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First published online October 5, 2007
Journal of Experimental Biology 210, 3538-3546 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.009084
The acoustic mechanics of stick–slip friction in the California spiny lobster (Panulirus interruptus)
Department of Integrative Biology, University of California, Berkeley, CA 94720-3140, USA
Author for correspondence (e-mail:
patek{at}berkeley.edu)
Accepted 6 August 2007
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Summary |
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 TOP Summary IntroductionMaterials and methodsResultsDiscussionReferences |
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Key words: friction, coefficient, sliding, static, sound, bioacoustics, lobsters, Palinuridae, Panulirus interruptus, stick, slip, tribology
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Introduction |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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; Persson,
2000; Rabinowicz,
1995). While the transitions between static and sliding friction
are key to many biological movements (e.g.
Goodwyn and Gorb, 2004;
Niederegger and Gorb, 2006;
Scherge and Gorb, 2001),
biological sound production generated through periodic stick–slip
frictional movements is both unusual and understudied. Here, we characterize
the acoustic mechanics of stick–slip friction in the California spiny
lobster (Panulirus interruptus)
(Fig. 1) using a combination of
kinematics, acoustic analyses and mechanical friction tests.
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).
Stick–slip friction between two translating surfaces can cause a system
to behave unpredictably (e.g. earthquakes and squeaky doors) or periodically
(e.g. bowed-stringed instruments) (Fig.
2) (Persson, 2000;
Urbakh et al., 2004).
Understanding and controlling the dynamic behaviour of these systems have
posed longstanding challenges to the fields of physics and engineering, and
the result is a rich field of theoretical and applied research on the
tribology of translating surfaces
(Persson, 2000;
Rabinowicz, 1995;
Scherge and Gorb, 2001).
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;
Patek, 2001;
Patek and Oakley, 2003). Most
spiny lobster species (Palinuridae) generate an anti-predator `rasp' sound by
rubbing the soft-tissue under-surface of the plectrum (an extension off of
each antenna) over a cuticular, rectangular file below each eye
(Fig. 1)
(Lindberg, 1955;
Meyer-Rochow and Penrose,
1974; Meyer-Rochow and
Penrose, 1976; Moulton,
1957; Moulton,
1958; Mulligan and Fischer,
1977; Parker,
1878; Parker,
1883; Patek, 2002;
Patek, 2001;
Patek and Oakley, 2003;
Phillips et al., 1980;
Smale, 1974). The file's
surface is covered with stiff, exoskeletal, microscopic shingles
(approximately 10 µm width) and the plectrum consists of large, soft tissue
ridges (approximately 0.1 mm in width) that are aligned parallel to their
movement over the shingles. The shingle edges increase the frictional force
between the two surfaces and oppose the movement of the plectrum as it sticks
and slips posteriorly to generate pulsed sound.
Previous physiological experiments and a biomechanical model derived from
bowed-stringed instruments demonstrated that spiny lobsters' pulsatile rasps
are generated due to stick–slip friction, causing the plectrum to
periodically slip then stick over the file surface
(Fig. 1)
(Patek, 2002;
Patek, 2001). Similar to
bowed-stringed instruments, such as the violin
(Benade, 1990), the
stick–slip mechanism in spiny lobsters can be modelled as a mass
suspended between two springs (plectrum), which is excited when moved over a
second, frictional surface (file) (Fig.
1). Supplementary material, Movie 1 and Movie 2, depict sound
production and associated morphology, respectively.
The best-studied acoustic stick–slip system is found in
bowed-stringed instruments. In these instruments, the bow cyclically sticks
and slips over the string and generates vibrations that are coupled to the
resonant body of the instrument (Benade,
1990). A player controls the oscillations of the string by varying
the frictional forces between the bow and string. One way to do this is to
simply increase the normal force by pressing the bow more firmly against the
string, and as a result, increase the static friction force
(Benade, 1990). In addition to
the role of the human playing the violin, the material dynamics of the rosin
applied to the bow hairs are responsible for the stick–slip behaviour of
the bow rubbing over the string. Recent studies have shown that the rosin
melts and hardens during each stick–slip cycle, suggesting a
thermodynamic role in the stick–slip dynamics of this system
(Day, 2007;
Schumacher et al., 2005;
Woodhouse et al., 2000).
In terms of biological systems, snail locomotion remains one of the few
stick–slip examples that has been experimentally analyzed
(Denny, 1980). Changes in the
viscosity of the mucus lodged between the snail's foot and substrate enable
snails to periodically oscillate between static and kinetic friction
(Denny, 1980;
Mahadevan et al., 2004).
During locomotion, translational waves travel down the foot of a snail. The
leading edge of the wave stresses the mucus and induces the liquid phase
(kinetic friction). Just behind this edge, the mucus solidifies and resists
the movement of the foot, thereby creating enough static friction for the foot
to push against and for the snail to move forward.
Both biological and engineered frictional systems are most commonly
described in terms of the coefficient of friction (µ), which is a
dimensionless number that expresses the relative contribution of the
frictional force opposing movement (Ff) to the normal
force (Fn) between two contacting surfaces:
 | (1) |
). The coefficient of kinetic friction (µk) is
measured during sliding. However, µk is difficult to measure in
stick–slip systems, because the sliding phase of stick–slip
systems occurs over a changing velocity and, often, a very short time period
(Heslot et al., 1994). Some
argue that it is not possible to measure µk in stick–slip
systems, because of the changing velocity
(Gratton and Defrancesco,
2006); others examine µk as a function of time and
surface–surface interactions (Heslot
et al., 1994). For example, Heslot et al. determined that
µk is proportional to the natural logarithm of the constant
driving velocity of one of the surfaces
(Heslot et al., 1994).
The magnitude of the change in µ and the maintenance of a periodic
stick–slip motion are caused by an interdependent constellation of
factors, including velocity, elastic energy storage and normal force
(Heslot et al., 1994;
Persson, 2000;
Urbakh et al., 2004;
Woodhouse et al., 2000). These
parameters can be used to characterize the rapid transitions between static
and sliding friction and, in order to model the system, calculate spring
constants and approximate surface dynamics
(Scherge and Gorb, 2001;
Yoshizawa and Israelachvili,
1993). Most stick–slip systems have a bounded region in
which periodic stick–slip movements occur given a particular range of
driving velocities and loads (Day,
2007; Persson,
2000). By measuring the coefficients of friction across a range of
loads and velocities, it is possible to define the mechanical space within
which periodic stick–slip motion occurs. While the existing mechanical
model of the acoustic mechanism in spiny lobsters provides a heuristic
explanation of the system, these underlying physical parameters governing the
periodic stick–slip behaviour have yet to be measured.
The primary goal of this study was to quantitatively characterize the acoustic mechanics of stick–slip sound production in the California spiny lobster (P. interruptus). The first step in understanding a frictional mechanism is to measure the frictional forces, the relative movement of the surfaces, and the functional consequences of variation in these parameters. Thus, in the spiny lobster system, we examined the kinematics, friction and acoustics in live animals and excised sound-producing structures. First, we examined the microscopic anatomy of the plectrum and file surfaces that had not previously been described in this species. Second, we synchronously recorded the sounds and movement of live, sound-producing animals to test whether plectrum kinematics are correlated with the acoustics of the rasp. Third, we measured the coefficients of friction and frictional forces in isolated plectrum and file preparations with which we characterized the stick–slip frictional mechanism in spiny lobsters. Ultimately, these results can be used to model variation in acoustics and friction mechanics within and across palinurid species, to understand the evolution of biological friction systems, and to contribute to the fascinating and complex realm of stick–slip mechanics in both engineered and biological systems.
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We measured the medial–lateral and anterior–posterior dimensions of 30 shingles at five locations along the length of each file. The length and width of five plectrum ridges in four specimens also were measured. With the shingle dimensions and the kinematics of the plectrum movements (described below), we calculated the rate of shingle excitation (shingles s–1) given the speed of the plectrum over the file.
Rasp kinematics and acoustics
Five California spiny lobsters Panulirus interruptus were
purchased from commercial sources (85–88 mm carapace length, Catalina
Offshore Products) and used for the kinematic and acoustic experiments. We
measured 5–6 rasps per individual. Each rasp consists of a series of
pulses, thus we measured a total of 18–28 pulses per individual. Animals
were housed in 395 l and 710 l tanks with filtered recirculating, synthetic
seawater (17–19°C). Shrimp and mussels were provided 5 days per
week.
Acoustic and kinematic data were simultaneously recorded using high-speed images (3000 frames s–1, 0.33 ms shutter duration, 1024x1024 pixel resolution, APX-RS high speed video camera, Photron USA Inc., San Diego, CA, USA) and sound (0.1 Hz–80 kHz, –206.1±0.25 dB re 1V/µPa, Model 8104 hydrophone, Brüel and Kjaer, Nærum, Denmark; 1 Hz–1 MHz, VP2000 voltage preamplifier, Reson, Slangerup, Denmark). The acoustic data were sampled at 30 000 samples s–1 (preamplifier set as bandpass filter: 1 Hz–15 kHz) using an analog-to-digital converter coupled to the high-speed video camera (Multi-Channel Data Link; Photron USA Inc.).
In order to track the movements of the plectrum over the file and correct for off-axis positioning of the lobster relative to the camera's plane of view, reflective dots were attached to the plectrum and antennular plate. The centroids of these reflective dots were tracked using a custom, automated, digital image analysis program (v.2006b, Matlab, The Mathworks, Natick, MA, USA). One dot was attached to the plectrum while the other two were affixed, at a known distance apart, to the side of the file and parallel to the movement of the plectrum. This second pair of dots was used to correct for off-axis positioning of the lobster during sound production. Changes in this distance during a video sequence provided the angle between the plane of the camera and the movement of the plectrum. Absolute scaling was determined by placing a ruler perpendicular to the camera at the focal distance of the lobster during recording. The ruler provided a pixel:distance conversion perpendicular to the camera's plane of view with which the actual distance between the two calibration dots on the lobster was calculated. The distance traveled by the reflective dot on the plectrum was tracked throughout each sequence.
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We measured the timing and amplitude of each rasp associated with the plectrum measurements described above. The acoustic data were first filtered with a 60 Hz high-pass filter, then the onset and offset times of each pulse within a rasp were measured. In addition, the peak voltage and RMS amplitude of each acoustic pulse were measured.
We examined the correlation between plectrum movement and sound production, specifically in terms of the onset/offset of sound production, pulse duration, pulse frequency, plectrum slip distance, plectrum velocity and pulse amplitude. Because the position of the hydrophone relative to the lobster's sound-producing apparatus varied across recording sequences, we scaled the peak amplitude of sound production within each sequence to a value of 1, such that pulses were measured as a fraction or multiple of the reference value. While the onset of each pulse was clear in the acoustic data, the offset was often obscured by acoustic reverberations in the recording tank. Thus, we predicted that the acoustic measurements of pulse duration would be greater than the kinematic measurements of slip duration.
The statistical correlation between plectrum movement and sound amplitude was analyzed using a nested least-squares model with rasps identified as random effects (repeated-measures design using the Residual Maximum Likelihood method) (JMP v. 5.0.1). Because the hydrophone was not held at a constant distance from the animals across experiments, the statistical analyses incorporated the raw amplitude data as well as amplitude data in which the pulses within each rasp were scaled to a reference value (as above).
Stick–slip friction measurements
To determine the coefficient of friction, we built a friction-measurement
device to record the frictional (Ff) and normal
(Fn) forces between the plectrum and file surfaces as they
generated sound (Fig. 3).
Friction measurements were recorded in nine plectrums and files from nine
individuals (82.5–90.2 mm carapace length; Catalina Offshore Products).
Ten experiments were conducted on each plectrum/file unit.
An excised plectrum and file were mounted on separate force beams positioned perpendicularly to each other (TBS-10 lb sensors, Transducer Techniques, Temecula, CA, USA). The plectrum was glued (Instant Krazy Glue, Columbus, OH, USA) to the vertical beam attached to a linear translation stage (0.5 µm resolution, ILS50CC translation stage, ESP300 universal motion controller/driver, Newport, Irvine, CA, USA). The vertical beam was positioned orthogonally to the stage and thus measured the frictional force opposing the movement of the plectrum. The file was glued to the horizontal beam located at the side of the translation stage. The horizontal beam measured the normal force that was applied perpendicularly to the movement of the plectrum. Both beams were calibrated by applying a range of known forces, measuring the corresponding voltage response, and constructing a linear interpolation with which voltages (V) were converted to Newtons (N).
Kinematic and force data were collected simultaneously as the translation stage moved the plectrum over the file. Force data were obtained via a custom data acquisition program (v.2006b, Matlab) through an analog-to-digital computer board (50 kHz sample rate, PCI-MIO-16E-4 DAQ board, National Instruments, Austin, TX, USA). The normal force between the plectrum and file was adjusted using a rod positioning system (Newport, Irvine, CA, USA) attached to the file and horizontal force beam (Fig. 3). Experiments were conducted across a range of normal forces (0.5–5 N) that produced a typical rasp sound.
The translation stage operated at a constant velocity (100 mm s–1) and step size (5 mm), which drove the plectrum's intermittent, stick–slip movement. Before each experiment, the plectrum and file surfaces were saturated with artificial seawater. In addition, the plectrum knob was positioned in the groove on the file (Fig. 4) such that the alignment was similar to the lobster's natural movement. We tracked the plectrum's movement by attaching a reflective dot, filming the movement (3000 frames s–1, 0.33 ms shutter duration, 1024x1024 pixel resolution, Photron APX-RS high speed video camera; Photron Inc.), and using the automated point-tracking system described in the previous section. We compared these plectrum movements to the kinematics measured in live individuals (described in previous section). The plectrum displacements were used to determine the times at which the plectrum started to slip as it was forced over the file. Slip durations and slip periodicities also were measured.
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The coefficient of friction was calculated by dividing the filtered friction results by the filtered normal force results, yielding values of µ as a function of time [µ=µ(t) (see Eqn 1)]. A low-pass filter at the resonant frequency of the force beams, 280 Hz, was applied to the force traces. Typically, the initial stages of stick–slip cycles are chaotic and then transition to more uniform oscillations. We also observed this phenomenon in the experimental rasps; thus, in our analysis, we only included the three stick–slip cycles at the most uniform portion of each rasp.
The peak static coefficient (µs) was defined as the time point along the curve µ(t) when the plectrum started to move (Fig. 2). As mentioned earlier, it is difficult to measure the sliding coefficient of friction, because the velocity changes throughout the slip period and, in our case, the beam reverberations obscured the transition between the slip and stick phases (see Results). Instead, we calculated the maximum change in µ(t) for each stick–slip cycle examined. This value represents the maximum difference between the static and sliding coefficients of friction. The force traces of the static phase were fit with a least-squares linear curve and changes in µ were determined by calculating the differences of the values of the line fits at times just before and after the slip phase. Due to force beam resonances, it was necessary to interpolate the values of µ from these curve fits.
The peak slip velocity and average load during the slip phase also were determined for each stick–slip cycle. The velocity profile of the plectrum movement was calculated by taking the derivative of the displacement data. In order to reduce noise and accurately measure the peak velocities, the displacement data were filtered with a 700 Hz low-pass filter (5th order Butterworth filter; v.2006b, Matlab). Average normal forces were calculated by taking the RMS of the load profile during the slip phase. The durations of the stick–slip cycles were determined from the kinematic displacement data.
The statistical relationships between the changes in the frictional coefficient, slip velocity and slip frequency were analyzed using a general linear model (analysis of covariance, ANCOVA) to examine the relationships between these variables and the effects of individual, trial and individual by trial on the resulting correlations (JMP v. 5.0.1).
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The width of each plectrum ridge spanned approximately ten shingles, and the length of the ridges spanned hundreds of shingles. Thus, as a plectrum slips over the file, it articulates with thousands of shingles rather than exciting a single region or series of shingles.
Rasp kinematics and acoustics
The correspondence between the kinematic and acoustic measurements of each
rasp was analyzed by comparing pulse duration to slip duration, acoustic
amplitude to plectrum speed, and pulse rate to plectrum speed. The number of
pulses measured was identical in high-speed video and hydrophone recordings
and consisted of an average 4.5±0.9 pulses (range 3–7).
Consistent with the expected acoustic reverberations in the tank compared to
the discrete offset captured by kinematic measurements, the mean acoustic
measurement of pulse duration was 7.9±2.0 ms (range 1.4–19.9)
whereas the mean kinematic measurement of slip duration was 3.6±1.3 ms
(range 0.6–9.0) (Fig. 5).
Similarly, the acoustic pulses s–1 (mean 87.6±15.9;
range 55.4–136.7) were lower than the kinematic pulses
s–1 (mean 94.9±14.7; range 61.6–133.5).
Plectrum speed and acoustic amplitude were positively correlated. During each slip, the plectrum moved an average 3.8±1.0 mm (range 0.22–10.8) at an average speed of 11.3±3.1 cm s–1 (range 2.3–29.6) and average peak speed of 22.8±3.7 cm s–1 (range 7.0–41.3). Plectrum speed was positively correlated with pulse amplitude, whereas plectrum slip distance was not (Table 1). Peak plectrum speed was strongly positively correlated with all measures of pulse amplitude and average plectrum speed was positively correlated with RMS average pulse amplitude (Table 1). None of the amplitude measures were correlated with plectrum slip displacement.
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Pulse rate increased with plectrum speed. Both peak and mean speeds were positively correlated with the kinematic measurement of pulse rate (mean speed: R2=0.5511, P=0.004, significant individual effects, P=0.002; peak speed: R2=0.4132, P=0.04, non-significant individual effects, P=0.07). Acoustic measurements of pulse rate were not significantly positively correlated with plectrum speed (P>0.05).
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Stick–slip friction measurements
The static coefficient of friction (µs) ranged from
0.4–3.5 (mean 1.7±0.3). As predicted by the stick–slip
model (Fig. 2), the coefficient
of friction decreased rapidly when the plectrum started to move
(Fig. 6). The maximum changes
in µ over the course of each stick–slip cycle were on average
1.1±0.3 and ranged from 0.1–3.6.
Slip velocity, stick–slip frequency (equal to acoustic pulse rate), µs and change in µ varied as we applied a range of normal forces from 0.5–5 N. Although the stage was driven at a constant velocity (10 cm s–1), the plectrum slipped at velocities ranging from 7.6–75.7 cm s–1 (mean: 28.0±7.7 cm s–1). Plectrum velocity was significantly positively correlated with Fn in six out of the nine individuals, but tests for individual effects on the overall dataset were significant (whole model: R2=0.6058; F=14.01, P<0.0001; significant effects of Fn, individual, and individual by trial). The change in µ was positively correlated with velocity, again with significant effects of dataset and trial by dataset (whole model: R2=0.8729, F=29.99, P<0.0001) while µs was not correlated with velocity (whole model: R2=0.8653, F=56.03, P<0.0001; no significant effect of velocity; significant effects of dataset, trial and trial by dataset). The stick–slip cycle frequency was negatively correlated with change in µ (R2=0.3323, F=8.82, P<0.0001; significant effect of dataset) and with Fn (R2 =0.4054, F=12.58, P<0.0001; significant effect of dataset). Peak plectrum velocity and stick–slip cycle frequency were negatively correlated (R2=0.7209; F=22.39, P<0.0001; significant effect of dataset).
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Discussion |
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California spiny lobsters shared the general acoustic and morphological
features as reported in other palinurids (Panulirus argus, Palinurus
elephas and Panulirus longipes)
(Fig. 4)
(Meyer-Rochow and Penrose,
1974; Meyer-Rochow and
Penrose, 1976; Patek,
2002; Patek and Oakley,
2003; Phillips et al.,
1980; Smale,
1974). The medial–lateral ridges present on each shingle in
P. interruptus were similar to other Panulirus species
(Meyer-Rochow and Penrose,
1976; Moulton,
1957; Moulton,
1958; Patek,
2002), although they are not present in Palinurus
(Patek, 2002) or
Puerulus species (S.N.P., personal observations). These surface
asperities are likely to increase the friction between the plectrum and file
surfaces compared to the smooth shingle surfaces of other palinurids. The
plectrum ridges appeared to be derived from setae, given that the posterior
limits of the plectrum ridges were constructed of fused setal bases
(Fig. 4E). The acoustic signal
features of P. interruptus were in the range of other spiny lobsters
(Patek and Oakley, 2003) with
short duration pulses (7.9 ms) and moderate pulse rates (90 pulses
s–1).
Given the basic principles of stick–slip friction, can lobsters
behaviourally control acoustic signal features and does variation in shingle
anatomy across species lead to differences in stick–slip acoustics? One
possible avenue for control of the system is through plectrum velocity and
normal force. The plectrum is moved over the file via a tonic
contraction of the promoter muscle, which extends from the base of the
antennae to the dorsal cephalothorax
(Patek, 2002;
Paterson, 1968). A series of
depressor muscles rotate the antennae ventrally and a lateral levator muscle
attaches to the lateral edge of the antennae and extends to the ventral
surface of the cephalothorax (Patek,
2002; Paterson,
1968). In addition to the promoter muscle, the lateral levator
muscle is often activated during sound production
(Patek, 2002;
Paterson, 1968). Thus,
variation in plectrum velocity and normal force is likely to be mediated by
the promoter and lateral levator muscles. In particular, the promoter muscle
has two lobes, which cover a substantial area of the dorsal and lateral
cephalothorax. Differential activation of these lobes may vary plectrum
velocity and load.
Plectrum velocity varied substantially in both the analyses of sound production in live animals and in the friction experiments. Together, these two sets of experiments shed light on the relevance to sound production and mechanical causes of this variability. Although the constant stage velocity (10 cm s–1) matched the average plectrum velocity (11 cm s–1) in live animals, the variation in velocity in both systems was fairly extreme, ranging from 7 to 76 cm s–1. The fact that the stage velocity was held constant, yet the plectrum still slipped at such a wide range of velocities, suggests that the variation in plectrum velocity and correlated acoustic amplitude observed in live animals may not be under direct control by rates of muscle contraction and may instead be a product of the stochasticity of oscillating stick–slip systems.
An alternative explanation for the correlation between plectrum velocity and acoustic amplitude in live animals is suggested by the positive correlation of plectrum velocity and normal force in the friction experiments. This correlation implies that if pulse amplitude is controlled by muscle contractions, and is not a stochastic effect of the mechanism, increasing the normal force between the plectrum and file may increase the acoustic amplitude. Changes in the relative contraction amplitude of the lateral levator or the lateral and medial lobes of the promoter muscle may alter the normal force between the plectrum and file.
The rate of stick–slip cycling (equivalent to the acoustic pulse
rate) typically is attributed to the velocity of the driving surface
(Persson, 2000;
Scherge and Gorb, 2001). A
minimum velocity is required to establish a stick–slip behaviour and
characteristic frequency; after a maximum velocity is reached, the system
again ceases to operate in the stick–slip realm. Between these two
critical velocities, the stick–slip frequency typically increases with
velocity (Scherge and Gorb,
2001). We did not investigate the velocity limits between which
stick–slip occurs in this system, focusing instead on the approximate
range utilized by the lobster. However, within this range in our experiments,
the relationship between velocity and stick–slip frequency was
inconclusive, if not contradictory, between the live animal and friction
experiments. In future studies, it would be informative to expand the range of
stage velocities to explore this `space' of stick–slip behaviour and to
determine the extent to which lobsters can vary the acoustic pulse rate of
their signals by changing the plectrum velocity or normal force.
The other major avenue for varying acoustic signal features and
stick–slip behaviour is through the structural, frictional interactions
of the plectrum and file surfaces. The average µs of P.
interruptus was 1.7, which is in the same range as an elastomeric
material (e.g. rubber) interacting with a hard metallic surface
(1.0–4.0) (Ashby and Jones,
1996). Although we were unable to accurately measure
µk because of the beam resonances and changing velocity of the
two surfaces throughout the slip phase, we were able to characterize relative
changes in µ (Fig. 6). The
maximum change in µ averaged 1.1 and spanned a 30-fold range in values.
Thus, while the stick–slip cycling maintained a characteristic form
across the experiments (Figs 2,
6), the magnitude of the
transitions varied substantially.
Parallels between the friction dynamics of ant adhesive foot pads also have
been drawn with the friction behaviour of engineered rubber materials
(Federle et al., 2004); in the
ant system, µs was estimated at 2.2. Similar to the spiny
lobsters, a liquid layer was present in this frictional system; however, based
on their µs estimates, the surface asperities exceeded the
height of the liquid layer, such that the surface dynamics were determined by
the rubbery behaviour of the ant's foot pad rather than fluid dynamics. In
contrast, the dry frictional system of a heteropteran wing-locking mechanism
has an average µk of 0.1–0.2 when slid at a maximum
velocity of 18.6 cm s–1, to which the authors draw a
comparison with `Babbitt alloy sliding over steel'
(Goodwyn and Gorb, 2004).
The presence of saltwater in the spiny lobster system almost certainly
influences the surface dynamics and friction forces. Static friction between
elastic rubber balls and a smooth glass plate is correlated with the viscosity
of the films of water (thickness >10 nm) sandwiched between the two
surfaces (Roberts, 1971;
Roberts and Tabor, 1971).
Previous investigations have noted that rubber materials warp and conform to
the interacting surface (Ashby and Jones,
1996). This conforming process increases the overall contact area
between the two surfaces, which can either supersede the effects of a fluid
layer or simply add an additional variable to the surface dynamics
(Federle et al., 2004). Our
experiments were conducted in air, because of the considerable challenges of
constructing the friction measurement system for immersion in saltwater.
Although we took great care to saturate the surfaces with saltwater, it is
possible that the absence of the surrounding body of water affected our
friction measurements.
The soft, elastic tissue of the plectrum (Figs
1,
4) is likely to be the primary
site of elastic energy storage in this system. Release of stored elastic
energy occurs during the slip phase; it is also during this time that sound is
generated. Controlled engineering experiments of stick–slip dynamics
have shown that most of the stored energy is dissipated during the slip phase,
with a relatively small proportion released due to momentum transfer when the
surface sticks (Klein, 2007).
The spring constant of the materials in stick–slip systems is central to
their behaviour (Heslot et al.,
1994; Klein, 2007),
thus it would be informative to examine the material and mechanical properties
of the plectrum ridges.
Whether the stick–slip system in spiny lobsters can be attributed to
surface asperities, fluid dynamics at the surface interface, or emergent
dynamics of the elastic plectrum and stiff file materials (e.g.
Mahadevan et al., 2004) is not
yet known. The relative roles of friction and mechanical interlocking between
the file's shingles and plectrum surface should be evaluated. While the scale
of each slip by the plectrum (average 3.8 mm) far exceeds the scale of the
shingles (average 7.4 µm), it is possible that the mechanical connections
between the plectrum and shingles play an important role in mediating the
overall stick–slip behaviour of the system. Further investigation of the
microscopic asperities, material properties and surface interactions is needed
in order to fully characterize the influence of both the surface roughness of
the file and the fluid dynamics of the film of saltwater between the plectrum
and file.
Understanding and characterizing the dynamics of friction have presented longstanding challenges to engineers, musicians and biologists. The spiny lobster's use of stick–slip friction to generate acoustic signals offers an interesting example of a complex, stochastic, yet robust, biological system. Through the integration of physics, engineering and acoustics, new insights into the evolutionary history and mechanics of biological friction systems will continue to emerge.
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Acknowledgments |
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Footnotes |
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* Both authors contributed equally to this work 
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References |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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Ashby, M. F. and Jones, D. R. F. (1996). Engineering Materials 1, An Introduction to their Properties and Applications. Oxford: Butterworth-Heinemann.
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