Three-dimensional hindlimb kinematics of water running in the plumed basilisk lizard (Basiliscus plumifrons)
Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
(e-mail: sthsieh{at}oeb.harvard.edu)
Accepted 18 August 2003
![]() |
Summary |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Kinematic variation among individuals was primarily related to size differences rather than sprint speed. Although basilisk lizards applied some of the same strategies to increase running velocity across water as other tetrapods do on land, their overall kinematics differ dramatically. The feet exhibit much greater medio-lateral excursions while running through water than do those of other lizards while running on land. Also, whereas the hindlimb kinematics of other lizards on land are typically symmetrical (i.e. limb excursions anterior to the hip are of similar magnitude to the limb excursions aft of the hip), basilisks running through water exhibit much greater excursions aft than they do anterior to the hip. Finally, ankle and knee flexion in early stance is a defining feature of a tetrapod step during terrestrial locomotion; yet this characteristic is missing in aquatic basilisk running. This may indicate that the basilisk limb acts primarily as a force producer as opposed to a spring element when locomoting on a highly damping surface such as water.
Key words: water running, hindlimb kinematics, bipedal locomotion, ontogeny, scaling, plumed basilisk lizard, Iguanidae, Basiliscus plumifrons
![]() |
Introduction |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Lizard locomotion has served as a model system for morphological and
functional studies because of the tremendous variation exhibited in life
history and growth patterns (Irschick and
Jayne, 1999). Although substantial descriptions of terrestrial
quadrupedal kinematics in lizards now exist
(Fieler and Jayne, 1998
;
Irschick and Jayne, 1998
,
1999
,
2000
;
Jayne and Irschick, 1999
;
Reilly and Delancey,
1997a
,b
),
very little is known about bipedal locomotion in lizards (except
Irschick and Jayne, 1999
).
Bipedality has evolved numerous times among lizards most notably among
those that live in sandy, rocky or open environments or lizards classified as
having semi-aquatic or semi-arboreal lifestyles
(Snyder, 1952
). Substantial
size variation also exists between juvenile and adult lizards
juveniles often increase in mass by as much as 50 times by adulthood
(Irschick and Jayne, 2000
).
How such a size difference affects locomotor capability is an issue of general
interest among physiologists and morphologists. Most of what is known about
the effects of size on limbed locomotion was derived from comparisons between
animals from wide-ranging phylogenetic taxa (e.g.
Alexander, 1977
;
Alexander and Jayes, 1983
;
Bertram and Biewener, 1992
;
Biewener, 1983
;
Cavagna et al., 1977
;
Farley et al., 1993
;
Heglund et al., 1974
). Far
fewer studies have examined ontogenetic effects on locomotion within one
species (Garland, 1985
;
Huey and Hertz, 1982
;
Irschick and Jayne, 2000
).
Although these studies have given valuable insight into how the mechanics of
motion change with size, they have all focused on movement over stiff
surfaces. A damping surface such as water exaggerates the effects of size on
motion because increased mass results in disproportionate increases in
energetic requirements. Whereas locomotion on stiff surfaces permits energy
storage in muscles and tendons, damping substrata dissipate this energy,
thereby requiring more energy to be expended with the subsequent step
(Lejeune et al., 1998
).
Aquatic locomotor capability among basilisks is size dependent; juveniles
more frequently run towards water to escape threats and appear to run through
water more easily than do adults (Barden,
1943; Laerm, 1973
;
Rand and Marx, 1967
). A
hydrodynamic model developed by Glasheen and McMahon
(1996a
,b
)
showed that basilisks are most constrained by their size-dependent ability to
produce forces on water. Large lizards can produce relatively much less of a
slap impulse than do small lizards. Additionally, all lizards are potentially
subject to hydrodynamic drag created by water surrounding their submerged
foot. Glasheen and McMahon
(1996a
,b
)
reported that the basilisks especially the large adults
extract their feet from an air cavity created during the stride, prior to
cavity collapse. This mechanism allows large lizards to minimize hydrodynamic
drag on the foot.
Even though the results from Glasheen and McMahon's studies give
substantial insight regarding mechanisms of water running, there were no
detailed descriptions of how basilisks move when running across water. The
only previously existing detailed basilisk water-running kinematics documented
several angular excursions of limbs
(Laerm, 1973), sprint
velocities (Rand and Marx,
1967
) and some qualitative descriptions of motion
(Barden, 1943
;
Laerm, 1973
;
Rand and Marx, 1967
). Two of
these three studies were based on observations in the field
(Barden, 1943
;
Rand and Marx, 1967
), and one
was based on two-dimensional data (Laerm,
1973
). Lizards are generally characterized as quadrupedal
sprawlers (Russell and Bels,
2001
). This limb posture forces lizards' limb movements to be
highly complex through space. Kinematic measurements in three dimensions are
therefore critical for accuracy.
The goals of the present study are: (1) to present the first detailed three-dimensional kinematic descriptions of basilisk water running; (2) to quantitatively examine the effects of size and sprint speed on water-running capability and (3) to compare these data from aquatic running with data on terrestrial lizard locomotion in the existing literature. I expected that large basilisks would sink deeper into the water as a result of their greater mass and therefore exhibit greater limb excursions along all three axes than would smaller basilisks. The concomitant increase in energetic requirements would thus limit larger basilisks to sprinting at a proportionately slower speed than do juvenile basilisks. As compared with terrestrial runs, basilisks should exhibit a more extended propulsive phase during aquatic running, so that more time during a stride would be dedicated to the generation of thrust and lift. Also, limb posture should be more crouched to enable greater force generation.
![]() |
Materials and methods |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
To assess how basilisks' shape changes with growth, I measured each animal's mass, snoutvent length (SVL), femur length, tibia length and foot length (defined as the distance from the heel to the tip of the fourth toe). Leg length (LL) was defined as the sum total of femur, tibia and foot lengths. To determine the mass of the tail relative to the total mass of the basilisk, the tails of three preserved striped basilisk (Basiliscus vittatus) specimens ranging in size from hatchling to adult were removed, just caudad of the cloaca, and weighed. In addition, two plumed basilisks (a juvenile and an adult) were sacrificed and their tails similarly removed and weighed. The relative mass of the tail in plumed basilisks coincided with that in striped basilisks. Longitudinal location of the basilisk's center of mass was determined by tying a thread around the body of a preserved specimen and repositioning the thread until the body balanced horizontally.
Experimental protocol
A 4.6 m-long water track was built by gluing together two 379-liter glass
aquaria that had the ends removed. A 0.2 m-long platform was glued to each end
of the track, 0.4 m above the bottom of the tank, with a hide box and heating
element placed at the left end (i.e. at the end of the run). Tanks were filled
with water such that each platform was flush to the water surface. All runs by
medium juvenile to adult animals extended the full length of the water track.
The track was shortened to 1.5 m for smaller juveniles and hatchlings (mass
<10 g). Axes were oriented such that the positive x-axis pointed
in the direction of travel, the positive y-axis pointed up and the
positive z-axis pointed to the left of the running lizards. A plastic
wall marked with a 2 cmx2 cm grid was mounted parallel to the front of
the tank such that it could be repositioned to narrow the width of the track.
All runs presented here represent the basilisks' preferred aquatic sprint
speed since it was not possible to control the speed at which the basilisks
ran (see Statistics section for more detailed discussion). The digitized
speeds for basilisks running across the water track in this study were within
the range of those speeds previously recorded in field conditions
(Rand and Marx, 1967).
Each run was filmed with two synchronized, high-speed Redlake PCI500 cameras (Redlake Imaging, Morgan Hill, CA, USA) operating at 250 frames s1 with a 1/1250 s shutter speed. Lizards took a minimum of three to four strides before entering the field of view, thus ensuring that basilisks were running at a constant speed. Each stride was represented by 2642 frames in each camera. Cameras were oriented such that one camera filmed the lateral view, and the other the dorsal view. Basilisks were placed on the platform on the right side of the track and encouraged to run by squeezing the base of the tail and tapping their back. Prior to each trial, eight landmarks were painted on each basilisk to facilitate digitizing (Fig. 1A). Four points marked the midline: between the eyes on the dorsum of the head (E), midway between the shoulders on the pectoral girdle (PC), midway between the hips on the pelvic girdle (PL) and midway between PC and PL on the midline (M). Four points marked the left hindlimb: hip (H), knee (K), ankle (A) and at the fourth metatarsalphalangeal joint, which will be referred to as the MP point or foot.
|
A run was deemed acceptable if the lizard ran truly bipedally such that its hands did not touch the water throughout the stride. Some leniency was granted for lizards weighing more than 60 g as they usually sank so far into the water that some contact of the hands with the water was inevitable. Among these heaviest animals, the run was accepted if the lizard's hands touched the water but it still kept its torso elevated above the water surface. For all lizards, regardless of size, runs were immediately discarded if the basilisk exhibited any clear breaks in motion (e.g. as a result of tripping), if any part of the limb or foot contacted any portion of the track's walls or if the lizard was running at a clear angle to the track (i.e. towards a wall). As a result of these selection criteria, out of the 30 animals filmed, only 11 of the runs from 11 animals were selected for data analysis each of the selected runs represents the only run analyzed from an individual lizard. The drawback of having so few acceptable runs was that the data could not be analyzed for individual variation. However, as a result of using stringent selection criteria, the data presented in this paper represent exclusively true bipedal water runs, and each data point represents a statistically independent event.
Direct linear transformation
The challenge of photogrammetric camera calibrations resides in accurately
relating two-dimensional camera images to actual three-dimensional space. This
is often not trivial because cameras being oriented slightly off-axis or lens
distortions caused by short filming distances or inconsistencies in
the lens (Hatze, 1988;
Hedrick et al., 2002
)
introduce errors into the final transformations. These errors are minimized in
most three-dimensional kinematics studies by limiting all motion to the center
of the field of view, such as on a treadmill or in a flow tank. As a result,
it is possible to simply overlay the xy and
xz coordinates from lateral and dorsal views to
obtain the three-dimensional coordinates. This study required fixed camera
locations with the basilisks passing through the field of view; as a result,
lens distortions at the edges of the field were problematic. To correct for
distortions, all digitized points were transformed into three dimensions using
a direct linear transformation (DLT) algorithm implemented in MATLAB (The
MathWorks, Inc., Natick, MA, USA) by Christoph Reinschmidt and Ton van den
Bogert of the University of Calgary (1997).
DLT is a technique in which 11 coefficients are calculated to correct for
linear forms of image distortion (Woltring
and Huiskes, 1990). These coefficients determine the positions of
the cameras relative to each other and a pre-set coordinate system. Once the
camera positions are known, a point seen in at least two cameras can then be
reconstructed in three-dimensional space. A minimum of 15 non-coplanar points
that maximally fill the area of interest is needed for this technique to work
properly (Reinschmidt and Bogert,
1997
). The calibration object was built from Duplo Lego
(Switzerland). Eighteen non-coplanar points were available on the calibration
object (0.27 mx0.10 mx0.15 m; length x width x
height), with a minimum of 16 non-coplanar points visible in both cameras. For
basilisks weighing up to 10 g, the calibration object filled the entire volume
of the recording space. Although the field of view was greater when filming
larger basilisks, the maximum field of interest measured 0.34 mx0.11
mx0.18 m (length x width x height); so the calibration
object always filled at least 80% of the recording space.
Kinematic variables
For ease of analysis, I divided each stride into four phases based on the
primary direction of motion of the MP joint
(Fig. 2), similar to those
defined by Glasheen and McMahon
(1996a,b
).
The slap phase began when MP first contacted the water, moving primarily
downwards (negative y-direction). The stroke phase began when MP
moved in the negative x-direction (opposite to the running
direction). Recovery up was defined as when MP began moving upwards such that
part of this phase is completed under water and part of this phase is
completed through the air. Recovery down completed the stride cycle, beginning
when MP started moving down and ending at the start of the next slap phase. As
compared with terrestrial locomotion, the slap and stroke phases appear to be
functionally equivalent to the stance period, whereas the recovery up and
recovery down phases appear to be equivalent to the swing period.
|
As a result of the extremely complex limb movement during water running, a
large number of variables were necessary to clearly describe limb positions
and motion. All kinematic variables, unless otherwise specified, were measured
in three dimensions. Angular data were calculated with a custom MATLAB program
and analyzed in Microsoft Excel. Digitizing error was calculated to be between
±0.2 mm for points that were never submerged through the stride and
±0.5 mm for points that were submerged in water, and therefore more
difficult to digitize. For each trial, I calculated a series of variables
describing the linear and timing characteristics of a stride, based upon
previous studies of terrestrial kinematics
(Fieler and Jayne, 1998;
Gatesy and Biewener, 1991
;
Irschick and Jayne, 1999
,
2000
;
Jayne and Irschick, 1999
).
These included whole-limb movements, movements of the hindlimb joints, and
limb postures.
To characterize the stride, general variables describing whole-limb movements included mean forward velocity (Uavg), stride length, stride duration and frequency, and duty factor (Df). Uavg was calculated by averaging the derivative of positional coordinates. Stride length was the three-dimensional distance traversed by the MP joint between footfalls by the left foot, and stride duration was the time to move one stride length. Stride frequency was defined as the inverse of stride duration. Duty factor for terrestrial locomotion is the ratio of stance duration to total stride duration. The stance phase in terrestrial locomotion is primarily responsible for production of thrust, and the swing phase brings the foot forward to begin the next step. In the case of lizards running through water, this distinction was not so clear since part of recovery up takes place while the foot is still submerged and moving slightly backwards. As a result, I calculated duty factor in two ways: the fraction of a stride in which the foot is submerged in water (Dfsub) and the fraction of a stride dominated by the slap and stroke phases (Dfstance).
To describe the movements of the hindlimb joints, coordinates of each joint
in space and relative to the hip were digitized, and their velocities
calculated. By holding the hip stationary, it was possible to isolate the limb
movements from pelvic roll and thus facilitate visualization of how the limb
points moved relative to each other through one stride cycle
(Fieler and Jayne, 1998).
Motions of the right limb are assumed to be mirror motions of the left limb
during the subsequent step. Velocities of each of the hind limb points were
calculated by taking the derivative of each joint's positional data along each
of the three axes. Magnitude reflects the speed, and sign reflects the
direction of movement (see above for axis assignments). The maximum and
minimum values in each direction for each of the three limb joints (hip, knee
and ankle) were used to calculate joint excursions (
X,
Y and
Z). For example, the total horizontal
excursion of the knee joint in one stride (
Xknee)
was calculated as Xknee,max
Xknee,min.
Limb posture during a stride was described primarily by two linear variables. Effective limb length (eLL) was a linear quantification of whole-limb flexion or extension. Measured as the three-dimensional distance between the hip and the MP points, a smaller value reflects a more crouched limb posture while a greater value indicates a more extended limb posture. Effective limb length was quantified at footfall (eLLff), and the mean was determined for the stroke phase (eLLstroke).
Joint positions were described by four linear and 15 angular variables, as
described below. Hip position was quantified with two variables: mean height
to the water surface (Yhip) and total vertical excursion
(Yhip), calculated as the difference between the
maximum and minimum heights of the hip in a stride
(Yhip,maxYhip,min).
Yhip,min reflected how far the animal sank into the water.
The remaining variables are all angular measurements.
Fig. 1B provides a graphical
explanation of how angles were measured. Three-dimensional joint angles
(
hip,
knee and
ankle)
were calculated from positional data at footfall (e.g.
hip,ff) and at the end of stance (e.g.
hip,es). Minimum joint angle at stance (e.g.
hip,min) was also calculated. Joint flexion resulted in
decreasing angles, and joint extension resulted in increasing angles. The
amount of extension and flexion of each joint was defined as the difference
between the angle at the end of stance and minimum joint angle and the
difference between the angle at footfall and minimum joint angle,
respectively. These definitions presume that the limb (not including the hip
point) is most flexed at footfall and most extended at the end of stance.
Pelvic rotation was determined to be the dorsal (xz
plane), two-dimensional angle formed by a line connecting the hip and pelvis
points, and a second line connecting the pelvis and eye points. Partial
correlations of pelvic rotation with sprint speed and mass yielded no
statistically significant effects (sprint speed, P=0.316; mass,
P=0.714). As a result, the primary focus of variables presented here
is on other limb joints and segments such as the knee, ankle, femur, tibia and
foot. Three of the angles were measured relative to the water surface (i.e.
the horizontal plane): footwater (
fw),
tibiawater (
tw) and bodywater angles
(
bw). Since
bw varied little through a
stride, only the mean value was calculated. For
fw and
tw, calculated values included the angles at footfall, as
well as the mean during stroke, and minimum and maximum angles during
recovery.
Statistics
All digitized data were fit with a mean square error quintic spline
algorithm following the method previously discussed by Walker
(1998). Spline tolerance was
determined to be the magnitude of data mean square error. Both linear and
angular velocities were then calculated by taking the derivative of the
resulting spline equation (from positional and angular data, respectively).
All angular data were also calculated from the spline of positional data.
To examine the effects of size on kinematics, linear variables were
adjusted by SVL and LL. Some previous studies on terrestrial
lizard kinematics have scaled linear variables to lizard SVL
(Irschick and Jayne, 2000;
White and Anderson, 1994
). It
has been established that distal limb elements in lizards can scale negatively
to lizard size (Garland, 1985
;
Irschick and Jayne, 2000
;
Marsh, 1988
;
White and Anderson, 1994
). If
linear bipedal locomotion parameters depend on hind limb motion, linear
variables scaled by SVL downplay the actual variation with size. In
the present study, all linear variables were normalized by LL (to
more accurately reflect how animal size affects locomotor parameters) and by
SVL (to permit comparisons with most established terrestrial lizard
kinematic data). I performed simple linear regressions (StatView v.5.0.1) on
these adjusted variables, with mass or sprint velocity as the independent
variable. Mass regressions were performed with all variables
log10-transformed. Two-tailed t-tests were used to
determine if regression slopes (
) were significantly different from
that expected for isometric scaling.
Covariation between size and sprint velocity was statistically controlled by partial correlation analysis. Partial correlation permits determination of the relationship between an independent and dependent variable by holding the covariates constant. In the present study, partial correlations of velocity (holding mass constant) and mass (holding velocity constant) were completed in two ways. Correlation coefficients between absolute velocity and unadjusted dependent variables were determined by linear correlation. Correlation coefficients between mass and unadjusted dependent variables were determined by fitting a two-parameter, exponential equation to the data with a GaussNewton least squares estimation model. Partial correlation analyses were performed using Systat 9.0 (SPSS, Inc., Chicago, IL, USA).
Unless otherwise indicated, all data are presented as means ± S.E.M.
![]() |
Results |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
|
|
General stride kinematics
In all but three of the analyzed runs, the footfall pattern could be
generalized as shown in Fig. 2.
At any moment, there was always at least one foot in the water, and often both
feet were in the water through all of slap and part of stroke. The three
exceptional runs exhibited a short period (412 ms;410% of a
stride) during which there was an `aerial phase' after stroke (i.e. both feet
were simultaneously out of the water). This footfall pattern was exhibited
only by basilisks weighing 8.9 g or less. Otherwise, footfall patterns changed
little with increased mass (see Scaling section).
Fig. 3 shows the trajectories of the pelvis, hip, knee, ankle and MP (foot) points for a 20.8 g basilisk lizard, broken down into their three axial components. During the slap (13.9±5.2% of the stride; mean ± S.D.; N=15), basilisks spread the toes of the left foot and plunge it down laterally and backwards. During this phase, the pelvic girdle and trunk roll towards the left. In most recorded runs, the right foot is part way through recovery up but still submerged in water. The left arm swings in phase with the left foot at this time, moving downwards and backwards. The right arm always moves out of phase with the left arm.
|
With the toes still spread, basilisks then plantarflex and stroke through the water, pushing their left foot backwards and slightly down, finishing this phase with the foot sweeping medially to the body midline. The stroke phase makes up 17.5±5.1% (mean ± S.D.; N=15) of a stride. Midway through the stroke phase for the left foot, the right foot is extracted from the water and completes the recovery up phase. The left arm is held mostly steady, with the wrist approximately in line with the shoulder, or it begins a slow forwards and upwards sweep at this time.
The left foot now moves into the recovery up phase the longest phase (49.1±4.4%; mean ± S.D.; N=15) of the stride at the start of which basilisks adduct their toes and plantarflex the ankle such that the foot is approximately in line with the long axis of the tibia. Whereas the foot moves slightly caudad at the start of this phase, the primary motion of the foot is up, forwards and lateral. The pelvic girdle and trunk rock towards the right as the left foot is drawn out of the water in line with the axis of the hindlimb. After exiting the water, the ankle dorsiflexes such that the foot is toe up by the end of recovery up. The final part of recovery up is characterized by a near horizontal and forward movement of the foot, which brings it almost directly above where the next step begins. Basilisks then begin to abduct their toes in preparation for the next slap phase. About midway through this phase, the right foot begins its next step, completing most of slap and stroke as the left foot completes recovery up. The arm and leg movements on the left side are now approximately 90170° out of phase, with the discrepancy of arm and leg movements in larger lizards exhibiting a greater phase shift.
The recovery down phase is short (19.5±6.8%; mean ± S.D.; N=15) and mostly involves the left foot moving down and medial to begin the next slap phase. The pelvic girdle once again begins to roll towards the left. At this time, the left arm is almost exactly out of phase with the leg: as the leg moves slightly forwards and down, the arm moves backwards and up. This phase completes the stride for the left foot as it contacts the water again, starting the slap phase for the next stride.
Basilisks' gait in dorsal view exhibited lateral undulations typical of reptilian locomotion. The eye and pectoral points moved out of phase with the midbody and pelvis points. The stride begins with the posterior half of the body concave left when the left foot first contacts the water. It becomes concave right by the end of the stroke, and bends back to concave left by the end of recovery up. The anterior half of the body follows a pattern opposite the posterior half of the body. The movement of the midline points characterizes a slow traveling wave. Apart from one trial, the eye point consistently exhibited the greatest medio-lateral excursion during a stride, with the amplitude of lateral excursion decreasing posteriorly.
Throughout the stride, waves pass down the length of the tail, which is fully submerged underwater. Digitizing the maxima of these waves showed that the mean backwards velocity of the tail wave was 10.4±2.0% greater than the forward body velocity (one-tailed t-test, P=0.0014).
Limb linear and timing variables
Positions of each of the limb points are shown relative to a stationary hip
point to better visualize the paths traced by the hindlimb through one stride
(Fig. 4). The kinematics used
on water are asymmetric, with the position of the hip located anterior to the
centers of all three circular paths traced by the knee, ankle and foot.
Furthermore, vertical excursion of the foot is much greater at the end of
stance (filled points) than at slap (points outlined in black). In the dorsal
aspect (xz plane), medio-lateral excursions of limb
points are large, moving as far as the body midline at maximum medial
excursion. Finally, in the posterior view (yz plane),
the knee and foot points trace circular paths positioned primarily lateral to
the hip. The knee traces a figure of eight, passing medial to lateral to
medial from slap through recovery up and moving laterally during recovery
down.
|
Fig. 5 shows pelvis and hind limb point velocities over a stride. Foot velocities in the foreaft direction had minima and maxima at the end of stroke and recovery up, respectively. Along the vertical axis, the foot moved most rapidly during slap (downwards) and during the first third of recovery up (upwards), when the foot was still in the water. After the foot exited the water, velocity plateaued until recovery down. Medio-lateral velocity fluctuations were large, with a slight phase delay distally along the hind limb.
|
All basilisks, regardless of size, ran at approximately the same absolute
velocity (1.3±0.1 m s1), although the smallest lizard
ran slower than the rest. Partial correlations for absolute velocity with mass
held constant exhibited few significant correlations with kinematics
(Table 3). Increased velocity
coincided with a longer step length (r2=0.65,
P=0.005). Stride frequency did not vary with velocity
(P=0.985). Other variables associated with increased velocity
included increased knee and ankle horizontal excursions
(Xknee: r2=0.64,
P=0.005;
Xankle:
r2=0.66, P=0.004), increased medio-lateral ankle
excursion (r2=0.41, P=0.045) and increased
medio-lateral stroke speed (r2=0.58, P=0.011).
Ankle extension during stance decreased with increased velocity
(r2=0.45, P=0.033). Duration of each of the four
stride phases expressed as percentage of stride duration did
not have any correlation with sprint speed.
|
Despite the lack of variation in absolute running speeds over a size range,
when all linear variables were adjusted for LL and SVL, many
variables were found to be speed-dependent
(Table 3). Higher relative
velocities coincided with higher hip position at footfall
(Yhip,ff; P=0.002). Vertical hip excursion
(Yhip,stance) during stance did not vary with
velocity. Basilisks increased relative sprint velocity
(Uavg) by increasing relative horizontal knee
(
Xknee) and ankle excursions
(
Xankle) and thereby increasing relative stride
length. They also decreased stride duration by shortening stance duration
(Dfstance). Finally, they produced more thrust by
increasing vertical foot stroke velocity (UY,stroke), as
well as medio-lateral foot velocity during both the slap
(UZ,slap) and stroke phases
(UZ,stroke).
Angular kinematics
Despite the large amount of variability in joint angles during a run, some
patterns were observed between runs (Fig.
6). In all but the three lightest animals, ankle and knee angles
at slap were less than 90°, indicating that the limb was highly flexed
upon contact with the water. During slap, the ankle and knee only extended.
Knee angle reached a maximum during the stroke phase (125±5°) and
the ankle reached maximum extension shortly thereafter at the beginning of
recovery up (140±3°). Whereas adult basilisks flexed their knee
more than juveniles at footfall (r2=0.70,
P=0.003), ankle angle at footfall exhibited no such pattern
(r2=0.32, P=0.088). There were also no
significant correlations between mass and knee or ankle angles at the end of
stance. It is particularly notable that the limbs exhibited only extension
during a stride. Maximum hip extension angles were during slap and stroke
(144±6° and 145±3°, respectively), and minimum extension
angles usually occurred at the end of recovery up (116±2°). The hip
was never flexed (i.e. <90°) throughout a stride, probably as a result
of pelvic roll.
|
Dorsal and lateral video images showed that toes were widely abducted (i.e. spread) during slap and stroke and then adducted during recovery up. The toe adduction, in combination with near complete ankle extension during recovery up (165±2°), may have acted to streamline the foot and decrease the drag acting upon it during a period when it may not be producing any thrust. Upon exiting the water, the toes gradually abducted once more and were fully abducted by the end of recovery down.
Although body angle appeared to remain constant during a stride, the lightest and heaviest animals ran with more erect postures than did the medium basilisks (<10 g, 51±2°; 1030 g, 46±1°; 6080 g, 62±3°).
Scaling
Only two of the stride phases were size-dependent
(Table 4) the stroke
phase increased and recovery down decreased in duration. Mean durations of
each phase, as a percentage of the stride cycle, are presented in
Fig. 2. Stride duration
exhibited positive trends (P=0.055), indicating that heavier animals
took fewer strides in a set period, with a greater proportion of the stride
dedicated to the slap and stroke phases (Dfstance;
P=0.004) or the total proportion of stride spent submerged in water
(Dfsub; P=0.004).
|
Most angular variables scaled negatively with mass. As a lizard increased
in mass, the limb was more flexed at slap, as indicated by decreased knee
angle at footfall (knee,ff; P=0.003). Larger
lizards also sank deeper into the water (Yhip,min:
r2=0.61, P=0.007). There was clear size
dependence with position of the foot to the water during slap
(Fig. 7). Animals weighing
''11.4 g slapped the water toe first or flat-footed (3±3°).
There appeared to be a transition in foot position at around 20 g, as lizards
around this mass slapped either flat-footed or heel first
(0.4±5°), and all but one of the heavier animals slapped the
water heel first (30±20°). One large adult (76.4 g) slapped
the water toe first. However, in this case, the basilisk's hands touched the
water; in the remaining analyzed runs, the hands were fully out of the
water.
|
Adjusted linear variables describing limb excursion also reflected the more
flexed limbs in adult basilisks (Table
4). Relative horizontal knee
[Xknee(SVL): r2=0.47,
P=0.029] and ankle [
Xankle(SVL):
r2=0.44, P=0.037] values normalized by
SVL decreased with increasing size. No size-dependent trend was
observed for relative vertical joint excursions of the knee and ankle,
although their absolute vertical excursions were closely associated with mass
(
Yknee: r2=0.84,
P<0.001;
Yankle:
r2=0.97, P<0.001). Finally, relative
medio-lateral excursions exhibited significant negative allometry only at the
ankle [
Zankle(SVL): r2=0.44,
P=0.035]. Other normalized linear variables that were negatively
allometric to lizard mass included Yhip,ff(SVL)
(r2=0.76, P=0.002),
eLLslap(SVL) (r2=0.51,
P=0.021), stride length(SVL) (r2=0.44,
P=0.036) and relative Uavg(SVL)
(r2=0.70, P=0.003). Linear variables normalized
by LL exhibited fewer significant trends because the lightest
basilisk (2.8 g) exhibited unusually low, outlying values probably a
result of its disproportionately long legs; however, when values from the
lightest basilisk are removed, scaling by SVL and LL exhibit
the same trends. In most cases, variables scaled by LL have greater
correlations with mass than do linear variables scaled by SVL.
![]() |
Discussion |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Basilisk kinematics and kinetics
The kinematics of basilisk water running varied considerably. Basilisks
weighing up to 20 g sometimes exhibited an aerial phase in a run. Yet it was
unclear which variables other than mass were responsible for this variability.
In general, the forearms `windmill' during a run but to different extents.
When basilisks ran with a large trunk angle to the water, they extended their
arms forwards with minimal rotation around the shoulder. By contrast, when the
trunk was held at 45° to the water the much more common body
posture basilisks' arm movements matched directions with the leg on
the contralateral side. In other runs, the arms moved with a slight delay to
the contralateral hindlimb and were sometimes so delayed that it nearly
matched the movements with the hindlimb on the same side. Windmilling the
forearms may serve to counteract torques placed on the body during a stride,
as have been reported in human studies to explain the pendulum-like motion of
the arms during walking (Li et al.,
2001
).
The function of the tail in lizard locomotion has been largely ignored in
most previous studies; yet the tail may play a major role as a counterbalance
in basilisk lizard locomotion (Snyder,
1949,
1962
) since it makes up
18% of basilisks' total body mass (present study). Basilisks drag their
tails behind them while running through water
(Fig. 1). The mass of the fluid
above the tail and skin frictional drag from the fluid surrounding the tail
could thus aid in keeping basilisks in an upright posture.
The tail may also produce some thrust as basilisks run. The wave velocity traveling posteriorly along the tail exceeds the forward velocity of the body on average by 10.4%. This classically would indicate that the tail is generating some thrust. In larger basilisks, the tail is laterally compressed at the base, which would aid in thrust generation. However, since the rest of the exceptionally long tail tapers to a very fine point, it is unclear whether it could generate enough thrust to add substantially to the forward progression of the animals.
Problems associated with sinking into a surface add another level of
complexity to basilisks' locomotion. Basilisks reduce hydrodynamic drag on the
foot in two ways: by avoiding submersion of the foot in water
(Snyder, 1949) and by
adducting the toes during recovery up
(Glasheen and McMahon, 1996a
;
present study). When basilisks slap the water, they create an air-filled
cavity surrounding their foot. Using a model of a basilisk foot, approximated
as a circular disk, Glasheen and McMahon
(1996a
,b
)
predicted that basilisks need to run at a minimum stride frequency
(fstr,min) that would allow them to retract their foot out
of the water prior to the time of air cavity closure
(tseal) and thus minimize hydrodynamic drag on the foot.
Results from the present study support this prediction since all measured
lizard stride frequencies were greater than the predicted
fstr,min.
Since the value of fstr,min is based upon a measured
tseal, cavity geometry substantially influences the
predicted value for fstr,min. The foot missile (Glasheen
and McMahon,
1996a,b
)
was dropped vertically and therefore does not simulate the lizards' stride
with kinematic accuracy. In an actual run, the final water cavity is formed
during the stroke phase of the stride. If the shape of the cavity created
during the slap phase or during the vertical disk drop is
approximated as a cylinder with its long axis positioned vertically, the
cavity created during the stroke is a cylinder on its side. The area of the
cavity at water level would thus be much greater in the cavity created during
stroke than that created during slap. Investigations on the behavior of air
bubbles in fluids have shown that the lowest energy shape for a bubble is a
sphere. As a result, the cylindrical cavities created in each phase would
collapse towards a spherical shape. How this would affect
tseal remains to be examined.
Although kinematic analysis provides only a preliminary insight into the
production of motion, it does permit some qualitative predictions about the
mechanics of motion. All basilisks weighing <20 g slapped the water
slightly toe first or flat-footed, indicating that the majority of force
generated was initially lift rather than thrust. Basilisks heavier than 30
gslapped the water heel first. As a result of the foot orientation, this
suggests that the large basilisks should experience reductions in forward
velocity during slap due to the production of thrust counter to the direction
of motion. The basilisks' ability to run through water is highly influenced by
its running speed (Rand and Marx,
1967), and the slap impulse produced is dependent on foot size to
the third power (Glasheen and McMahon,
1996a
,b
).
It is therefore interesting to note that, irrespective of size, all basilisks
ran at similar absolute velocities as has been reported in field
studies (Rand and Marx,
1967
).
Additional insight into the novel kinematics of aquatic running may be
gained from human swimming. Basilisk limb movements during the stroke phase of
water running are surprisingly similar to the arm kinematics recorded for
competitive swimmers during the propulsive stroke of front-crawl (i.e.
`freestyle') swimming. The shoulder of a swimmer is analogous to the pelvic
girdle of a basilisk, and a swimmer's arms are analogous to a basilisk's
hindlimbs. During the propulsive stroke, the arm moves down, back and
medially, as does a basilisk hindlimb. Although the actual function of the
medial sweep remains controversial, hypotheses on how it increases propulsive
forces in swimming have included (1) the curved hand path increasing the
distance traversed by the hand, and thereby allowing a greater amount of
propulsive force to be produced over a stroke, and (2) the medial movement
allowing larger muscle groups to be utilized for propulsion. A contrasting
view is that the medial movement results from the natural body roll associated
with this style of swimming and thus does not necessarily enhance swimming
performance (Hay et al., 1993;
Liu et al., 1993
). The
relevance of these limb movements to water running remains to be determined,
although the aforementioned hypotheses do provide some initial ideas.
Effects of size on kinematic variables
Juveniles ran proportionately much faster than did adults because of their
smaller size. In the present study, those animals that ran at a higher
adjusted speed also maintained a significantly greater relative hip height at
footfall. The ability to stay on water relies on a combination of forces
generated during the slap and stroke (Glasheen and McMahon,
1996a,b
)
and was affected more by basilisk size than sprint speed. Forces produced by a
slap impulse among juvenile lizards can make up more than 60% of the needed
impulse to stay on water; yet, during the same phase, adult basilisks can
produce only about 1020% of the necessary force to stay on water
(Glasheen and McMahon,
1996a
,b
).
As a result, maximizing force production during the stroke phase as
opposed to during slap becomes even more important to adult basilisks.
This can manifest itself as an extended stroke phase or faster stroke speed
with increased basilisk mass.
Adult basilisks do employ an extended stance phase, as indicated by
increased duty factor and prolonged stroke phase duration. However, they also
stroke through the water with slower absolute velocities than do juveniles.
Adults do not exhibit greater foreaft ankle excursions over a stride,
so the prospect of producing less force over a longer distance for ultimately
greater total force production also seems unlikely. Finally, adult basilisks
potentially produce less power at footfall than do juveniles. A study
examining power output during two-legged jumps in humans reported maximum
power output between knee angles of 110° and 130°
(Zamparo et al., 1997).
Although none of the mean basilisk knee angles at footfall are within the
range of the power plateau for humans, the smallest basilisks weighing less
than 10 g come closest to this range (104±6°). The largest lizards
fall far outside this range (59±8°). If power curves generated by
basilisks are similar to those generated by humans, then large basilisks are
producing much less power with their hind limbs at slap.
The results show that large basilisks are simply at a disadvantage. Their disproportionately greater mass, smaller feet and slower relative running speed all contribute to increased difficulty running through water.
Aquatic versus terrestrial locomotion
When walking on a stiff surface, work done on the environment is close to
zero, assuming the foot does not slip or move the substratum. Most of the work
done by the muscles and tendons in the first half of a step is therefore
absorbed and stored in the stretched elements as elastic energy
(Cavagna, 1985;
Farley and González,
1996
; McMahon and Greene,
1979
). This energy storage manifests itself as flexion of both the
ankle and knee joints, as reported in terrestrial running humans
(Farley and González,
1996
; Ferris et al.,
1998
; Gatesy and Biewener,
1991
; Lejeune et al.,
1998
; McMahon and Greene,
1979
) and lizards (Fieler and
Jayne, 1998
; Irschick and Jayne,
1999
,
2000
;
Jayne and Irschick, 1999
). By
contrast, when running on water, basilisks only extended their ankle and knee
joints during stance (slap and stroke phases). This suggests that unlike
during land runs, the muscles and tendons in basilisk legs no longer serve a
dual function for producing force and for storing elastic energy; instead,
they are used only to produce force.
Basilisk trunk angle decreased the most during the recovery phases in
terrestrial (Snyder, 1949) and
aquatic (present study) runs. However, basilisks run with a more upright
posture during aquatic runs (52±2°) than they do during terrestrial
runs (815°; Snyder,
1949
), indicating that their center of mass is shifted caudally
when running through water. Lateral undulations of the trunk are similar when
running through water or on land but exhibit much more exaggerated amplitudes
when running through water (Laerm,
1973
). This may result from the foot sinking into the surface,
forcing the body to undergo greater axial rotation during stance. Pelvic
rotation was much greater in aquatic runs for basilisk lizards
(87°97°) than for terrestrial runs among other bipedal lizards
(45°55°; Irschick and
Jayne, 1999
).
Limb excursion during a stride across water is greater than that on land.
During terrestrial basilisk runs, limb joint positions never exceed hip height
and are kinematically symmetrical; the eLL (linear distance between H
and MP points) at the beginning of stance is only slightly shorter (91%) than
the eLL at the end of stance (Snyder,
1949,
1954
). Similar results are
also reported for other bipedal lizards
(Irschick and Jayne, 1999
),
birds and humans (Gatesy and Biewener,
1991
). On water, limb joints exceed or match hip height, and the
eLL at the end of stroke is up to three times as long as the
eLL at footfall (Fig.
4A). Since the greatest amount of propulsion is produced between
the time the foot passes beyond the hip to the end of stance
(Snyder, 1949
), the greatest
propulsive phase would last about 50% of the stance period in symmetric
terrestrial runs. However, in aquatic running, as a result of greater limb
retraction caudad, the propulsive phase lasts a proportionately greater
duration for one stride. On a surface that is so much more yielding than solid
ground, and also slips with each step
(Laerm, 1973
), an extended
propulsive phase for more sustained force production (both lift and thrust)
would be important to keep the lizard's center of mass at a constant height
above water.
Strategies to increase sprint speed through water are similar to those used
on land by other tetrapods. On water, relative sprint speed is increased by
lengthening the stride and increasing stride frequency
(Table 3). Stride length
probably plays a larger role in increasing sprint speed than does stride
frequency, as evidenced by its steeper regression slope. Quadrupedal lizards
running on land (Fieler and Jayne,
1998), humans (Gatesy and
Biewener, 1991
) and birds
(Gatesy and Biewener, 1991
)
have all shown similar trends. However, contrary to recent findings indicating
lizards adopt a more extended limb posture at higher sprint speeds
(Irschick and Jayne, 1998
;
Jayne and Irschick, 1999
),
basilisks assume a more crouched posture.
The present study has focused on water-running kinematics. Actual forces
generated during water running are still unknown. Future work will include an
analysis of the magnitude and direction of forces involved in basilisk aquatic
running, using particle imaging velocimetry (PIV) to visualize fluid motion.
This technique has already been applied numerous times to fish swimming
studies for the analysis of fin function (e.g.
Drucker and Lauder, 1999;
Lauder, 2000
;
Liao and Lauder, 2000
) and
insect flight (Birch and Dickinson,
2001
; Dickinson et al.,
1999
). Other directions will involve measuring kinematics and
forces produced by basilisks running bipedally on land, so that a direct
comparison can be made for how locomotor strategy changes in response to
different surface properties.
List of symbols
![]() |
Acknowledgments |
---|
![]() |
References |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Alexander, R. McN. (1977). Mechanics and scaling of terrestrial locomotion. In Scale Effects in Animal Locomotion (ed. T. J. Pedley), pp.93 -110. London: Academic Press.
Alexander, R. McN. and Jayes, A. S. (1983). A dynamic similarity hypothesis for the gaits of quadrupedal mammals. J. Zool. 201,135 -152.
Barden, A. (1943). Notes on the basilisk at Barro Colorado Island, Canal Zone. Copeia 24,407 -408.
Bertram, J. E. A. and Biewener, A. A. (1992). Allometry and curvature in the long bones of quadrupedal mammals. J. Zool. 226,455 -467.
Biewener, A. A. (1983). Allometry of quadrupedal locomotion: the scaling of duty factor, bone curvature and limb orientation to body size. J. Exp. Biol. 105,147 -171.[Abstract]
Birch, J. M. and Dickinson, M. H. (2001). Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412,729 -733.[CrossRef][Medline]
Cavagna, G. A. (1985). Force platforms as ergometers. J. Appl. Phys. 39,174 -179.
Cavagna, G. A., Heglund, N. C. and Taylor, C. R. (1977). Walking, running and galloping: mechanical similarities between different animals. In Scale Effects in Animal Locomotion (ed. T. J. Pedley), pp.111 -125. London: Academic Press.
Dickinson, M. H., Lehmann, F.-O. and Sane, S. P.
(1999). Wing rotation and the aerodynamic basis of insect flight.
Science 284,1954
-1960.
Drucker, E. G. and Lauder, G. V. (1999).
Locomotor forces on a swimming fish: three-dimensional vortex wake dynamics
quantified using digital particle image velocimetry. J. Exp.
Biol. 202,2393
-2412.
Farley, C. T., Glasheen, J. W. and McMahon, T. A.
(1993). Running springs: speed and animal size. J.
Exp. Biol. 185,71
-86.
Farley, C. T. and González, O. (1996). Leg stiffness and stride frequency in human running. J. Biomech. 29,181 -186.[CrossRef][Medline]
Ferris, D. P., Louie, M. and Farley, C. T. (1998). Running in the real world: adjusting leg stiffness for different surfaces. Proc. R. Soc. Lond. Ser. B. Biol. Sci. 265,989 -994.[CrossRef][Medline]
Fieler, C. L. and Jayne, B. C. (1998). Effects
of speed on the hindlimb kinematics of the lizard Dipsosaurus dorsalis.J. Exp. Biol. 201,609
-622.
Garland, T. J. (1985). Ontogenetic and individual variation in size, shape and speed in the Australian agamid lizard Amphibolurus nuchalis. J. Zool. 207,425 -439.
Gatesy, S. M. and Biewener, A. A. (1991). Bipedal locomotion: effects of speed, size and limb posture in birds and humans. J. Zool. 224,127 -147.
Glasheen, J. W. and McMahon, T. A. (1996a). A hydrodynamic model of locomotion in the basilisk lizard. Nature 380,340 -342.[CrossRef]
Glasheen, J. W. and McMahon, T. A. (1996b).
Size-dependence of water-running ability in basilisk lizards (Basiliscus
basiliscus). J. Exp. Biol.
199,2611
-2618.
Hatze, H. (1988). High-precision three-dimensional photogrammetric calibration and object space reconstruction using a modified DLT-approach. J. Biomech. 21,533 -538.[Medline]
Hay, J. G., Liu, Q. and Andrews, J. G. (1993). The influence of body roll on handpath in freestyle swimming: a computer simulation study. J. Appl. Biomech. 9, 227-237.
Hedrick, T. L., Tobalske, B. W. and Biewener, A. A.
(2002). Estimates of circulation and gait change based on a
three-dimensional kinematic analysis of flight in cockatiels (Nymphicus
hollandicus) and ringed turtle-doves (Streptopelia risoria).
J. Exp. Biol. 205,1389
-1409.
Heglund, N. C., Taylor, C. R. and McMahon, T. A. (1974). Scaling stride frequency and gait to animal size: mice to horses. Science 186,1112 -1113.[Medline]
Huey, R. B. and Hertz, P. E. (1982). Effects of body size and slope on sprint speed of a lizard (Stellio (Agama) Stellio). J. Exp. Biol. 97,401 -409.
Irschick, D. J. and Jayne, B. C. (1998).
Effects of incline on speed, acceleration, body posture, and hindlimb
kinematics in two species of lizard Callisaurus draconoides and
Uma scoparia. J. Exp. Biol.
201,273
-287.
Irschick, D. J. and Jayne, B. C. (1999).
Comparative three-dimensional kinematics of the hindlimb for high-speed
bipedal and quadrupedal locomotion of lizards. J. Exp.
Biol. 202,1047
-1065.
Irschick, D. J. and Jayne, B. C. (2000). Size
matters: ontogenetic variation in the three-dimensional kinematics of
steady-speed locomotion in the lizard Dipsosaurus dorsalis. J. Exp.
Biol. 203,2133
-2148.
Jayne, B. C. and Irschick, D. J. (1999).
Effects of incline and speed on the three-dimensional hindlimb kinematics of a
generalized iguanian lizard (Dipsosaurus dorsalis). J.
Exp. Biol. 202,143
-159.
Laerm, J. (1973). Aquatic bipedalism in the basilisk lizard: the analysis of an adaptive strategy. Am. Midl. Nat. 89,314 -333.
Lauder, G. V. (2000). Function of the caudal fin during locomotion in fishes: Kinematics, flow visualization, and evolutionary patterns. Am. Zool. 40,101 -122.
Lejeune, T. M., Willems, P. A. and Heglund, N. C.
(1998). Mechanics and energetics of human locomotion on sand.
J. Exp. Biol. 201,2071
-2080.
Li, Y., Wang, W., Crompton, R. H. and Gunther, M. M.
(2001). Free vertical moments and transverse forces in human
walking and their role in relation to arm-swing. J. Exp.
Biol. 204,47
-58.
Liao, J. and Lauder, G. V. (2000). Function of
the heterocercal tail in white sturgeon: flow visualization during steady
swimming and vertical maneuvering. J. Exp. Biol.
203,3585
-3594.
Liu, Q., Hay, J. G. and Andrews, J. G. (1993). The influence of body roll on handpath in freestyle swimming: an experimental study. J. Appl. Biomech. 9, 238-253.
Marsh, R. L. (1988). Ontogenesis of contractile properties of skeletal muscle and sprint performance in the lizard Dipsosaurus dorsalis. J. Exp. Biol. 137,119 -139.[Abstract]
Maturana, H. R. (1962). A study of the species of the genus Basiliscus. Bull. Mus. Comp. Zool. 128, 1-34.
McMahon, T. A. (1975). Using body size to
understand the structural design of animals: quadrupedal locomotion.
J. Appl. Phys. 39,619
-627.
McMahon, T. A. and Greene, P. R. (1979). The influence of track compliance on running. J. Biomech. 12,893 -904.[Medline]
Rand, A. S. and Marx, H. (1967). Running speed of the lizard Basiliscus basiliscus on water. Copeia 1967,230 -233.
Reilly, S. M. and Delancey, M. J. (1997a).
Sprawling locomotion in the lizard Sceloporus clarkii: quantitative
kinematics of a walking trot. J. Exp. Biol.
200,753
-765.
Reilly, S. M. and Delancey, M. J. (1997b). Sprawling locomotion in the lizard Sceloporus clarkii: the effects of speed on gait, hindlimb kinematics, an daxial bending during walking. J. Zool. 243,417 -433.
Reinschmidt, C. and van den Bogert, T. (1997). Kinemat: A MATLAB Toolbox For Three-Dimensional Kinematic Analyses. Calgary: Human Performance Laboratory, The University of Calgary.
Russell, A. P. and Bels, V. L. (2001). Biomechanics and kinematics of limb-based locomotion in lizards: review, synthesis and prospectus. Comp. Biochem. Physiol. A 131,89 -112.
Snyder, R. C. (1949). Bipedal locomotion of the lizard Basiliscus basiliscus. Copeia 1949,129 -137.
Snyder, R. C. (1952). Quadrupedal and bipedal locomotion of lizards. Copeia 1952,64 -70.
Snyder, R. C. (1954). The anatomy and function of the pelvic girdle and hindlimb in lizard locomotion. Am. J. Anat. 95,1 -45.[Medline]
Snyder, R. C. (1962). Adaptations for bipedal locomotion of lizards. Am. Zool. 2, 191-203.
Wainwright, P. C. and Richard, B. A. (1995). Scaling the feeding mechanism of the largemouth bass (Micropterus salmoides): motor pattern. J. Exp. Biol. 198,1161 -1171.[Medline]
Walker, J. A. (1998). Estimating velocities and
accelerations of animal locomotion: a simulation experiment comparing
numerical differentiation algorithms. J. Exp. Biol.
201,981
-995.
White, T. D. and Anderson, R. A. (1994). Locomotor patterns and costs as related to body size and form in teiid lizards. J. Zool. 233,109 -128.
Woltring, H. J. and Huiskes, R. (1990). Stereophotogrammetry. In Biomechanics of Human Movement (ed. N. Berme and A. Capozzo), pp.108 -127. Worthington, OH: Bertec Corporation.
Zamparo, P., Antonutto, G., Capelli, C., Girardis, M., Sepulcri, L. and di Prampero, P. E. (1997). Effects of elastic recoil on maximal explosive power of the lower limbs. Eur. J. Appl. Phys. 75,289 -297.[CrossRef]