Roughness-dependent friction force of the tarsal claw system in the beetle Pachnoda marginata (Coleoptera, Scarabaeidae)
1 Biological Microtribology Group, Division II, Max-Planck-Institute of
Developmental Biology, Spemannstrasse 35, D-72076, Tuebingen,
Germany
2 College of Mechanical and Electric Engineering, Nanjing University of
Aeronautics and Astronautics, 29 Yudao Street210016, Nanjing, China
* Author for correspondence at present address: Evolutionary Biomaterials Group, Max-Planck-Institut fuer Metallforschung, Heisenbergstrasse 3, D-70569 Stuttgart, Germany (e-mail: s.gorb{at}mf.mpg.de )
Accepted 15 May 2002
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Summary |
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Key words: friction, locomotion, leg, cuticle, insect, biomaterials, biomechanics, material properties, Pachnoda marginata, Scarabaeidae, Coleoptera
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Introduction |
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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.
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Materials and methods |
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The sandpaper used for the experiments is covered by Al2O3 particles (Wirtz-Buehler GmbH, Düsseldorf, Germany). The grit number, particle diameter and surface roughness (Ra) are listed in Table 1. Surface profile was measured using the perthometer M1 (Mahr GmbH, Göttingen, Germany). Ra was defined as the square root value of the difference between heights to its average height (see Appendix A). Ra was not measured for the sandpaper types P60 and P100, because their roughness was beyond the measuring range of the perthometer.
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The platform was covered by sandpaper of different particle size
(Table 1). A beetle with a
Plexiglas angle, glued onto the dorsal surface of its thorax, walked on the
sandpaper in the direction of the crossbeam until the angle contacted with the
beam. Since the angle was only about 3 % of the beetle's weight, it did not
change the beetle's locomotion. The beetle continued to walk in the same
direction for a while trying to overcome the obstacle by pressing against the
crossbeam. Forces generated by such an action were monitored by the sensor.
Knowing the distance (30-40 mm) between the contact point of the Plexiglas
angle and the crossbeam (X), the force monitored by the sensor
FS was recalculated in the actual force generated by the
beetle FB:
![]() | (1) |
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.
Forces of the freely moving legs
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.
Mechanical strength of the claw
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 forcedistance 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.
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Results |
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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±3.5 µm thick (N=2, n=8) and (3) the central lumen (25.0-30.0 µm) (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).
Breaking stress of the claw
Knowing the breaking force (Fig.
4B) and geometry of the claw
(Fig. 2), the strength of the
claw material can be calculated. During the break test, load linearly
increased with the deflection distance, and suddenly decreased when the claw
broke. Average breaking force was Fbk=197.6±7.7 mN
at an average length of the bend beam L=0.38±0.04 mm
(n=7). For further calculations, the claw was considered as a curved
cantilever beam (Fig. 2). The
mean bending torque M=Fbk·L was
7.51x10-5 N m. The maximum bending stress
max can be calculated by:
![]() | (2) |
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.
Friction force on different textures
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.
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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.
Output force of a single leg
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.
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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.
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Discussion |
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Claw material
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.
Model of the contact between claw tip and sandpaper particles
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 , describing the relationship between claw tip
radius and particle size, is large enough. At a certain minimal
,
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.
The limiting situation is derived from the equilibrium condition. In the
direction normal to the contact point, contact force N, based on the
force equilibrium condition, is
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![]() | (4) |
From equations 3 and 4, we have
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From Equation 5, the limit of the horizontal force F for a
certain weight W can be obtained, when the angle is big enough
(tan
-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 . This leads to a negative left part
of equation 5 (tan
-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 50-270
µm.
Claw attachment system of insects and natural substrata
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 insectplant 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 insectplant 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.
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Appendix A |
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![]() | (A1) |
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Appendix B |
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The moment of inertia IA for part A of the
claw is
![]() | (B1) |
The distance YA from the flexural center
XA of part A to its boundary N
(Fig. 1) is:
![]() | (B2) |
![]() | (B3) |
The distance YB from the flexural center
XB of part B to its boundary Z
(Fig. 2) is:
![]() | (B4) |
![]() | (B5) |
![]() | (B6) |
![]() | (B7) |
YT is the distance from the flexural center
XT of the whole structure to the boundary N
(Fig. 2). It is determined as:
![]() | (B8) |
![]() | (B9) |
![]() | (B10) |
![]() | (B11) |
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Acknowledgments |
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