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First published online July 17, 2009
Journal of Experimental Biology 212, 2426-2435 (2009)
Published by The Company of Biologists 2009
doi: 10.1242/jeb.026880
Dynamics and kinematics of ant locomotion: do wood ants climb on level surfaces?
Freidrich-Schiller-University, Seidelstr. 20, Jena, Germany
* Author for correspondence (e-mail: lars.reinhardt{at}uni-jena.de)
Accepted 16 May 2009
| Summary |
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Key words: Formica polyctena, arthropods, ground reaction force, locomotion
| INTRODUCTION |
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|
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Comparatively slow walking insects such as stick insects
(Graham and Cruse, 1981
), leaf
beetles (Pelletier and Caissie,
2001
) and locusts (Burns,
1973
; Duch and Pflüger,
1995
) display an alternating tripodal gait. This is also true of
cockroaches at higher running speeds
(Delcomyn, 1971
). To
distinguish between the two categories Seidl and Wehner
(Seidl and Wehner, 2008
)
describe two basic forms of insect locomotion. The first mode, largely relying
on sensory feedback, is well known from the slow moving stick insect
Carausius morosus (Cruse,
1979
). The second type, known from faster moving cockroaches, is
characterized as a dynamically stable bouncing gait
(Full and Tu, 1990
;
Full and Koditschek, 1999
).
Several studies substantiate the notion that locomotion in arthropods follows
the same rules as those observed for a wide range of terrestrial vertebrates.
In eight-, six-, four- and two-legged animals ranging in size from cockroaches
to humans, the force patterns were found to be consistent with a simple spring
loaded inverted pendulum (SLIP) model. This model describes the general
mechanics of the centre of mass (COM) during dynamically similar types of
locomotion such as running, hopping or trotting, in the sagittal plane
(Blickhan and Full, 1993
).
Schmitt et al. (Schmitt et al.,
2002
) developed an analogue model for the horizontal plane –
the so called lateral leg-spring (LLS) model. This has been validated with
experimental data from the cockroach Blaberus discoidalis
(Full and Tu, 1990
). Both
models are based on a typical time course for the resulting ground reaction
forces. During a complete stride at slow running speed a sinusoidal pattern is
expected, oscillating with the stride period around the net load in both a
vertical (body weight) and a lateral direction. At higher speeds of locomotion
the animals only remain in contact with the surface for a fraction of the
natural period of the system. A sinusoidal trajectory with a negative
(braking) momentum at the beginning and a positive (accelerating) one at the
end is expected in the fore–aft force
(Blickhan and Full, 1993
;
Schmitt et al., 2002
).
As mentioned above, cockroaches use an alternating tripodal gait when
running or trotting (mean speed: 35 cm s–1). In fact, the sum
of the ground reaction force components from the three synchronously acting
legs (total force) complies with the conditions of the SLIP and the LLS. All
active legs generate rather similar, outwardly directed, forces during one
tripod. Consequently, the centre of mass is pushed to the side, where only the
middle leg supports the animal. Similar to the lateral force component, the
vertical one also describes a roughly parabolic curve progression for each
leg. Consequently and in agreement with the SLIP model, the time course of the
total force component in this direction is also unimodal. In the direction of
motion the negative horizontal force of the front leg is approximately
cancelled out by the positive contribution of the hind leg. Only the
sinusoidal course of the middle leg remains to constitute the fore–aft
component of the whole system (Blickhan and
Full, 1993
). During running then, the total force equates to the
expected sinusoidal pattern. Kinematic analysis of ant locomotion reveals
similarities to cockroaches. According to Zollikofer
(Zollikofer, 1994
)
Formica ants trot with comparable velocities and the same gait
pattern (tripod). Formica pratensis for example moves with about 9
body lengths s–1 (Weihmann and Blickhan, 2009). This is
exactly the average relative speed reached by Blaberus discoidalis in
the experiments described by Full and Tu
(Full and Tu, 1990
). Although
similarities in terms of running velocity and gait pattern are obvious,
differences in movement control do seem to occur. Evidence suggests that both
types of movement control described above are used within the subfamily
Formicinae. There are species adapted to fast running across flat terrain and
others that negotiate their rugged habitat mostly by scrambling. Recent
kinematic studies have revealed differences between Cataglyphis and
Formica pratensis despite their kinship, similar anatomy and similar
sensory configuration (Weihmann and Blickhan, 2009). The high relative
velocity of Formica ants [according to Sponberg and Full
(Sponberg and Full, 2008
), the
influence of control and feedback loops is limited] and the rhythmic
fluctuations of the COM which occur in this species point to a cockroach-like
type of locomotion (Seidl and Wehner,
2008
; Weihmann and Blickhan, 2009).
Weihmann and Blickhan (T.W. and R.B., submitted) demonstrate that wood ants
do not make larger posture adjustments to inclines than the desert ant
Cataglyphis fortis, and postulate that wood ants always try to find a
secure foothold on the substrate, as do chameleons
(Higham and Jayne, 2004
).
Our aim was to analyze whether the similarities to cockroach locomotion
found in the kinematics of ant locomotion are also reflected in the ground
reaction forces, or whether a permanent clinging to the substrate can be
detected despite higher relative velocities than those reached by chameleons
or stick insects. The first experiments were conducted in the horizontal plane
to permit a comparison with previous studies
(Full et al., 1991
). In order
to answer the questions we have set ourselves we built a miniature force plate
to measure ground reaction forces in the micronewton range. For the first
time, we are able to resolve three-dimensional forces during free locomotion
of very small insects (body mass ca. 10 mg).
| MATERIALS AND METHODS |
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Force plate
As no three-dimensional (3-D) force platforms with micronewton resolution
are commercially available, the measurements required the development of a
custom-built device. This platform consists of a cross of four horizontal
beams fixed to a metal frame (Fig.
1A). These bars (cross) take up the vertical component of the
force. In the centre of the cross two orthogonally oriented bars are mounted
for transmitting the two horizontal forces (anterior–posterior,
lateral). At the end of the beam, a square tread is attached (side length 4
mm). This design minimizes weight and allows for the attachment of small
semiconductor strain gauges. Selection of suitable materials (PVC) allows for
a sufficiently high natural frequency (lowest component: 280 Hz; critically
damped). Contact times of the investigated runs amounted to 61.7±15.2
ms (mean ± s.d.). The ant's footfall position was measured from a
synchronous high-speed video recording of the runs. We analyzed runs in which
only a single leg stepped onto the force plate. The unamplified sensitivities
of the plate are given in Table
1 together with the residuals of humming and noise remaining after
the filter process (analogue 2 pole low pass at 300 Hz). The signals were
amplified (factor: 60000) using a commercial amplifier (Vishay 2100, Micro
Measurements; Vishay Electronic GmbH, Selb, Germany) and a custom-built
amplifier. Forces applied to the plate via a needle mounted onto a
sensitive bending bar allowed calibration. Owing to the design of the force
plate, crosstalk could not be completely eliminated. Without any mathematical
corrections this influence could reach values up to 30%. By taking into
account the point of force application with an accuracy of 0.1 mm, the maximum
crosstalk effect could be reduced to 4–6%.
|
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Video analysis
Runs were recorded using a high-speed video system (HCC-1000, VDS
Vosskühler GmbH, Osnabrück, Germany) with a resolution of
1024x512 pixels and a sample rate of 922 frames per second. A mirror
provided a side view (Fig. 1B).
The camera was mounted perpendicularly at a distance of about 15 cm above the
running track. The images were digitized using commercial software (WINanalyze
v2.1; Mikromak®; Berlin, Germany) and were used to select suitable runs
(typical movement pattern, straight runs, constant speed). Only trials in
which the ants ran straight along the path without touching the walls were
evaluated. To ensure that the laboratory animals have to run straight the test
canal were very narrow (15 mm; Fig.
1B). Speed was determined by analyzing four consecutive step
cycles with the step on the plate in the central segment.
System of coordinates
As we only analyzed straight runs along the direction of the force
platform, the animal-fixed system of coordinates was valid for both the
kinematic and dynamic investigations (Fig.
1C). The y-axis is parallel to the animal's long axis in walking
direction. The x-axis is laterally to the right, parallel to the substrate,
and the z-axis is perpendicular to the xy-plane. Positive ground reaction
forces in the forward direction (Fy) accelerate the
animal. Positive lateral forces (Fx) accelerate the animal
to the right, and positive vertical forces (Fz) push the
animal upwards. We do not distinguish between left and right legs. All results
on the left side are mapped to the right. Correspondingly a positive forward
force observed for the front leg implies pulling and negative force implies
pushing. For the right middle leg a positive lateral force implies pulling,
and for the hind leg a positive forward component implies pushing.
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| RESULTS |
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Points of touchdown of the legs
During contact, the tarsi moved almost parallel to the long axis of the
animal's body (Fig. 3). The
lateral distance of the start and end values, with respect to the petioles
[about centre of mass; see Zollikofer
(Zollikofer, 1994
)], did not
differ (t-test, P>0.05;
Table 2). The front legs
contacted the ground closer to the body axis (xtd=2.21 mm)
than the middle and hind legs (5.25 mm and 4.03 mm). Touchdown occurred
anterior to the petiolus for the front and middle legs
(ytd=5.39 mm and 3.00 mm) but posterior for the hind legs
(–2.97 mm). Although the front and hind legs stayed anterior or
posterior to the petiolus, respectively, the middle leg switched side and was
lifted off posterior to the petiolus (–1.83 mm).
|
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The distance covered in direction of the long axis (
y;
Table 2) was shorter for the
hind legs than for the front and middle legs (Tukey's test,
P<0.05). The high-speed video recordings confirmed that after
complete extension, the hind legs were dragged along and did not change their
position with respect to the body. This peculiarity is also supported by the
force recordings described below. Contact times on average amounted to
61.7±15.2 ms (mean ± s.d.). There was a slight but not
significant tendency towards shorter times from the front to the hind legs. In
agreement with the findings of Seidl and Wehner
(Seidl and Wehner, 2008
), all
observed ants ran with a tripod gait. Our results can be explained by the
function and arrangement of the different legs. Front legs contribute to
propulsion largely by flexion, whereas hind legs do this by extension. Middle
legs generate thrust by leg rotation.
Dynamics
Ground reaction forces
The force patterns were variable. Nevertheless, a basic pattern emerged
that differed from previous findings in other walking and running insects.
|
Middle legs
The lateral component of the ground reaction force (Fx)
of the middle leg (Fig. 5) had
a sinusoidal time course similar to that observed for the front leg, but
forces changed sign at about the middle of the stance. The negative maximum
(–41.4±20.0 µN) was reached after about 25% of the contact,
the positive maximum (26.1±14.6 µN) was reached after
66.2±8.0% of contact.
|
Hind legs
Forces observed for the hind legs were much more reproducible
(Fig. 6). All components showed
an unimodal time course. Laterally, after 47.1±12.5%, a minimum
(–17.6±8.2 µN) was reached. Anteriorly, after
42.5±10.2% of stance, the animal pushed with 29.1±6.4 µN.
Within the last third of the ground contact, a small negative force (pulling)
of about –8.8±5.7µN was observed. It results from dragging the
tarsi across the surface (see above). The vertical component
(Fz) has its maximum (44.4±13.1 µN) at about
44.1±11.4% of the contact time.
|
Table 3 shows the average extrema of the ground reaction forces and their relative times during stance phase. In all legs the vertical force component was dominant. Vertical load was about evenly distributed among the legs. There was no significant difference between the legs (ANOVA, P=0.29). The anterior forces were lower and less evenly distributed. The highest propulsive forces were generated by front and hind legs. The front legs strongly contributed to braking. Although the hind legs largely pushed outward, the middle and front legs pushed and pulled with about the same magnitude sideways.
|
More relevant than the peak forces are the net contributions to momentum by each leg (Table 4). In the vertical component there was no net difference with respect to leg number (ANOVA, P=0.67). Weight was thus evenly distributed among the legs. In the direction of locomotion, the front and hind leg both contributed considerably to propulsion whereas the contribution of the middle leg was negligible. Here the braking and accelerating segments cancel each other out. With respect to the lateral component the tripodal walking pattern must be taken into account. Above we mapped all forces measured for the left legs to the right legs of the body. Within the tripod the left middle leg generates forces in concert with the right front and hind legs and vice versa. The momentum of the right hind leg pushing the animal to the left was largely compensated by the sum of the momentums generated by the right front leg and the left middle leg (Table 4).
|
Vectors of the ground reaction force
Figs 7,
8,
9 show projections of the force
vector during stance with respect to the body fixed (petiolus) co-ordinate
system (for convention see Fig.
1C). Here too, the forces generated by the tripod are depicted
(right front leg, left middle leg, right hind leg). Drawing the vectors in
that way helps to visualize the action of the ground reaction forces with
respect to the centre of mass.
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In the sagittal plane the projection of the ground reaction force of the hind leg reached a maximum value at 39% of contact time (time III, Fig. 8). Its orientation of 58 deg. with respect to the y-axis was largely maintained during stance. The vector of the ground reaction force of the middle leg roughly remained perpendicular to the substrate (y-axis) or parallel to the z-axis. In the first leg, orientation changed from braking to forward acceleration, as observed in the horizontal plane. The angle with respect to the y-axis shifted continuously during stance from 145 deg. to 0 deg. at the end of the stance phase.
In the projection into the transverse plane, again, the orientation of the
vector of the ground reaction force of the hind leg shifted only little. At
the instant of maximum force development (39% of contact time; time III,
Fig. 9), the angle with respect
to the x-axis amounted to 106 deg. and the vector clearly pointed above the
centre of mass. For the front and middle legs, the pattern observed in the
horizontal perspective was visible again. The vectors of the ground reaction
force were close to mirror-image symmetrical with respect to the zy-plane. At
the beginning of stance they pointed towards the centre of mass and then the
directions reversed. Although the angle included with the x-axis decreases
from approximately 120 deg. to 30 deg. for the front leg, this angle increases
about the same amount (
90 deg. from 60 deg. to 150 deg. for the middle
leg. For both legs the instant of the force maximum was observed again at
about 20% of stance (time I, Fig.
9).
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| DISCUSSION |
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As mentioned above, the net momentum in the lateral direction was zero, i.e. the animal maintained its straight path. As we had selected runs in which the animals maintained a constant speed, we would have expected the net anterior component of momentum to be very small, generating just sufficient thrust to overcome aerodynamic drag. However, air drag is negligible, because even with an overestimated drag coefficient of 4 and a frontal area of 12 mm2, the estimated drag force is only 0.3 µN. Thus, the measured forward momentum (1000 nN s–1, Table 4) is much larger than the braking momentum because of air drag (0.3 µNx60 ms=18 nN s–1).
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So far, comparable measurements in other ant species are not available. The
most direct comparison is possible with data on the cockroach Blaberus
discoidalis (Full et al.,
1991
). This insect also runs with an alternating tripod gait, but
it is about 250 times heavier (body mass
2 g) and runs about four times
faster than our ants (average speed 37.8 cm s–1).
The ground reaction forces in B. discoidalis differ from our
findings in several aspects (Fig.
12). With the exception of the fore–aft component
(Fy) of the middle leg, all forces were found to be
unimodal (Full et al., 1991
).
As in our study, the vertical forces were evenly distributed among cockroach
legs. However, the time course of the frontal and lateral components was much
simpler. Laterally all legs continuously pushed outwards. The front legs were
found to mainly decelerate, compensated by the propulsion generated by the
hind legs. In contrast to Formica ants, the abdomen of B.
discoidalis did not generate significant braking forces.
Although the relative speed was similar to our experiments with F.
polyctena, Kram et al. (Kram et al.,
1997
) found a significantly lower duty factor of 0.53 in
Blaberus discoidalis. This results in a negligible tripodal overlap.
The sum of the single leg forces of one tripod could be considered to be the
total force acting on the centre of mass. Full et al.
(Full et al., 1991
)
(Fig. 8) present a single
measurement in which a cockroach steps onto the platform with all three legs
in succession. These data were used to estimate that the sum of the mean
vertical force of one tripod only amounts to approximately 70% of the average
body weight. Assuming that these cockroaches do not drag their abdomen above
the ground, the subject's body weight in this single registration was clearly
lower than the specified mean value of 2.1 g.
The net pattern of ground reaction forces of the cockroach very much
resembles that observed for running, hopping and trotting vertebrates. This
can be described by a lumped parameter model, the spring loaded inverted
pendulum model (SLIP) (Blickhan,
1989
; Blickhan and Full,
1993
; Full and Koditschek,
1999
; McMahon and Cheng,
1990
). A planar version of the spring mass system can also be used
to describe the kinetics of locomotion of cockroaches in the horizontal plane
(Schmitt and Holmes, 2000
;
Seipel et al., 2004
). In
Formica the pattern of the lateral component of the ground reaction
force revealed small oscillations of higher frequency
(Fig. 10), which may represent
higher modes of oscillation of a spring mass model (cp.
Geyer et al., 2006
), but it
clearly differs from the observations in cockroaches. As pointed out above,
vertical oscillations take place in the ant. However, due to the influence of
the abdomen, the lumped parameter model may not be applicable to our present
data. The kinetics of many gaits is not sufficiently described by the spring
mass system (Blickhan and Full,
1993
). Examples are creeping, galloping and climbing. Formica
pratensis seems to adapt its kinematics only slightly when walking across
different slopes (T.W. and R.B., submitted). Wood ants adapted to structurally
complex substrates (e.g. forest floor, vegetation) may always tend to cling to
their substrate, in agreement with our measurements. After a short period of
deceleration, the ants pulled inward with both front and middle legs. This
allows secure attachment to the substrate with the aid of adhesive pads or
claws (Federle et al., 2001
;
Frantsevich and Gorb, 2004
).
On smooth surfaces, ants stick with their pretarsal arolium
(Federle et al., 2001
). In
Formica these pads are well developed
(Gladun and Gorb, 2007
). They
unfold on smooth substrates when the leg is pulling proximally. The thin fluid
film between arolium and substrate can compensate for small-scale surface
roughness and ensures an intimate contact between the viscoelastic cuticle of
the arolium and the substrate (Drechsler
and Federle, 2006
). Adhesive pads can achieve very high friction
forces (Federle and Endlein,
2004
; Federle et al.,
2002
).
Goldman et al. (Goldman et al.,
2006
) published single-leg force measurements for vertically
climbing Blaberus discoidalis. As expected, the force patterns
differed from those observed during locomotion on level ground (compare
Fig. 12), whereas the
kinematics did not. In contrast to level running, all legs generated
exclusively positive forces in the fore–aft direction to overcome
gravity. Additionally, the two forelegs pulled laterally towards the midline
to cling to the substrate. While the front legs pulled the head towards the
wall, the hind legs pushed the abdomen away from it. Our results for the later
stance phase of ants running on level ground show similarities to these force
patterns, which are mainly indicated by the positive Fx
values of the front and middle legs and the positive Fy
value of the front leg. Although differences are observable in the initial
stance phase and in the absolute values, the qualitative similarities to
cockroach climbing forces are greater than to those reaction forces generated
during level running (for a comparison, see above). We assume that the
dominating factor in the similar vertical force patterns is the direction of
the gravity vector, which also affects the other force components.
The activity of the hind legs seems to be independent of slopes and other influences. On upward slopes it always pushes against the substrate, generates propulsion and determinates the clearance. The only difference between hind leg activity in level and vertical locomotion in cockroaches is that the extrema of Fy and Fz are interchanged because of weight bearing caused by the directional change of the gravity vector.
Pelletier and Caissie (Pelletier and
Caissie, 2001
) provided evidence that pulling a load during
horizontal locomotion influences the speed of operation in a similar way to
the angle of the gravity vector during running on slopes. We therefore suppose
that the ant's gaster serves a similar role in the fore–aft direction as
gravity does during climbing.
As pointed out by Seidl and Wehner
(Seidl and Wehner, 2008
),
insects display two basic forms of locomotion: (i) slow locomotion largely
relying on sensory feedback, as in the stick insect Carausius morosus
(Cruse, 1976
), and (ii)
dynamically stable bouncing gaits, as in cockroaches
(Full and Tu, 1990
). Based on
kinematic observations, Seidl and Wehner assumed the latter for ants. This may
well be valid for the desert ant Cataglyphis. Formica polyctena seems
to bounce too, but the general dynamics are more complicated and no longer
described sufficiently by a simple spring mass model. To what extent this gait
is controlled by sensory feedback is not known and requires further
investigation. Formica employs a much higher cycle frequency (5 Hz at
9 cm s–1) than Carausius morosus (
2 Hz)
(Wendler, 1964
), but
neuromuscular signal transmission in the ant may be facilitated by short legs.
However, the mean speed reached by the ants in our investigation was 12 body
lengths s–1 higher than that observed for the cockroach (9
body lengths s–1) in the force analysis
(Full and Tu, 1990
;
Ting et al., 1994
) but lower
than the peak values observed for a cockroach running on two legs
(Full and Tu, 1991
). Compared
with the stick insect, the wood ant may be adapted to fast locomotion on a
variable and unstable substrate. This may be because of the relatively more
muscular coxae of the ants, which enable them to generate the necessary
propulsion forces.
The mechanical (non-neuronal) feedback available in spring-like
musculo–skeletal systems (Blickhan et
al., 2007
; Daley and Biewener,
2006
; Daley et al.,
2007
; Grimmer et al.,
2008
; Seyfarth et al.,
2002
; Sponberg and Full,
2008
) provides further stability and permits the unloading of the
neuronal control system during planar locomotion across rough terrain. Other
environments may require different measures to achieve a similar goal.
Sponberg and Full (Sponberg and Full,
2008
) proved the existence of self-stabilising mechanisms that are
independent of classical spring mass models (SLIP, LLS) in insects. For
example, no adaptations in leg kinematics or muscle activation could be
detected. It is probable, therefore, that certain habitat-specific mechanisms
lead to a dynamic stabilization of the locomotive system, as defined by
Grimmer et al. (Grimmer et al.,
2008
). The spiny legs of spiders and cockroaches, for example,
help to transfer forces and energy on a `gap-filled' terrain with rather
sparse footholds (Spagna et al.,
2007
) and enable the animals to uphold their motion pattern. It
remains to be shown in future studies whether the strategy of initial pushing
with the front legs offers an advantage for the species investigated within an
environment where slopes, solidity and roughness may differ considerably from
step to step.
The locomotion of ants is also relevant in the context of orientation.
Excellent and extensive information about ant orientation has been gathered by
Wehner and his co-workers. Experiments with Cataglyphis fortis proved
the existence of an internal navigation system
(Wittlinger et al., 2007
;
Müller and Wehner, 1988
;
Seidl and Wehner, 2008
;
Sommer and Wehner, 2004
). This
so-called path integrator performs some kind of vector analysis. Wohlgemuth et
al. (Wohlgemuth et al., 2002
)
demonstrated that this mechanism is used on flat surfaces and works just as
well for three-dimensional paths. However, Grah et al.
(Grah et al., 2007
) concluded
that Cataglyphis essentially represents its environment in a
simplified, two-dimensional fashion. Therefore, the ants must be able to
monitor and recalculate the influence of slopes. Here, the animals may make
use of graviception. Primarily the hair field mechanoreceptors at nearly all
joints of the insects provide this information
(Markl, 1974
) and their
stimulation depends on changes in segment angles. Similar information is
provided by chordotonal organs. In addition the campaniform sensilla are used
in this context as they detect strains in the exoskeleton of the legs and may
be important for slope detection. These sensors are affected by and depend on
changing load distribution among the legs
(Ehmer and Gronenberg, 1997
;
Weidner, 1982
).
This study provides the first ever information about force patterns during planar locomotion in wood ants. Contrary to expectations formed on the basis of other arthropod studies, the dynamics do not reflect the pure spring-like mechanisms suggested by the rhythmic oscillating type of COM kinematics. Although gravity presses the animal onto its support during level locomotion, the ground reaction forces have significant similarities to those involved in climbing and less to those at work in cockroaches running on a horizontal surface. There is evidence that the locomotion of wood ants is in fact a `climbing' style characterized by a permanent clinging to the substrate. Even though the ant's force patterns resemble those of both horizontal and vertical cockroach locomotion, we have to answer the question posed in the title with `yes'. Wood ants obviously climb on level surfaces. Similarities to horizontal cockroach locomotion, particularly remarkable in the vertical component of the ground reaction force, are probably caused predominantly by the formative direction of the gravity vector. Our results could be the starting point for future comparisons under variable loading and sloped regimes.
| Footnotes |
|---|
| References |
|---|
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