Roughness-dependent friction force of the tarsal claw system in the beetle Pachnoda marginata (Coleoptera, Scarabaeidae)
Zhendong Dai1,2,
Stanislav N. Gorb1,* and
Uli Schwarz1
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
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Fig. 1. Force measurement system of the beetle Pachnoda marginata. The
system consists of a platform covered by sandpaper, force sensor, and
videorecorder. 100 mm long crossbeam was connected to the force sensor on one
side and supported on the other side. The height of the beam (D) relative to
the sandpaper plane was adjusted to be 1-3 mm higher than the dorsal surface
of the walking beetle. The force generated by the beetle was transferred by
the beam to the sensor and monitored by the load cell force transducer and the
signal amplified by the MP-100 system (Biopac system Inc. USA). The data were
finally sampled and processed with the aid of a computer. A binocular
microscope equipped with a video camera connected to a videorecorder was used
to collect images of the beetle during the force measurements. From these
images, the distance from the beetle to the sensor (X) was obtained. Force
generated by the beetle FB was calculated as
FB=100FS/(100-X), where
FS is the force measured with the sensor.
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Fig. 4. Measurements of the mechanical strength of the claw. (A) Principle of force
measurements using the force tester Basalt-01 (Tetra GmbH, Ilmenau, Germany).
The claw (CL) was glued to the platform (PF). The metal spring (MS) was driven
downwards by the piezo-drive until the claw was broken. Displacement of the
spring tip equipped with a mirror M was detected in the vertical direction by
the fiber optical sensor (FOS). (B) Force—distance curve obtained in
experiments with the claw and used to calculate breaking stress of the
claw.
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Fig. 2. Claw geometry. (A) Claw shape of the hind-, mid- and forelegs (drawings are
based on SEM micrographs). (B) Five arcs used for quantitative description of
the claw geometry (see Table
2). (C) Cross-section model of the claw for stress calculation.
The model is based on SEM data (see Fig.
3E,F). The claw consists of three parts in its cross section: (1)
a dense layer of the exocuticle (gray), (2) a loosely packed endocuticle, and
the claw lumen. Semicircular (A') and rectangular (B') parts of
the claw were calculated separately. XA,
XB and XT are bending centers of
sections A, B and A+B, respectively. For an explanation of
other symbols, see text, Table
3 and Appendix B.
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Fig. 3. Claws of Pachnoda marginata. (A-C) Claw positions of the foreleg
(A), midleg (B) and hindleg (C) during walking on a rough surface. Black
arrows indicate direction of leg movements. (D) SEM image of the claw tip.
(E,F) SEM images of the claw fractured in the cross plane. The line of the
arrow shows the symmetry axis of the claw and points to the dorsal direction.
cl, claw lumen; endo, endocuticle; exo, exocuticle; r, radius of the tip
hemisphere.
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Fig. 5. Force generation by the beetle on different textures. (A) Surface texture
of sandpaper types (12 µm, P400 and P280). Ra, surface
roughness; Rz, average height of surface irregularities.
(B) Comparison of the claw tip dimensions with the sandpaper texture (12 µm
type) (above: side view, below: top view). (C) An example of the typical force
recording used for data processing. (D) Forces generated by beetles walking on
different substrate textures. When the diameter of particles is comparable
with the claw tip, the claw slips out of the particle. When the diameter of
the particles is larger than that of the claw tip, the claw is interlocked
with the particles.
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Fig. 6. Mean (white bars ± S.D.) and maximum (black bars) forces of the
beetle legs (hindleg, n=94; midleg, n=45; foreleg,
n=62).
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Fig. 7. Model of claw tip interaction with surface irregularities. (A) Geometry of
the contact between the claw tip and a particle of the sandpaper. (B)
Dependence of the force ratio F/W on the contact angle
( ) at different friction coefficients between the claw and particles of
the sandpaper. (C) Dependence of h/R on the contact angle () at
different values of the relationship RPD=R/r
(particle radius/claw tip radius). When the diameter of a particle is
comparable to the claw tip diameter (RPD=1), both
structures cannot interlock even at the friction coefficient f=0.5.
When RPD is greater than 4, the structures may interlock
even at f=0.2. If the relationship between the immersion depth and
particle radius (h/R) is >0.5, the relative maximum force
F/W is not larger than 5. The model predicts the relative
maximum force depending on the friction coefficient at contact, the diameter
of particles and the immersion depth. Broken lines divide ranges of at
which interlocking (self-locking) takes place (left side) at a particular
friction coefficient; , contact angle; F, leg force;
fN, line running perpendicular to the normal line N running through both
centers of the particle and the claw tip; h, immersion depth of the
hemispherical particle; r, claw radius; PT, contact point; R, particle radius;
W, weight acting on the claw.
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© The Company of Biologists Ltd 2002
