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First published online December 14, 2005
Journal of Experimental Biology 209, 66-77 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.01969
Take-off and landing forces in jumping frogs
1 Department of Biology, University of Antwerp (UIA), Universiteitsplein 1,
B-2610 Wilrijk, Antwerpen, Belgium
2 Department of Movement and Sports Sciences, University of Ghent,
Watersportlaan 2, B-9000 Gent, Belgium
* Author for correspondence (e-mail: sandran{at}mail.uri.edu)
Accepted 3 November 2005
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Key words: locomotion, anura, frog, Rana esculenta, ground reaction force, jumping, spring-dashpot model
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;
Marsh and John-Alder, 1994;
Choi et al., 2000,
2003) and ground reaction
forces (GRFs) measured using a force plate (e.g.
Calow and Alexander, 1973;
Wilson et al., 2000;
Nauwelaerts and Aerts, 2003),
or (2) direct measures of jumping distance (e.g.
Wermel, 1934;
Zug, 1972;
Emerson, 1978;
Hirano and Rome, 1984;
Lutz and Rome, 1994;
Marsh, 1994). Although these
variables are considered appropriate as general performance parameters,
conceptual concerns arise when examining locomotion in an ecological context.
For instance, escaping from a predator means realizing a distance as large as
possible between predator and prey, as fast as possible. This implies that
factors other than jumping distance, take-off velocity or GRFs can become
crucial in saltatory locomotion. One of these factors is the larger landing
forces that inevitably result from increased take-off velocities and GRFs
during propulsion. Valuable time could be lost during damping of the impact
force and the recovery that follows. Simply jumping further by taking off
faster may not represent the optimal ecological solution. The idea that
recovery may be as important as take-off comes from the observation that
during endurance tests frogs seem to have a preferred jumping distance that
was smaller than their maximal jumping distance (S.N., unpublished data). This
observation led to the hypothesis that it may not be ideal to increase the
jumping distance beyond a certain limit because of its consequences on
recovery.
A jumping cycle can be divided into four sub-phases: propulsion, flight,
landing and recovery. To escape optimally, all phases must be of short
duration with large displacements of the center of mass (COM). Anurans take
off by extending their hindlimbs and using their forelimbs for landing. The
forelimbs touch the ground and form a pivot, about which rotation of the body
occurs. This can play a crucial role in supporting and stabilizing the frog as
it lands (Peters et al.,
1996). Since the forelimbs are considerably shorter than the
hindlimbs and provide less deceleration distance, impact forces on the front
limbs are expected to be high. The landing phase could therefore be a limiting
factor in the jumping capacity of a frog for jumps where the frogs remain
terrestrial. By determining the durations of the four sub-phases of a jumping
cycle, we will answer the following question: (1) what fraction of the total
locomotor cycle does the landing phase take up during saltatorial locomotion
in frogs? By recording the GRFs we can answer: (2) are peak landing forces
higher than peak propulsive forces in jumping frogs?
The forelimbs are not only used during landing
(Peters et al., 1996), but
also must perform a number of other functions. During feeding, they are used
to manipulate and bring prey towards the mouth
(Gray et al., 1997) and during
wiping behavior, forelimb movements help to protect the skin by keeping it
moist. To realize these functions, the forelimbs need to be flexible. During
the breeding season, male frogs use forelimbs in combat to repel rival males
(Peters and Aulner, 2000).
Males also grip females with their forelimbs during amplexus
(Duellman, 1992). This
activity demands strong isometric force production from the forelimb muscles
with the forelimbs in a flexed position. If the forelimbs also play a major
role during landing by damping the kinetic energy from the flight phase, the
extensor muscles of the forelimbs are expected to work as dampers. By flexing
the elbows, the impact forces can be reduced by increasing the braking
distance. Performing various tasks that have conflicting demands might
restrict the capacity of the forelimbs to perform landing effectively. By
recording the landing forces of jumping frogs and the timing of forelimb
action for a range of distances, we can answer an additional question: (3)
does stiffness of the arms increase with jumping distance? Lastly, based on
high-speed video recordings of the landing phase and predictions made by a
spring-dashpot model, we can answer the final question: (4) does arm angle at
touchdown influence the landing phase?
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Experimental set-up
The animals were placed upon a small force plate [AMTI MC3A-6-100, AMTI,
Watertown, MA, USA; Sensitivities vertical GRF (Fv)=1.35
µV/(V N) and horizontal GRF (Fh)=5.4 µV/(V N),
natural frequency 300 Hz] with a top plate of 11.7 cmx12 cm and were
induced to jump onto a second, larger force platform [AMTI OR6-6-2000;
Sensitivities Fv=0.08 µV/(V N) and
Fh=0.34 µV/(V N), natural frequency 1000 Hz] with a top
plate of 50.8 cmx46.4 cm. Some cross-talk always exists when using
strain-gauge type force plates, but the effect was minimized by including the
correction terms in the calibration matrix. Slipping was prevented by covering
the force platforms with water-resistant parquet sandpaper (P15U). To reduce
mechanical noise, the small force plate was placed in a plastic container
filled with wet sand. The two force plates were positioned 10-30 cm apart, to
ensure a full jump distance range. Both force plates measured the
three-dimensional GRFs during jumping. The output of the strain gauges was
sent to an amplifier and A/D converted at 1 kHz (AMTI MCA strain gauge
amplifier). Digital traces of the force platform and a signal from a LED
(light emitting diode), used to synchronise force measurements with video
recordings, were read into a PC. Forces were subsequently smoothed using a
fourth order zero phase shift Butterworth filter in a custom-made Labview
program.
We examined landing behaviour by videotaping the jumps (high-speed video camera, Redlake, MASD Inc., San Diego, CA, USA) at 250 Hz and zooming in on the second force plate. Simultaneous lateral and frontal views were obtained by placing a mirror at a 45° angle next to the second force plate. The propulsive phase was also visible in the mirror view. In order to obtain the total jumping distance for each jump, a Sony 50 Hz camera was placed above the set-up, in order to provide a simultaneous view on both force plates. The set-up was lit using a Tri-lite light (Cool Light Co., Inc., Hollywood, CA, USA; 3x650 W).
Five jumps for each animal, resulting in a total of 25 jumps, were selected for further analysis. The selection of the trials was made on the basis of the jumping distance, aiming to obtain the largest possible distance range for each animal.
Timing variables
Three key timing variables were obtained from the high-speed video
recordings: (1) timing of first contact of the arms with the force plate, (2)
timing of body contact with the plate and (3) timing of full recovery (i.e.
frog is back in launch position).
Force recordings and derived measurements
Horizontal forces Fh and vertical forces
Fv were plotted for each jump and the resultant force
Fr was computed. The angle of the resultant force was
calculated for both the propulsion and landing phases.
Force profiles were used to determine the durations of the propulsion, flight and landing phases. Landing was defined as the phase from the first contact on the force plate to the time when the vertical GRF equalled the weight of the animal. Recovery was defined as the phase between the end of landing, based on the force profiles, and full recovery, based upon the high-speed video recordings.
Accelerations in two directions were determined from the force profiles. To obtain vertical acceleration av, body weight BW was subtracted from Fv and divided by total body mass Mb. The first and second time integrals of the accelerations yielded the velocities vh and vv and the displacements d of the COM. Calculations for landing were done by starting with vh and vv at take-off, taking gravity into account (vv-gt, where g is the gravitational acceleration and t the duration of flight). Instantaneous power (P) profiles were calculated by multiplying force F by v. The time integral of the force profiles provided the impulses (I) and work (W) was obtained by integrating the power profiles. Total work for propulsion and landing was calculated by summing the absolute values of the maxima of the work profile in two directions. In addition, work done by only the forelimbs (Wf) was analysed separately.
Stiffness of the forelimbs Kf was calculated as GRF during landing (Fl,r) divided by resultant displacement of the COM (dr) during landing.
Muscle-specific mechanical power was calculated from the GRFs and divided by the forelimb muscle mass Mm,f, determined as a fraction of Mb (4%, measured on two dead animals). Similar calculations were done for the hindlimbs for propulsion (hindlimb muscle mass Mm,h taken as 15% of total Mb, measured on 40 dead animals as part of a different study; S.N., unpublished data).
Total jumping distance Dj was measured from the dorsal 50 Hz video recordings, by digitising the snout at the start and end of the jump using a NAC-1000 XY coordinator (NAC Image Technology, Inc., Tokyo, Japan) connected to a PC.
Spring-dashpot model
We used a simple model of a mass mounted on a linear spring and a
velocity-dependent dashpot to test the effect of arm angle 
f
at the moment of touchdown on the course of the consequent landing phase. Data
from a real sequence where the arms perform the whole deceleration action were
used to parameterize the model, i.e. to obtain stiffness and damping
coefficients. The simulation was ended when the mass was about 1 cm above the
ground surface, which coincided with the body making contact with the force
plate. The landing phase of the chosen sequence lasted 33 ms and ended with
the body COM positioned approximately 1 cm above the force plate with a
vertical velocity of zero. These landing conditions could be reproduced in the
model with a stiffness value K of 70 N m-1 and damping
coefficient c of 1.4 Ns m-1 with an arm angle of 125°
at touchdown, so these stiffness and damping coefficients were used in all
simulations. At touchdown, the model showed some residual
vh (about 50 cm s-1), which in reality would be
dissipated by frictional forces between body and the force plate surface, and
by deformation of the body. The high-speed video recordings showed that when
the forces become large, the body sometimes slipped forward during landing,
illustrating this phenomenon. The forces in the spring-dashpot were similar to
the GRFs measured in the real sequence: peak vertical force was approx. 3 N
(Fl,v,max) and peak horizontal force
(Fl,h,max) was approx. 2 N, and they both had decelerating
actions throughout the landing phase. The model was used to test the effect of
arm angle f, increasing f from 110 to
140° in 1° increments. Simulations were carried out for five jumping
heights between 0.20 m and 0.40 m and for five horizontal velocities between
0.73 m s-1 and 2.19 m s-1 (or the initial value,
determined from the real sequence; ±25% and ±50%).
High-speed video recordings
To test whether frogs optimise f according to the
spring-dashpot model, we recorded additional video material on the landing
behaviour of frogs using a NAC-1000 high speed video camera at 500 Hz. We
recorded a total of 90 landing phases from 11 frogs. These recordings were
used to obtain arm angles at touchdown and 25 ms prior to touchdown. The
change in position of the COM (calculated as the midpoint on a line drawn
between snout tip and cloaca) during this period of time (25 ms) was used to
estimate vh and vv at touchdown.
Height h was calculated from vv.
Statistical analysis
Peak forces Fmax were compared among phases
(propulsion-landing) and within phases using a paired t-test.
A correlation matrix of all selected variables with total jumping distance was built to test direct relationships. A second correlation matrix, with the peaks of all measured forces, was used to test within-phase (propulsion and landing) and between-phase relationships. In addition, a third correlation matrix was built to detect correlations between the durations of the four sub-phases of a jump.
We found two types of force profiles during landing, depending on whether the peak force was mediated by only the forelimbs or by a combination of forelimbs and trunk. We used a t-test to test for differences in peak forces and jumping distances between the two types of profiles.
To test whether frogs adjust their arm angle at touchdown, linear regressions were performed on arm angle vs height and vs horizontal velocity.
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N and
N, P=0.494). Propulsion lasted on average 0.187±0.008 s. After
the flight phase (
s), during which no GRFs are recorded, the landing phase
(
s) was initiated
by the arms touching the force plate. Peak landing forces
differed significantly from
propulsive forces (P<0.001) and were about three times greater
than propulsive forces
(
N
and 
N). For landing forces,
differed significantly
from 
(P<0.001). The end of the landing phase was defined as the moment
when horizontal forces become small and the vertical GRF
(Fv) was approximately equal to weight (BW). This moment
coincided with the start of the recovery phase
(
s), the end of
which was determined by high-speed recordings. On average, the duration of
landing and recovery comprised 38±4% of the total cycle.
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were
reached while only the arms were in contact with the force plate. The timing
of body contact in a type II profile preceded the timing of
. Forces were on average higher in
type II profiles, but this did not correspond to a large difference in jumping
distance (Table 1).
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For the experiment in which GRFs were recorded, jumping distances Dj ranged between 0.32 m and 0.76 m. These distances were distributed equally over the five frogs and within each frog's jumping distance range. For the arm angle experiment, the animals jumped distances between 0.04 m and 0.79 m.
The angle of Fp (p,r) was fairly
stereotyped (Fig. 2). At the
start of propulsion phase, the resultant GRF (Fr) was
directed at an angle of 88° to the horizontal (viewed from the right).
p,r decreased exponentially to around 50°, after which
it increases again to an angle between 51° and 75°. At this stage, the
forces became so small that the angle calculation became unreliable and
usually dropped sharply to zero. In seven sequences, the angle profile
decreased almost linearly from 88° to a value between 40° and 60°.
However, we could not detect any differences between these seven sequences and
the others, so we assumed that this slight difference in profile was due to
undetermined variation. Typically, the angle profile during landing
l,r had a U shape, with a plateau around 120° and the
edges increasing steeply. The timing of the angle and magnitude of the GRF in
relation to the posture of the animal is exemplified in
Fig. 3 (propulsion) and
Fig. 4 (landing). As previously
stated, the forces during propulsion were stereotyped, while there was
considerably more variation in the landing force profile.
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A correlation matrix was built using the peak forces of the force components during both propulsion and landing (Table 2). Both within-phase correlations and between-phase correlations were expected between the horizontal and vertical components. Apart from the expected correlations that would occur in a purely elastic, passively behaving structure like a forward bouncing ball, Fp,v,max also correlated significantly with Fl,h,max.
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There were no significant difference in impulses of propulsion and landing,
although mean impulse I during landing was mathematically smaller in
both directions.
(
Ns
vs 
Ns;
Ns
vs 
Ns).
Power and work profiles for propulsion and landing were calculated for each
sequence (Fig. 1). In absolute
values, peak power was on average higher during landing in both directions:
W
vs 
W and
W
vs 
W.
The values were negative for the landing phase because the energy was absorbed
during this phase. Absolute total work was slightly larger during landing as
opposed to the total work of propulsion, due to larger vertical work during
landing. On average,
J and
J,
while the corresponding values for landing were
J and
J. The work
delivered by the front limbs was on average
J
and 
J, which meant that the front limbs delivered 55±20% of the total
negative work in the direction of the movement and 78±22% of the total
vertical negative work. Muscle mass specific power for propulsion was on
average 195±16 W kg-1 and maxima up to 338 W
kg-1; for landing the muscle mass specific power was on average
-2292± 218 W kg-1 with maxima up to -5000 W
kg-1.
Mean stiffness of the hindlimbs 
during propulsion was on average 14±1 N m-1, while mean
front limbs' stiffness 
was on average
100±5 N m-1.
Changes with jumping distance
To determine which variables change with distance, a correlation matrix of
all variables was built (Table
3). The Fp,h,max increased with total jumping
distance while Fp,v,max remained constant over the range
of jumping distances. In contrast, both Fl,h,max and
Fl,v,max increased with jumping distance. More positive
Wp,h and more negative Wl,h,f were
delivered with increasing distance. Stiffness of the arms
Kf was constant over the jumping distance range.
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Correlations within the phase durations and with distance Dj are shown in Table 4. There was a significant positive correlation between the duration of propulsion and the duration of landing. This was due to a shared negative correlation with jumping distance. Flight duration was positively correlated with distance. Finally, the duration of recovery was only correlated with Fh of landing (not shown).
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Effect of arm angle
A lateral view of the path of the model mass at landing is shown in
Fig. 5 for three simulations
with different arm angles. Fig.
5A, with the arms at an angle f of 125° from
the horizontal, is based upon a real sequence in which the data were used to
tune the model (see Materials and methods). The spring-dashpot becomes shorter
and rotates to a vertical position during landing. To show the considerable
effect of the arm angle on the course of the landing, two scenarios are shown
where only the arm angle has been changed. An increase of the arm angle to
140° yields a totally different result
(Fig. 5B): the arms will rotate
in the opposite direction to the 125° scenario and impact velocity on the
body will be much greater, especially for the vertical velocity (1.5 m
s-1). Decreasing the arm angle to 110° results in a landing
where the arms will rotate over the vertical and will flip backwards, and
horizontal velocity will be high at body impact
(Fig. 5C).
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We also investigated the effect of changing the input parameters, height
and horizontal velocity, mimicking the effect of different take-off
conditions. The optimal angle at which the arms are best placed clearly
depends on these conditions. The optimal angle was defined as the angle for
which impact will be smallest, with impact being expressed as the velocity
squared (
) at the moment the mass
would hit the ground. This was done because landing means dissipating kinetic
energy. The corresponding angle at the point of intersection between
horizontal 
and vertical
was chosen as the optimal angle
(Figs 6 and
7). Varying the height of the
jump will principally influence the vertical velocity at impact, but
horizontal velocity will also be affected to a lesser degree
(Fig. 6). The optimal angle
decreases linearly with increasing height. The linear equation through these
data points can be used to predict the optimal angles over a wider range of
heights. We plotted the angles that were observed during additional high-speed
recordings of landing and superimposed the predicted equation for optimal
angle versus height (Fig.
6). There is considerable scatter in the measured data, but
f increased significantly with height (P=0.048),
but not with horizontal velocity (P=0.29). The predicted value of
f is an overestimation when height is taken as a crucial
factor (P<0.001, d.f.=89). On the other hand, when the optimal
angle is calculated from its relationship to horizontal velocity
(Fig. 7), the measured data do
not differ from the predicted data (P=0.45, d.f.=89).
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). The GRF decreases rapidly during the roll-off of the digits
(the metatarsals and the phalanges). The horizontal force pattern is similar
to the force profile of a jumping galago
(Günther et al., 1991).
The vertical force profile, however, is different because it is more
symmetrical. Both species (Rana and Galago) do not use a
countermovement while jumping, making the first part of the force profile
similar.
Halfway through the propulsion phase, the GRF runs behind the centre of
gravity, building up an angular impulse that results in a clockwise angular
momentum at take-off (looking at an animal that jumps from left to right). Due
to conservation of angular momentum, the body rotates around its centre of
gravity during flight. This makes the frog land on its forelimbs instead of
its hindlimbs. In Galago, this mid-air rotation is avoided by
dorsi-flexion of the tail, which counterbalances the torque of the trunk's
inertia (Günther et al.,
1991). The fact that there is considerable variation in landing
forces probably means that the frogs are not always performing the landing
phase optimally, causing the landing phase to be less predictable, although we
could detect some general patterns.
What fraction of the total locomotor cycle does the landing phase take up during saltatorial locomotion in frogs?
Landing and recovery phases together comprise more than one third of the
jumping cycle during which the frog is essentially not moving forward.
Combined with the one third that is taken up by the flight phase, the
saltatory way of locomotion may cause the frog's trajectory to be highly
predictable and therefore easy to intercept by a predator. Taking smaller
jumps can increase the maneuverability because the animal would be able to
change direction during the propulsive phase and would, in theory, spend less
time on the same spot during landing and recovery. However, the frogs do
decrease landing duration when they jump further, suggesting that they are not
working against their limits to damp the kinetic energy from flight and they
are motivated to decrease all phase durations. The duration of recovery was
not correlated with distance, but was correlated with
during landing, which does suggest that a larger jump will take up more
recovery time if the arms are not placed optimally (see further).
Are landing forces larger than propulsive forces in jumping frogs?
Peak landing forces are on average almost three times larger than
propulsive forces and landing phase duration is more than two times shorter.
Both peak forces are probably overestimations of the maximal forces in the
field because muddy surfaces decrease the peak forces through damping.
Compliant surfaces are known to decrease the vertical force peaks through
energy absorption (Demes et al.,
1995; Giatsis et al.,
2004). When we normalize the force data by dividing the forces by
total BW, we obtain a 2.7 factor for the propulsive forces, similar to the
3.5xBW reported by Hirano and Rome
(1984). The normalized landing
forces amounted to 9.2xBW. Only studies on primates
(Demes et al., 1995;
Demes et al., 1991) and birds
(Bonser and Rayner, 1996) are
available for comparison of the landing forces. Although take-off forces for
birds are in a range similar to the frogs' propulsive forces, their landing
forces are much smaller (1.8xBW). Birds are capable of altering their
landing mechanics with their wings (Green
and Cheng, 1998). Primates, on the other hand, attain much higher
forces during take-off (9.6-10.3xBW), but have lower landing forces
(6.7-8.4xBW: Demes et al.,
1999). It has been stated that primates change their posture
during flight to improve aerodynamic performance
(Demes et al., 1991) and
possibly their landing conditions. Many primates and birds use the same limbs
for take-off and landing, making the potential acceleration and deceleration
distance the same. In frogs, the forelimbs are much shorter than the
hindlimbs. This means that the potential acceleration and deceleration
distance is different, causing the landing forces inevitably to be larger if
propulsion and landing have the similar duration.
Does stiffness of the arms increase with jumping distance?
Since the stiffness of the arms Kf stays constant over
the full jumping range, it is possible that this is a limiting factor in the
ability of the forelimbs to work as dampers. Human legs and other mammalian
locomotor limbs also maintain a constant stiffness, regardless of speed during
normal running (Glasheen and McMahon,
1995; Farley et al.,
1993), but the stiffness of the leg spring doubles when humans hop
in place at different frequencies (Farley
et al., 1991). Because of the constant stiffness regardless of
speed, the forelimbs of a frog can be regarded as locomotor limbs, unlike the
human arm that operated differently by increasing its stiffness with speed
(Glasheen and McMahon, 1995).
Limb stiffness depends on the torsional stiffnesses of the joints and the
geometry of the musculoskeletal system
(Farley et al., 1998;
Ferris and Farley, 1997). It
is also affected by muscle activation (Morasso et al., 1999) and GRF alignment
(Farley et al., 1998). In our
definition of stiffness, we used the resultant GRF. This force does increase
with jumping distance, so the arms compress more with distance. This is easy
to achieve by bending the elbows outwards. There is, however, a limit to how
much they can bend before the frog's trunk hits the ground. By controlling arm
stiffness, frogs can absorb the first impact peak with their forelimbs.
However, this is limited by forelimb length and, during long jumps, the
highest peak will be absorbed by a combination of forelimbs and trunk. In
addition to elbow flexion, the pectoral girdle is probably used as a damper.
In frogs, the scapula is divided into two parts. The two scapula parts
articulate through a joint that could contribute to damping during landing. In
addition, the upper part (suprascapula) is mainly cartilaginous
(Shearman, 2005). Ranids have
a firmisternal pectoral girdle in which the epicoracoids are fused
midventrally. It has been hypothesized that a firmisternal girdle is less
useful for landing than an arciferal (overlapping halves) girdle because the
cartilages rotates in the horizontal during landing in the latter girdle,
allowing the animal to decelerate over a greater distance
(Emerson, 1988). However, the
coracoid of the firmisternal girdle was not found to be loaded anywhere close
to the breaking strength of the bone and seems to perform as well as an
arciferal girdle (Emerson,
1983). Also, no correlation was ever found between pectoral
morphology and jumping ability in frogs
(Emerson, 1984). A thorough
comparative functional morphological study during landing in frogs seems to be
necessary to further elucidate the function of the pectoral girdle.
Maximal power generated by the hind limb muscles exceeds 300 W
kg-1 muscle, which is near the theoretical maximum, meaning that
all the muscle fibers of all hind limb muscles should be recruited and
contributing directly to the mechanical power, unless some form of power
amplifier is present. It has been hypothesized that these supra-maximal powers
result from the rapid release of strain energy from elastic elements
(Marsh, 1999;
Roberts and Marsh, 2003). Such
power amplifiers have been shown in other animals
(Aerts, 1998;
Bennet-Clark, 1975) and usually
rely on a preloading of elastic components by muscular action
(Roberts and Marsh, 2003),
causing muscle tension to built up followed by a rapid release and a sudden
increase in velocity and therefore in power. The maximal powers generated
during landing are even more extreme. Since the muscles work eccentrically
during braking, the muscle specific power output is expected to be 1.5-2 times
higher (Rijkelijkhuizen et al.,
2003; James et al.,
1996) than the power output during concentric work. Our data far
exceed this maximum. Rotational stiffness was not considered. The protactor
muscles in the forelimbs are very small and we therefore assume that most of
the damping was done passively. The high power output, together with the fact
that stiffness does not increase with jumping distance, seems to confirm the
presence of a passive viscous damper that can either be the pectoral girdle
(see earlier) or the frog's body through deformation.
Does arm angle/position at touchdown influence the landing phase?
If the take-off and landing conditions are the same, as for a bouncing
elastic ball, we would expect there to be correlations, due to ballistics,
between the force components of the same direction because the angle of the
GRF during take-off would be complementary to that for landing. Although these
correlations are observed in jumping frogs, the unexpected, additional
correlation between the Z-force of propulsion and the
Y-force of landing indicates that this landing angle of the GRF is
actively changed. The angular momentum and the difference in stiffness between
the front- and hindlimbs are the most plausible causes of this angle change.
The role of the front limbs during landing proved to be considerable. Two
types of jumps were observed, depending on whether the impact peak was
mediated by the arms or by the body. Although the peak forces were on average
larger when the body mediated the forces, no clear arm function limits could
be detected in peak force, power or work. A mechanical limit is highly likely,
but could be hard to detect because of its interaction with the positioning of
the arms. The spring-dashpot model shows a spectacular effect of arm angle on
the course of the landing phase (Fig.
5). In the simulation that was based on a real sequence, landing
with an arm angle of 125° caused a rotation of the arm during landing to a
vertical posture at body contact, purely due to the spring-dashpot action.
Positioning the arms at an angle of 110° or 140° at touchdown results
in a higher impact and a body posture with the arms flapped backwards and
forwards respectively, thus hampering recovery. Frogs increase the arm angle
with the height of the jump. When we define the optimal angle as that for
which the kinetic energy at the moment of body contact is minimal in
horizontal and vertical directions, the optimal arm angle is found to increase
with horizontal velocity and to decrease with height. The measured arm angle
of the landing frogs follow the predictions of the optimal arm angle
calculated from the horizontal velocity. Avoiding remainders of horizontal
kinetic energy at body contact, that would have to be cancelled by frictional
forces, seems to be of major importance.
f
h
f
r
p,r
l,r
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Acknowledgments |
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References |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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Aerts, P. (1998). Vertical jumping in Galago senegalensis: the quest for a hidden power amplifier. Phil. Trans. R. Soc. B 353,1607 -1620.[CrossRef]
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