cross section of the claw

 
• f

  Friction coefficient between the claw tip and particle

 
• F_bk

  Average breaking force of claw

 
• F

  Force generated by leg muscles and directed along the surface

 
• F_S

  Force monitored by the sensor

 
• F_B

  Force generated by the beetle

 
• H, h

  Heights of bending squares

 
• h

  Immersion depth of particles in the glue

 
• I_A

  Moment of inertia for part A of the claw

 
• I_B

  Moment of inertia for part B of the claw

 
• I_T

  Moment of inertia for the bending-load bearing area A and B

 
• L

  Average length of the bend beam of the claw

 
• M

  Mean bending torque acting on the claw

 
• N

  Boundary running through centre of outer and inner circles

 
• N

  Normal force between the claw and particle

 
• r

  Radius of the claw tip

 
• R

  Particle radius

 
• R_a

  Surface roughness

 
• R_z

  average height of surface irregularities

 
• S_A, S_B

  Areas of sections of parts A and B, respectively

 
• X

  Distance from beetle to sensor beam

 
• X

  Distance between the sensor to the contact point of the Plexiglas angle on the crossbeam

 
• X_T

  Flexural centre

 
• Y_A

  Distance from the flexural center X_A of part A to its boundary N

 
• Y_B

  Distance from the flexural center X_B of part B to its boundary Z

 
• Y_T

  Maximum distance from the flexural center X_T to the boundary N

 
• Y_max

  Distance from X_T to point ofσ _max

 
• W

  Weight acting on the claw

 
• Z

  Boundary of flat part of the claw section

 
• s(x)

  Surface height at point x in the surface profile

 
• \({\bar{s}}(x)\)

  Average height of the surface profile

 
• n

  Number of points measured for the surface profile

 
• α

  Contact angle

 
• σmax

  Maximum bending stress of the claw

Sincere thanks to J. Berger for help with SEM preparations, W. Vötsch for help with video equipment and V. Kastner for linguistic corrections. Two anonymous reviewers provided valuable suggestions and points for discussion. This work was supported by the Federal Ministry of Science of Germany (BMBF)grant BioFuture 0311851 to S.G.