Mechanical power output during running accelerations in wild turkeys
Department of Zoology, Oregon State University, 3029 Cordley Hall,
Corvallis, OR 97331-2914, USA
Present address: Department of Biology, Baylor University, Waco, TX
76798-7388, USA
* e-mail: robertst{at}bcc.orst.edu
Accepted 5 March 2002
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Summary |
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Key words: locomotion, muscle, work, power, bird, running, turkey, Meleagris gallopavo
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Introduction |
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During running, muscletendon units operate like springs, storing and
recovering mechanical energy as the limbs flex and extend with each step
(Alexander, 1988;
Alexander and Bennet-Clark,
1977
; McMahon and Cheng,
1990
). Some of this cyclical work is done by muscle contractile
elements that absorb work as they are actively stretched and produce work as
they shorten. However, most of the spring-like function of the limb could be
performed by the passive stretch and recoil of tendons because steady-speed
running on level ground involves no net change in the average mechanical
energy of the body. Elastic mechanisms can allow muscle contractile elements
to operate as near-isometric struts, developing force without shortening or
producing significant power (Roberts et
al., 1997
; Biewener and
Roberts, 2000
; Dickinson et
al., 2000
). The spring-like function of muscletendon units
allows for economic force development by minimizing muscular work.
The mechanical function of muscles during acceleration must differ
fundamentally from their function during steady-speed running. The work done
to increase the kinetic energy of the body with each step in an accelerating
animal must be performed by contraction of skeletal muscle because passive
elastic mechanisms cannot perform net work (i.e. they can only store and
recover energy, they cannot increase the net mechanical energy of the body).
An animal's ability to accelerate quickly may be critical for avoiding
predation or for capturing prey (Elliott
et al., 1977; Huey and Hertz,
1983
), and selection for acceleration has probably been an
important factor shaping the design of the musculoskeletal system. Therefore,
it might be expected that, during the highest accelerations, all available
muscle would be recruited to operate at maximal power output. However, there
is little information available to test this idea.
We sought to determine the power developed by the hindlimb musculature during acceleration in running turkeys. The study was motivated by the question: Can a muscular system that effectively minimizes muscular power during steady-speed running also act to maximize muscular power for acceleration? Because the spring-like function of muscletendon units during steady-speed running differs fundamentally from the motor-like function required during acceleration, we also investigated how turkeys alter some of the mechanical features that are characteristic of a bouncing gait but unfavorable or impossible for an animal accelerating effectively.
First, we examined how turkeys alter horizontal propulsive forces to
produce accelerations without losing their balance. The propulsive and braking
components of the horizontal (foreaft) ground reaction force developed
during steady-speed running are important for balance because they maintain
the alignment of the resultant ground reaction force with the center of mass
of the body (Clark and Alexander,
1975). To increase speed, a runner must produce a net propulsive
force impulse either by reducing braking forces or by increasing accelerative
forces, or both. Humans appear to be able to produce purely accelerative
forces during the first one or two steps of acceleration in a sprint
(Cavagna et al., 1971
) by
leaning forward to position the center of mass in line with the
forward-oriented ground reaction force
(Harland and Steele, 1997
).
The posture of running birds makes this kind of adjustment unlikely, and it is
unclear how birds might eliminate braking forces and still maintain balance.
To determine how turkeys maintain balance while increasing propulsive
horizontal forces during accelerations, we measured limb kinematics and ground
reaction forces over a range of accelerations.
We also examined the pattern of mechanical energy changes of the body
during a step to determine whether turkeys could generate exclusively positive
work during a single step of an acceleration. Steady-speed running involves
negative work; the kinetic and potential energies of the body decrease as the
limb compresses in the first half of the step. Acceleration will be maximized
if these mechanical energy losses are minimized. Any loss of energy from the
body requires muscletendon units to absorb energy and reduces the time
available during ground contact for positive work production by muscles. It is
unclear whether the natural compliance and spring-like behavior
(McMahon and Cheng, 1990;
Farley et al., 1993
) of the
limbs of runners might make this energy absorption phase difficult to
eliminate. We measured the pattern of change in mechanical energy of the body
during a step to determine whether turkeys could completely eliminate negative
work done on the body.
Many of the features of the mechanics of gait and muscle function appear to
be common among vertebrate runners (Close,
1972; Cavagna et al.,
1977
; Dickinson et al.,
2000
). We used wild turkeys to investigate muscle function during
acceleration because they are able runners and have served as a useful model
for investigating the energetics and mechanics of muscle function during
locomotion (Roberts et al.,
1997
,
1998
). We measured the
mechanical power output developed during a single step as turkeys accelerated
over a force plate. To estimate the muscle-mass-specific power output of the
entire hindlimb musculature, we measured total hindlimb muscle mass. We
hypothesized that, despite the potential constraints imposed by the
spring-like properties of the limbs, turkeys would develop power outputs
during maximal accelerations that were near the limit expected for full
recruitment of their hindlimb extensor muscles.
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Materials and methods |
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Turkeys were trained to run along a 10 m track way. The runway was covered
with a rubber surface 3 mm thick. For running trials, animals were positioned
0-2 m from the force plate, and ground reaction force and video were recorded
as the animals accelerated. Only a small subset of the recorded runs could be
included for analysis. To calculate the power output of a single limb, it was
necessary to limit the analysis to runs in which only one foot contacted the
force plate, and this contact had to be preceded and followed by an aerial
phase (i.e. there could be no double-support period). In practice, this meant
that the steps that could be analyzed were typically the second or third
footfall of an acceleration. To minimize the effects of variation in speed,
only accelerations in which the mean speed was between 1.75 and 2.25 m
s-1 were analyzed. This speed range was chosen in part because it
was difficult to elicit accelerations at higher speeds. Studies of sprinting
humans suggest that maximal powers are developed within the first steps of an
acceleration (Cavagna et al.,
1971), but it is possible that turkeys develop higher power
outputs than those measured at the speeds used in the present study.
Video analysis
Movements in the sagittal plane were recorded from a high-speed video
camera (Redlake Motionscope 1000) operating at 250 Hz. Joint centers of
rotation were marked with reflective tape (3M; 70610WS). The location of the
hip was determined from a marker glued to the back at a known distance from
the acetabulum. Another back marker located anterior to the first was used to
determine the angle of the body. Video recordings were digitized to a
Macintosh computer with a Scion LG-3 video capture card. The locations of the
joint centers of rotation and back markers were determined using a
custom-designed macro written for NIH Object-Image (a version of NIH Image
adapted by Norbert Vischer;
http://simon.bio.uva.nl/objectimage.html
) and smoothed in the program Igor (Wavemetrics) using a cubic spline
interpolation (smoothing factor 1, S.D.=0.001 m).
Video data were used to determine limb protraction and retraction angle,
the rotation of the body during stance and the initial velocities of the body
for force-plate integrations. Protraction and retraction angle were calculated
as the angle from vertical of a line drawn from the hip to the
tarsometatarsal/phalangeal joint (Gatesy
and Biewener, 1991). Protraction angle was measured at toe-down,
and retraction angle was measured at toe-off. Two markers along the back were
used to determine the angle of the back relative to the horizontal.
Mechanical energy and power
Force-plate (Kistler 9233a) measurements were used to determine the
mechanical energy changes of the center of mass during single footfalls.
Force-plate signals were acquired to computer with a 12-bit A/D board
(National Instruments PCI-MIO-16E-1) using Labview software. Force signals
were acquired at 1000 Hz and filtered in software with a bidirectional
low-pass Butterworth filter with a cut-off frequency of 100 Hz. The start of
video recording and force acquisition was triggered from an external signal to
allow for synchronization of the two signals.
Changes in potential and kinetic energy during the contact period were
calculated from the integrated vertical and horizontal forces
(Cavagna, 1975). Integration
of the horizontal forces allows determination of the change in horizontal
kinetic energy during stance, and vertical force integration allows
calculation of changes in potential and vertical kinetic energy. The sum of
horizontal kinetic, vertical kinetic and gravitational potential energies
gives the total mechanical energy change of the center of mass during the
contact phase. Differentiation of the change in energy with respect to time
yields the instantaneous power during foot contact. The mean rate of
acceleration during the step was measured from the mean horizontal force
divided by the mass of the animal.
In addition to the ground reaction forces, calculation of the energy changes of the body during a step requires a measure of the initial velocities of the center of mass. The horizontal and vertical positions of the hip were digitized for approximately 10 frames prior to toe-down, and these position data were differentiated with respect to time to estimate the velocity of the center of mass at the time of toe-down. Rotation of the body may cause some error in estimating center of mass velocity from the velocity of the hip. Estimates of the rotation of the body at toe-down indicate that this error would be less than 0.2 m s-1 for the initial vertical velocity and negligible for the initial horizontal velocity. A sensitivity analysis indicated that error in the initial velocity of the body had the largest effect on the calculated value for peak instantaneous power, and this error was less than 10% of the calculated value.
Muscle-mass-specific power output was determined from the center of mass power and the total extensor muscle mass of the limb. The total limb extensor muscle mass of a single limb of three birds was determined by weighing each muscle. The muscle-mass-specific measures of work and power were calculated by dividing the estimates of the mechanical energy changes of the center of mass by the total hindlimb muscle mass. The resulting value gives the mean muscle power per unit hindlimb muscle mass necessary to power the measured changes in mechanical energy of the body.
It was assumed that the mean power output during stance represents the power developed by muscle contractile elements. Although elastic elements influence instantaneous power output at any given time during a muscle contraction, they cannot perform net work. Therefore, the mean power developed during a muscle contraction must be developed by muscle contractile elements. We assumed that significant elastic energy is not stored during the swing phase and recovered during stance.
Statistical analyses
Least-squares linear regression was used to determine the effect of
acceleration on variables of interest. It was determined by analysis of
covariance (ANCOVA) that there was no significant effect of individual bird on
any of the values measured. Therefore, data for individuals were pooled for
least-squares regressions.
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Results |
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Ground reaction forces and balance
Turkeys accelerated by both decreasing the braking component of the
horizontal ground reaction force and increasing the propulsive force. This is
illustrated by the representative plots of ground reaction force during a
single stance phase in a steady-speed run
(Fig. 2A) and a high
acceleration (Fig. 2B). Peak
horizontal forces during steady-speed runs (acceleration approximately zero)
were approximately 10% of peak vertical force, a value typical for running
animals (Cavagna et al.,
1977). During the highest accelerations, turkeys produced peak
propulsive forces exceeding one body weight and braking forces at or near zero
(Fig. 3A). Peak vertical forces
also increased with acceleration (Fig.
3A). Horizontal forces increased more than vertical forces; peak
propulsive horizontal forces were more than 40% of peak vertical force during
the fastest accelerations (Fig.
3B).
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Increases in horizontal propulsive forces were associated with a more anteriorly oriented resultant ground reaction force vector (Figs 2, 3C). During steady-speed running, the ground reaction force is posteriorly oriented during the first half of the step and anteriorly oriented during the second half, such that the average orientation of the ground reaction force is vertical (Fig. 2A). Limb protraction and retraction angles mirror this pattern, and the average position of the limb during stance is vertical. If the limb posture observed during steady-speed running were maintained during accelerations, the anteriorly oriented ground reaction force would lead to excessive pitching of the body about a transverse axis. We found that in accelerating turkeys alignment between the center of mass and the ground reaction force was maintained in part by changes in limb kinematics. Turkeys decreased limb protraction angle and increased limb retraction angle as their rate of acceleration increased (Figs 2, 4A,B). These changes tended to position the center of mass more anterior to the point of force application and therefore helped maintain the alignment between the center of mass and the more anteriorly oriented ground reaction force during accelerations. On average, increases in limb retraction angle equaled decreases in limb protraction angle, resulting in no change in the total angle swept by the limb during stance (P=0.67). Changes in limb angle helped to maintain alignment between the center of mass and the ground reaction force, and there was no significant change in the net body rotation during the contact phase as a function of acceleration (Fig. 4C).
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Mechanical power output
Turkeys increased power output for acceleration by decreasing the negative
power developed by the hindlimbs and increasing the positive power
(Fig. 5). The power profiles
during accelerations were asymmetrical, peak power outputs occurred late in
the stance phase. The area under the negative region of the curves represents
energy absorbed by muscletendon units (negative work), while the area
under the positive region of the vertical axis is the positive work done by
the muscletendon. As expected, negative and positive work at steady
running speeds were approximately equal, resulting in negligible net work
(Fig. 5).
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Most of the increase in the net muscle work performed during accelerations resulted from an increase in the positive work done by muscles (Fig. 6). A decrease in the mechanical energy loss of the center of mass (negative work) also contributed to the increase in net work with acceleration. During the highest accelerations, the total mechanical energy of the body showed no period of decrease, and only positive work was performed.
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Muscle-mass-specific mechanical power and work
The hindlimb muscle mass potentially available to power accelerations was
measured from turkeys of similar age and condition to those used for the
running experiments. The total mass of all hindlimb muscle (including hip,
knee, ankle and phalangeal extensors and flexors) was 7.7 ±0.3 % of
body mass for one limb (N=3 animals, mean ± S.D.).
The power and work produced per unit limb muscle mass was remarkably high during high accelerations. Fig. 7 shows the peak instantaneous power output of the muscletendon units of the hindlimb, calculated from total hindlimb extensor muscle mass and the body center of mass power. Peak muscle-mass-specific power outputs increased with increasing acceleration. The highest measured peak power outputs exceeded 400 W kg-1 muscle mass. The mean power produced during the stance phase also increased with increasing acceleration, with the highest values exceeding 150 W kg-1 muscle. This measure gives a conservative estimate of muscletendon power output because it assumes complete activation of all muscles, which is unlikely during our measurements.
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Discussion |
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Do turkey muscles operate at high power outputs during accelerations? A few
direct measurements of muscle power output in vivo in locomotor
systems that should be specialized for power production provide a source of
comparison. Swimming and flying both require high muscle power outputs to
overcome drag. Direct measurements of in vivo muscle function in
swimming scallops (Marsh et al.,
1992) and flying pigeons
(Biewener et al., 1998a
) reveal
muscle power outputs that are similar to those observed for the hindlimb
musculature of turkeys during acceleration (to eliminate the effects of duty
cycle, Table 1 compares only
the power developed during muscle contraction, or stroke power). Estimates of
power developed during take-off in quail indicate substantially higher power
outputs (Askew et al., 2001
).
Differences between pigeon and quail power output in
Table 1 are due in part to
submaximal power outputs required during steady-speed, level flight; kinematic
studies suggest that muscle power outputs during take-off can be twice those
measured for level flight (Dial and
Biewener, 1993
). Power outputs for turkey hindlimbs are also much
lower than estimated values for quail pectoralis.
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Differences in contractile properties probably explain some of the
variation in power output. Quail pectoralis is composed of fast glycolytic
fibers and can power flight for only brief bursts. The hindlimb musculature of
galliforms is capable of powering sustained running and contains a mixture of
fiber types (Talesara and Goldspink,
1978). Measurements of the contractile properties of the
gastrocnemius of wild turkeys (F. E. Nelson and T. J. Roberts, unpublished
observations) indicate peak isotonic power outputs similar to those measured
for fast oxidative muscles in mice (372.4 W kg-1 for mouse extensor
digitorum longus; Askew and Marsh,
1997
) and lower than the sustained mean power output observed in
quail (Askew et al., 2001
).
The peak instantaneous values for hindlimb muscle mass power output during high accelerations in turkeys exceeded 400 W kg-1. The high instantaneous power output suggests an elastic contribution to power output late in stance phase. Even if the intrinsic power-generating capacity of the turkey hindlimb musculature exceeds 400 W kg-1, is it likely that some muscle-tendon units must produce instantaneous power outputs in excess of muscle capacity during maximal accelerations. The measured values for muscle-mass-specific power output are calculated on the basis of the assumption that all hindlimb skeletal muscles actively produce power during acceleration, because it is difficult to eliminate definitively any given muscle from some potential contribution to power output during accelerations. However, it is likely that some muscles cannot contribute. For example, flexors of the ankle and hip are unlikely to produce significant power output during the stance phase of acceleration because these joints do not undergo significant flexion. Muscles involved primarily in adduction or abduction of the limb may also be less likely to contribute to powering forward locomotion. The present study also underestimated mechanical power output because the work necessary to accelerate the mass of the limbs during the step and the work associated with co-contraction of muscle antagonists were not estimated. These components of work are expected to be small relative to the work required to accelerate the body but would require some muscle power output during acceleration.
Ground reaction forces produced during acceleration.
One of the features of a bouncing gait that allows muscletendon
units to operate economically as springs is the pattern of braking and
propulsive horizontal ground reaction forces developed in each step.
Horizontal forces produced during a steady-speed running step actually
increase the work muscletendon units must do
(Clark and Alexander, 1975),
but they improve muscle mechanical advantage, reduce the muscle force required
to support body weight (Chang and Kram,
1999
; Full et al.,
1991
) and contribute to balance by limiting body pitching
(Clark and Alexander, 1975
).
The importance of maintaining the alignment of the ground reaction force and
center of mass is illustrated by the observation that humans running in
reduced gravity reduce their horizontal forces in proportion to the reduced
vertical force to maintain a similar ground reaction force angle
(Chang and Kram, 1999
).
To accelerate, an animal must produce forward-oriented ground reaction forces while still maintaining balance and reasonable joint moments. A turkey running with the limb kinematics observed during a steady-speed run and the ground reaction force observed during a high acceleration would experience a mean moment about the center of mass of 9 N m that would tend to pitch the body about a transverse axis. This moment would result in 300° of body rotation in 200 ms, approximately the time of one step (based on an estimated body moment of inertia of 0.035 kg m2). Thus, in the absence of a mechanism to maintain the alignment of the ground reaction force and the center of mass, the propulsive forces produced by an accelerating turkey would be sufficient to produce nearly a full backward rotation of the body in a single contact period.
Interestingly, examples from three studies of acceleration reveal three
different mechanisms for maintaining alignment between the ground reaction
force and the center of mass during accelerations. To maintain alignment
between the center of mass and ground reaction force, an accelerating runner
must either position its center of mass more anteriorly (relative to
steady-speed running) or position the point of force application more
posteriorly. Human runners rely primarily on the first of these options,
leaning forward during the accelerative portion of a sprint to position the
center of mass anterior of the foot and in line with the forward-oriented
ground reaction force vector (Harland and
Steele, 1997). In contrast, dogs accelerate during a trot by
redistributing vertical force between the fore- and hindlimbs to position the
mean origin (center of pressure) of the ground reaction force more posteriorly
(Lee et al., 1999
).
Some of these mechanisms are unavailable to running birds because their center of pressure is constrained to the area of their foot and their center of mass is positioned anterior to their hip during normal running. Instead, during an acceleration, turkeys alter their angle of limb retraction and protraction to keep the center of mass anterior to the foot during most of the step. Changes in the pattern of force development also contribute to the alignment of the center of mass and ground reaction force during acceleration. An increase in the magnitude of the vertical force means that the angle from vertical of the ground reaction force for any given propulsive force is smaller. Also, during accelerations, the development of the vertical ground reaction force is delayed with respect to the time of foot contact so that the body is positioned more anteriorly by the time significant force is developed (Fig. 2). These mechanisms allow turkeys to produce the high propulsive forces needed in an acceleration without losing balance.
How quickly can turkeys accelerate?
There is little information available to estimate how quickly animals can
accelerate to top speed. Our measurements are based only on power outputs
during single footfalls near one running speed, but they can provide a first
estimate of the time it would take a turkey to accelerate to top speed,
assuming that they maintain the same power output across their entire speed
range. At a top speed of 7 ms-1 (based on our own observations of
free-running turkeys), a turkey's kinetic energy is 24.5 J kg-1
body mass. The maximum stroke power measured here of 11.5 W kg-1
body mass suggests that the animal would be able to accelerate to this top
speed in just over 2 s (assuming a duty factor of 0.5). If we assume a mean
stride frequency of 2.5 Hz (Gatesy and
Biewener, 1991), the animal would reach maximum speed in
approximately four strides.
Elastic energy storage and recovery during accelerations
What role does elastic energy storage and recovery play in accelerations?
Two features of the power profile suggest that redistribution of muscle power
by storage and recovery of strain energy in elastic elements is important
during powerful accelerations. First, values for peak instantaneous power
output of the entire hindlimb musculature during the highest accelerations
exceed 400 W kg-1. Although recent data suggest very high
power-generating capacity in pectoralis muscle of galliform birds (as high as
400 W kg-1 sustained power), it is likely that the very high power
output measured during turkey accelerations results in part from the
amplification of muscle power by the recoil of elastic elements late in the
step. Second, our estimates of the high mean stroke power developed during the
step indicate that the muscle contractile units must operate at a relatively
constant, high power output during the entire step
(Fig. 7B). Given the very low
power applied to the body during the first half of the step
(Fig. 5), a high mean muscle
power output is possible only if, during this time, muscle power is applied to
the stretch of elastic elements rather than to increasing the mechanical
energy of the body. The asymmetric power profile is consistent with the idea
that muscle shortening directly stretches elastic elements to store elastic
strain energy in the first half of the step. Then, during the second half of
the step, both muscle power and released elastic power are applied to the
body.
A similar mechanism of elastic energy redistribution of muscle power has
been suggested for specialized jumpers, frogs
(Marsh and John-Alder, 1994)
and galagos (Aerts, 1997
).
Jumping humans also use store and recover muscle work as tendon strain energy
during squat jumps; modeling suggests that tendons store and recover nearly
the same amount of energy in a squat jump and a counter-movement jump
(Anderson and Pandy, 1993
), and
elastic energy recovery in the second half of a jump enhances
muscletendon shortening velocity and power output
(Bobbert, 2001
;
Kurokawa et al., 2001
). The
similarity between the power profiles for jumping animals and accelerating
turkeys suggests that the redistribution of muscle power by elastic mechanisms
may be generally important for muscle-powered accelerations in
vertebrates.
Why store and recover muscle work in elastic elements during an acceleration? The most obvious explanation is that, by necessity, tendons must stretch and recoil whenever muscular force is produced. The difference between steady-speed running and acceleration appears to be the source of the stored elastic strain energy. During steady-speed running, some of the mechanical energy of the body is converted into elastic strain energy as the body slows and lowers during the first half of the step. During maximal accelerations in turkeys, there is no decline in the total mechanical energy of the body, and stored elastic strain energy must be supplied directly from active shortening of muscle fibers. Although this redistribution may result simply from the fact that elastic storage and recovery cannot be avoided, it seems likely that elastic energy storage and recovery may actually enhance muscular power production during accelerations. Redistribution of muscle power may facilitate the dramatic change in muscle fiber shortening necessary as muscles transition between the strut-like function of muscle contractile elements during steady-speed running and the power-producing motor-like function during acceleration. Because muscle shortening is applied to tendon stretch rather than to movements of the body, this mechanism may allow an uncoupling of body movement and muscle movements necessary to produce high muscle power outputs.
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Acknowledgments |
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References |
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---|
Aerts, P. (1997). Vertical jumping in Galago senegalensis: the quest for an obligate mechanical power amplifier. Phil. Trans. R. Soc. Lond. B 353,1607 -1620.
Alexander, R. McN. (1988). Elastic Mechanisms in Animal Movement. Cambridge: Cambridge University Press.
Alexander, R. McN. and Bennet-Clark, H. C. (1977). Storage of elastic strain energy in muscle and other tissues. Nature 265,114 -117.[Medline]
Anderson, F. C. and Pandy, M. G. (1993). Storage and utilization of elastic strain energy during jumping. J. Biomech. 26,1413 -1427.[Medline]
Askew, G. N. and Marsh, R. L. (1997). The
effects of length trajectory on the mechanical power output of mouse skeletal
muscles. J. Exp. Biol.
200,3119
-3131.
Askew, G. N., Marsh, R. L. and Ellington, C. P.
(2001). The mechanical power output of the flight muscles of
blue-breasted quail (Coturnix chinensis) during take-off.
J. Exp. Biol. 204,3601
-3619.
Biewener, A. A., Corning, W. R. and Tobalske, B. W.
(1998a). In vivo pectoralis muscle forcelength
behavior during level flight in pigeons (Columbia livia).
J. Exp. Biol. 201,3293
-3307.
Biewener, A. A., Konieczynski, D. D. and Baudinette, R. V.
(1998b). In vivo muscle forcelength behavior
during steady-speed hopping in tammar wallabies. J. Exp.
Biol. 201,1681
-1694.
Biewener, A. A. and Roberts, T. J. (2000). Muscle and tendon contributions to force, work and elastic energy savings: a comparative perspective. Exerc. Sport Sci. Rev. 28, 99-107.[Medline]
Bobbert, M. F. (2001). Dependence of human
squat jump performance on the series elastic compliance of the triceps surae:
a simulation study. J. Exp. Biol.
204,533
-542.
Cavagna, G. A. (1975). Force plates as
ergometers. J. Appl. Physiol.
39,174
-179.
Cavagna, G. A., Heglund, N. C. and Taylor, C. R.
(1977). Mechanical work in terrestrial locomotion; two basic
mechanisms for minimizing energy expenditure. Am. J.
Physiol. 233,R243
-R261.
Cavagna, G. A., Komarek, L. and Mazzoleni, S. (1971). The mechanics of sprint running. J. Physiol., Lond. 217,709 -721.[Medline]
Chang, Y.-H. and Kram, R. (1999). Metabolic
cost of generating horizontal forces during human running. J. Appl.
Physiol. 86,1657
-1662.
Clark, J. and Alexander, R. McN. (1975). Mechanics of running by quail (Coturnix). J. Zool., Lond. 176,87 -113.
Close, R. I. (1972). Dynamic properties of
mammalian muscles. Physiol. Rev.
52,129
-197.
Dial, K. P. and Biewener, A. A. (1993).
Pectoralis muscle force and power output during different modes of flight in
pigeons. J. Exp. Biol.
176, 31-54.
Dickinson, M. H., Farley, C. T., Full, R. J., Koehl, M. A. R.,
Kram, R. and Lehman, S. (2000). How animals move: an
integrative view. Science
288,100
-106.
Elliott, J. P., Cowan, I. M. and Holling, C. S. (1977). Prey capture by the African lion. Can. J. Zool. 55,1811 -1828.
Farley, C. T. (1997). Maximum speed and
mechanical power output in lizards. J. Exp. Biol.
200,2189
-2195.
Farley, C. T., Glasheen, J. and McMahon, T. A.
(1993). Running springs: speed and animal size. J.
Exp. Biol. 185,71
-86.
Full, R. J., Blickhan, R. and Ting, L. H. (1991). Leg design in hexapedal runners. J. Exp. Biol. 158,369 -390.[Abstract]
Gatesy, S. M. and Biewener, A. A. (1991). Bipedal locomotion: effects of speed, size and limb posture in birds and humans. J. Zool., Lond. 224,127 -147.
Harland, M. J. and Steele, J. R. (1997). Biomechanics of the sprint start. Sports Med. 23, 11-20.[Medline]
Hill, A. V. (1950). The dimensions of animals and their muscular dynamics. Sci. Prog. 38,209 -230.
Huey, R. B. and Hertz, P. E. (1983). Effects of body size and slope on acceleration of a lizard (Stellio stellio). J. Exp. Biol. 110,113 -123.
Kurokawa, S., Fukunaga, T. and Fukashiro, S.
(2001). Behavior of fascicles and tendinous structures of human
gastrocnemius during vertical jumping. J. Appl.
Physiol. 90,1349
-1358.
Lee, D. V., Bertram, J. E. and Todhunter, R. J.
(1999). Acceleration and balance in trotting dogs. J.
Exp. Biol. 202,3565
-3573.
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]
Marsh, R. L. (1990). Deactivation rate and
shortening velocity as determinants of contractile frequency. Am.
J. Physiol. 259,R223
-R230.
Marsh, R. L. and John-Alder, J. B. (1994).
Jumping performance of hylid frogs measured with high-speed cine film.
J. Exp. Biol. 188,131
-141.
Marsh, R. L., Olson, J. M. and Guzik, S. K. (1992). Mechanical performance of scallop adductor muscle during swimming. Nature 357,411 -413.[Medline]
McMahon, T. A. and Cheng, G. C. (1990). The mechanics of running: how does stiffness couple with speed? J. Biomech. 23,65 -78.[Medline]
Roberts, T. J., Chen, M. S. and Taylor, C. R.
(1998). Energetics of bipedal running. II. Limb design and
running mechanics. J. Exp. Biol.
201,2753
-2762.
Roberts, T. J., Marsh, R. L., Weyand, P. G. and Taylor, C.
R. (1997). Muscular force in running turkeys: the economy of
minimizing work. Science
275,1113
-1115.
Swoap, S. J., Johnson, T. P., Josephson, R. K. and Bennett, A.
F. (1993). Temperature, muscle power output and limitations
on burst locomotor performance of the lizard Dipsosaurus dorsalis.J. Exp. Biol. 174,185
-197.
Talesara, G. L. and Goldspink, G. (1978). A combined histochemical and biochemical study of myofibrillar ATPase in pectoral, leg and cardiac muscle of several species of birds. Histochem. J. 10,695 -710.[Medline]
Weyand, P. G., Sternlight, D. B., Bellizzi, M. J. and Wright,
S. (2000). Faster top running speeds are achieved with
greater ground forces not more rapid leg movements. J. Appl.
Physiol. 89,1991
-1999.