Adjusting muscle function to demand: joint work during acceleration in wild turkeys
Oregon State University, Department of Zoology, 3029 Cordley Hall, Corvallis, OR 97331-2914, USA
* Author for correspondence at present address: Brown University, Ecology and Evolutionary Biology Department, Box G-B205, Providence, RI 02912, USA (e-mail: thomas_roberts{at}brown.edu)
Accepted 17 August 2004
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Summary |
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We also measured the change in joint moment and angular excursion with acceleration to determine whether the mechanism for increasing work output at a joint involved an increase in muscle force or muscle shortening. The increase in joint work at the hip and ankle resulted almost entirely from an increase in joint angular excursion during stance. Hip extension increased by more than threefold from the lowest to the highest accelerations, and the angular excursion of the ankle increased from 24.8±4.7° (net flexion) at the lowest accelerations to 33.0±12.8° (net extension) at the highest accelerations. Mean stance joint moment was unchanged with acceleration at the ankle and increased by approximately 35% at the hip across the range of accelerations. These patterns of joint moment and excursion indicate that turkeys increase mechanical work for acceleration primarily by increasing muscle shortening, rather than muscle force.
Key words: locomotion, muscle work, muscle power, avian, running
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Introduction |
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We measured the moment of force, power and velocity at individual joints in
accelerating turkeys to address two questions. First, where is the power for
acceleration developed? Previously we found very high power outputs of the
entire hind limb (Roberts and Scales,
2002), and therefore we predicted that work output of all hind
limb joints would increase with increasing acceleration. Alternatively,
high-power activities like acceleration might be powered by only a subset of
limb muscles. For example, there is evidence that dogs recruit longer-fibered
more-proximal muscles to power jumping, while the ankle extensor
muscletendon units provide the same spring-like function during both
jumping and galloping (Alexander,
1974
). The second question motivating our study was, how is muscle
work increased at individual joints? Work is the product of force and
displacement, and the joint work performed during stance could be increased by
increasing one or both of these variables. We predicted that joint work would
increase primarily as a result of increases in joint excursion. This
prediction was based on measurements of force and strain in individual
muscles, which indicate that for several muscles an increase in muscle work
from level to incline running is achieved primarily by an increase in muscle
shortening (Roberts et al.,
1997
; Daley and Biewener,
2003
; Gabaldon et al.,
2004
).
We measured joint mechanics during single footfalls as turkeys ran across a force-plate in a trackway. Strides for analysis were chosen that were all approximately the same running speed, but varied in the amount the animal accelerated during the step. Joint moment, angle and power were measured by high-speed video and force-plate measurements using inverse dynamics. We tested two hypotheses: (1) work output increases at all major joints in direct proportion to acceleration and (2) any increase in work is due to an increase in the net joint angular excursion.
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Materials and methods |
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The running protocol has been described in detail previously
(Roberts and Scales, 2002).
Force and video measurements were recorded from single footfalls as animals
ran over a trackway at mean speeds of 1.752.25 m s-1. A
total of 49 runs over a wide range of accelerations was recorded. The mean
stance horizontal force divided by body mass was used as a measure of
acceleration. Runs were chosen for analysis such that data for individual
birds were evenly distributed across the range of accelerations.
Force measurements
A piezoelectric force-plate (Kistler 9233aa; Kistler USA, Amherst, NY, USA)
placed in the trackway was used to measure ground reaction force magnitude and
position during single footfalls. Force-plate signals were acquired to
computer at 1000 Hz with a 12-bit A/D board (National Instruments
PCIMIO-16E-1) using Labview (National Instruments, Austin, TX, USA) software.
The start of video and force acquisition was triggered from an external signal
to allow synchronization of the two signals. Force data were smoothed in
software with a bidirectional low-pass Butterworth filter with a 100 Hz cutoff
frequency.
Video measurements
Joint positions in a sagittal plane were determined from high-speed video
recordings (Redlake Motionscope 1000, San Diego, CA, USA). Small reflective
markers (3M; 70610WS) were applied to the skin. Markers were applied at the
center of rotation of the tarsometatarsalphalangeal (TMP) joint and the
ankle (intertarsal) joint. Knee and hip centers of rotation could not be
marked directly because the wing obstructed the view of the hip, and knee
movement occurred independently of skin movement. To locate the position of
the knee in the video, two markers were placed along the tibiotarsus at about
a third and two-thirds the distance from the ankle to the knee. These markers
were aligned such that the position of the knee center of rotation could be
extrapolated from the position of the ankle marker and the known distance from
the ankle to the center of rotation of the knee. A similar technique was used
to determine the position of the hip using a marker glued to the back of the
animal just above the hip. Because there is virtually no movement of the skin
on the back, this marker was fixed relative to the acetabulum, thus providing
a good indicator of the position of the center of rotation of the hip. These
methods for determining joint centers of rotation have been validated
previously using high-speed x-ray cine analysis, which indicated that the
largest error in joint marking occurs at the most proximal joints and is less
than 0.5 cm (Roberts et al.,
1998). To determine the rotation of the body (for the calculation
of hip angle), two markers were attached along the back of the animal.
Video data was captured into a Macintosh Computer using a Scion LG-3 frame-grabbing card. Marker positions were digitized using a custom-designed macro written for NIH Object-Image (a version of NIH Image adapted by Norbert Vischer; http://simon.bio.uva.nl/object-image.html). Joint position data were smoothed in software using a cubic spline interpolation available in Wavemetrics Igor (smoothing factor=1, S.D.=0.001). Joint position data and force data were combined in software (Microsoft Excel and Wavemetrics Igor) for calculation of joint moments and powers.
Net muscle moment, velocity and power
Net muscle moments (Mm) were determined from the ground
reaction force (GRF) and joint positions as illustrated in
Fig. 1. The net muscle moment
is calculated from the product of the GRF, and the joint out-moment
arm (R) (the orthogonal distance from the GRF to the center
of rotation of the joint; Biewener,
1989):
![]() | (1) |
|
By convention, we assigned positive values to moments produced by muscles
that tend to support body weight during normal standing. Thus, positive
moments represented net extensor muscle moments for the hip, knee and ankle.
At the toe, flexion supports body weight and has the potential to contribute
positive power to lift and accelerate the body, therefore net flexor muscle
moments at the TMP joint were considered positive. Muscle moments necessary to
accelerate the limbs relative to the body and to balance gravitational forces
on the limbs were not calculated. These moments are expected to be negligible
at more distal joints and small at proximal joints in birds
(Clark and Alexander, 1975).
These moments also do not contribute to accelerating the center of mass of the
animal.
Joint angles were determined from joint position data as shown in Fig. 1. To determine the extension of the femur at the hip, we calculated the sum of the angle of the femur to the horizontal and the angle of the back relative to the horizontal. This assumes that changes in the back angle accurately represent changes in pelvic angle. Joint velocity was calculated from the time derivative of joint angle using the differentiation function in Wavemetrics Igor (central-point difference differentiation). The sign conventions used for joint velocities were the same as those for joint moment: positive velocities at the hip, knee and ankle were recorded when the joints were extending, while positive velocities at the TMP joint represented joint flexion.
The mechanical power developed at a joint, Pm, is equal
to the product of the net muscle moment, Mm and the joint
velocity, :
![]() | (2) |
Positive power (work performed by muscles) is developed when the sign of
the moment and the velocity are the same, i.e. net muscle extensor moments are
produced while the joint extends or muscle flexor moments are produced as the
joint flexes. Negative work (energy absorbed at a joint) is performed when the
joint velocity and moment have opposite signs, i.e. the joint flexes as
extensor muscles produce force. It is important to note that the calculated
joint powers represent the power produced at a joint, but not necessarily the
power developed by the muscles at that joint. Muscles that cross more than one
joint can act to transfer power from one joint to another
(van Ingen Schenau et al.,
1992; Jacobs et al.,
1993
). Thus, the power measured at a given joint represents the
sum of the power applied directly by muscles at that joint as well as power
transferred from other joints.
The net work performed at a joint during stance was calculated from the area under the powertime curve for that joint. Positive power outputs represent positive work (work done by muscletendon units) and negative power outputs represent negative work (work absorbed by muscletendon units). Elastic elements can store and recover energy but they cannot perform net work. Thus, we assumed that net work performed during an entire step was equal to the net work performed by muscle contractile elements.
The total work done on the center of mass (COM) during a step was
determined from force-plate ergometry
(Cavagna et al., 1964). A
detailed description of these methods has been presented previously
(Roberts and Scales,
2002
).
Least-squares linear regression was used to determine the effect of acceleration on variables of interest. The criteria for significance was P<0.05. It was determined by ANCOVA (analysis of covariance) that there was no significant effect of individual bird on any of the values measured. Therefore, data for individual birds were pooled for least-squares regressions.
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Results |
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Work output at the hip and ankle increased with acceleration, while knee
and TMP work was unchanged (Fig.
3). Hip work and ankle work increased at about the same rate with
increases in acceleration (the slope of the regression of net work
versus acceleration was 0.154±0.017 for the hip and
0.192±0.012 for the ankle). The extensor muscle mass at the hip is
nearly equal to that of the ankle (Roberts
et al., 1998). Thus, the contribution of work from the hip and the
ankle is approximately in proportion to the extensor muscle mass at these
joints. Work output at the knee was most frequently positive but was
independent of acceleration.
|
Joint moment and excursion
To determine whether muscle work output was increased by increasing the
force that muscles developed, or the distance over which they shortened, we
measured changes in joint moment and angular excursion for each joint as a
function of acceleration. There was a small but significant increase in mean
joint moment with acceleration for all joints except the ankle
(Fig. 4). To determine whether
the changes in joint moment with acceleration resulted from a change in ground
reaction force or a change in mean joint mechanical advantage
(Equation 1), we estimated the
mean moment arm of the ground reaction force (R) during stance.
Because the knee produces both net flexor and extensor moments during stance,
we measured the mean moment arm for flexion and extension separately for the
knee. There was a significant change in mean moment arm during a step for
negative (flexor) moments at the knee (Fig.
5). The regression of hip R on acceleration also produced
a significant slope.
|
|
There was a significant increase in the net joint excursion (angle at
toe-off minus angle at toe-down) at the hip, knee and ankle
(Fig. 6). A comparison of
values for the five lowest accelerations (0.22±0.08 m
s-2, approximately steady speed) and the five highest accelerations
(4.86±0.27 m s-2) indicates that net hip extension
approximately tripled from steady speed to the highest accelerations
(10.3±7.9° versus 34.5±13.2°). The mean ankle
angular excursion for the five lowest accelerations was
24.8±4.7° (net flexion) versus
33.0±12.8° (net extension) for the five highest accelerations.
Because these joints produce positive extensor moments of force, increases in
net extension result in increases in positive work. As acceleration increased,
the net flexion at the knee decreased. The reduction in knee flexion may be
related to the need to reduce leg protraction angle during the stance phase of
accelerations (Roberts and Scales,
2002), as much of the reduction in knee flexion resulted from a
decrease in knee angle at toe-down.
|
Figs 7,
8,
9,
10 present joint moment, angle
and power for representative steps for zero (steady-speed), moderate and high
acceleration. Fig. 7
illustrates that although a relatively large moment was produced at the hip,
power and work (the area under the power curve) during steady-speed running
were low because of the limited excursion at this joint in avian runners
(Gatesy, 1999). Power output
increased with acceleration as the joint extended more during force
production. At all accelerations, the work absorbed at the hip (area under the
negative portion of the power curve) was small because the flexion at the
joint was small. The high power produced late in stance during accelerations
was associated with a shift in timing of force production, from early to
mid-stance during steady-speed running to late stance for acceleration. The
time of peak joint moment, expressed as a fraction of total contact time,
increased significantly with acceleration (linear regression,
y=0.322+0.042x; r2=0.51,
P<0.01). Late stance force production coincided with the period of
the most rapid extension of the hip, explaining in part the increase in power
and work from steady speed to acceleration.
|
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The power profile at the knee was complex (Fig. 8). Early in the stride, the knee produced a net flexor moment at the same time that it flexed, to result in positive power. The knee also produced some positive power later in the step, when it produced an extensor moment as it extended. The initial flexion of the joint decreased with acceleration, resulting in a small decrease in power output during this portion of the step. Joint moment profiles were similar at all accelerations.
Net power (or work) output at the ankle increased with acceleration because the energy absorbed at the joint (negative power) decreased, and the power produced increased (Fig. 9). Generally, as acceleration increased, the ankle was more flexed at toe-down and more extended at toe-off. It tended to flex to the same minimum angle at all accelerations. Joint moments changed with acceleration, but this change was small relative to the change in joint excursion. As with the hip, the time of peak joint moment, expressed as a fraction of total contact time, increased significantly with acceleration (linear regression, y=0.38+0.036x; r2=0.46, P<0.01).
The TMP produced a brief burst of positive power during rapid extension in late stance (Fig. 10). This positive power was generally balanced by negative power earlier in stance to result in no net work.
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Discussion |
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The high work and power outputs measured at the ankle and hip during
accelerations indicate high power and work outputs of the extensors of those
joints. This conclusion requires the assumption that the power measured at the
ankle and the hip was not produced by extensors at another joint (e.g. the
knee) and transferred via biarticular muscles
(van Ingen Schenau et al.,
1992). Transfer of power between joints has been demonstrated in
studies of human jumping, where much of the power developed at the ankle
results from a transfer of power from knee extensors to the ankle via the
biarticular triceps surae (Bobbert et al.,
1986
). Transfer of mechanical power via analogous
biarticular linkages is possible in avian runners. However, we believe that
the conclusion that hip and ankle powers measured in the present study reflect
power generated primarily by the extensors of those joints is justified by a
consideration of avian limb anatomy. The muscle mass of knee extensors in
birds is too small to account for the very high mechanical work measured at
the ankle during high accelerations. The knee extensor muscle mass in a single
limb is only 0.7% of body mass, while ankle extensors represent 2.5% of body
mass (Roberts et al., 1998
).
The work done at the ankle during the most rapid accelerations, approximately
0.8 J kg-1 body mass, would require a work output of 114 J
kg-1 muscle if transfer of power from knee extensors provided all
of this work. Power can be transferred only while the knee is extending, and
this occurs only for approximately 70 ms in rapid accelerations. To produce
the work performed at the ankle in this amount of time, the knee extensors
would have to develop a mean power in this period of more than 1600 W
kg-1. Similarly high values of muscle work and power would be
necessary if the work measured at the hip were supplied by knee extensors. The
estimate of 114 J kg-1 is nearly double the estimated maximum
capacity for work production of rapidly contracting vertebrate skeletal muscle
(Peplowski and Marsh, 1997
),
and 1600 W kg-1 is approximately 4x the maximum power output
of turkey hind limb muscle (Nelson et al.,
2004
). Thus, while transfer of power from knee extensors may
occur, it cannot explain the high work outputs measured at the hip and ankle
during accelerations.
The relatively short fibers and long tendons of turkey ankle extensors are
features typically associated with a spring-like function for running
(Ker et al., 1988). The
stretch and recoil of tendon springs can allow active muscle fibers to produce
force while undergoing little change in length. These low-work contractions
reduce metabolic cost. Short fibers also improve the economy of force
production in these muscles, because a smaller volume of muscle must be active
per unit force produced (Rall,
1985
; Biewener and Roberts,
2000
). The results from the present study indicate that in running
turkeys, ankle extensors that act as effective springs during steady-speed
running can also effectively perform net mechanical work for accelerations.
These results are not consistent with the idea that architectural features of
spring-like muscles limit their ability to develop mechanical work.
Models of muscle contraction during acceleration suggest that the stretch
and recoil of tendon springs may facilitate high muscle power outputs by
allowing muscle contractile elements to contract at relatively constant
velocities (Roberts, 2002).
The energy stored in a muscle's tendon depends only upon the force that is
applied to it. Thus, during both acceleration and steady-speed running,
tendons store and recover mechanical work as force rises and falls with each
stance period. During steady-speed running, the source of the stored elastic
energy is primarily the decline in potential and kinetic energy of the body
during the first half of the step. At the level of the joint, this is apparent
in negative power during, for example, ankle flexion
(Fig. 8). The negligible
negative power observed at the ankle during rapid accelerations suggests that
energy that must be loaded into tendons during the first half of the step
comes directly from shortening muscle contractile elements. These two
different mechanisms storage and recovery of mechanical work of the
body versus storage and recovery directly of muscle work
reflect the different roles that elastic mechanisms play during steady-speed
running versus acceleration. During steady-speed running elastic
mechanisms improve metabolic economy by reducing muscular work, while during
maximal accelerations the stretch and recoil of elastic elements redistributes
in time the application of muscle power to the body. The redistribution of
muscle power by elastic mechanisms in the turkey ankle extensors may actually
enhance a muscle's ability to develop power, because it may allow the muscle
to contract at a relatively constant velocity and power output even when the
velocity and power of the joint fluctuate
(Roberts, 2002
). The favorable
effects of elastic energy storage and recovery on muscle power development
that have been observed for jumping
(Bobbert et al., 1986
;
Alexander, 1995
;
Aerts, 1997
;
Roberts and Marsh, 2003
), may
apply generally to muscle-powered accelerations.
Mechanisms for altering hip and ankle net work
How is muscle work output increased from steady-speed running to
acceleration? The work performed during a muscle contraction is the product of
the muscle force and the distance shortened. In the transition from
steady-speed running to acceleration, the increase in net work might be
achieved by an increase in the force output of muscles that undergo
significant shortening during steady-speed running. Alternatively, muscles
that produce force during steady-speed running could shorten more to provide
net work for acceleration. Either of these strategies would be apparent in an
increase in joint moments or joint excursion, respectively.
The primary mechanism for increasing the mechanical work output of the turkey hind limb musculature from steady-speed running to acceleration was an increase in joint angular excursion, rather than joint moment. Joint moment was unchanged with acceleration at the ankle and increased by approximately 35% at the hip from the lowest to the highest accelerations. By contrast, hip net extension during stance increased more than threefold from the lowest to the highest accelerations, and ankle excursion increased from a net flexion of 24.8±4.7° to 33.0±12.8° net extension. At the ankle, this increase in net excursion during stance resulted from both an increase in joint extension and a decrease in joint flexion (Fig. 9). If we assume that muscle shortening is proportional to net joint excursion and muscle forces are proportional to joint moments, these results indicate that the primary mechanism for increasing mechanical work output from steady-speed running to accelerations is an increase in muscle shortening, rather than an increase in muscle force.
The pattern of joint moment observed during accelerations also suggests
that a change in timing of force production may play a role in increasing
joint work. Hip and ankle moments reached a maximum at approximately
mid-stance during steady-speed runs (Figs
7,
9). During accelerations, peak
moments occurred late in stance, corresponding to the period of rapid joint
extension. Because joint power is the product of joint velocity and moment,
this shift in the timing of joint moment resulted in an increase in joint
power. A similar mechanism for altering power output has been observed in
individual muscles of guinea fowl and turkeys running on different inclines
(Daley and Biewener, 2003;
Gabaldon et al., 2004
).
We were interested in determining whether mechanical advantage was altered
from steady-speed running to acceleration because we expected that the change
in orientation of the ground reaction force associated with acceleration
(Roberts and Scales, 2002)
would result in a change in R, the distance from the GRF
vector to the joint center of rotation (see
Fig. 1). The mechanical
advantage can be defined as the ratio of the muscle moment arm and the
GRF moment arm, R. A difference in mechanical advantage has
been observed at the ankle in humans running at a steady speed versus
accelerating (Carrier et al.,
1994
). Of the joints that contributed work to acceleration in our
study, only the hip showed a significant change in step-averaged R
across the range of accelerations. The small increase in muscle moment at the
hip resulted from both an increase in GRF magnitude and a change in
R (see equation 1). The
contribution of possible differences in muscle moment arm to changes in
mechanical advantage during steady-speed running versus acceleration
was not estimated in this study. Mechanical advantage might also be influenced
by differences in muscle moment arm between conditions, as the ankle and hip
operated at different joint angles for steady-speed running and
accelerations.
Variation in the mechanical advantage during the course of a step may also
influence muscle function. Carrier et al.
(1994) found that the
mechanical advantage of the ankle extensors in running humans decreased
throughout the foot contact period, reducing the variation in muscle velocity
during the step. We also observed differences in the pattern of R
that reflect possible differences in mechanical advantage between steady-speed
running and acceleration. During accelerations, the change in R
during a step at the ankle indicates that mechanical advantage increased
steadily throughout the contraction (Fig.
11). This pattern is the opposite of that observed in running
humans, and would presumably be unfavorable for muscle contractile units
operating alone. However, modeling of muscle-powered accelerations suggests
that when muscles operate in series with significant elastic elements, muscle
work may be maximized when the muscle operates through a continuously
increasing mechanical advantage (Roberts
and Marsh, 2003
). The pattern of increasing mechanical advantage
observed for accelerating turkeys may therefore reflect a variable leverage
that operates to allow effective storage and release of elastic strain energy
during each step.
|
Muscle shortening velocity for acceleration versus steady-speed running
The changes in joint moment and excursion with increasing acceleration in
turkeys suggest that, generally, muscles produce similar forces for both
steady-speed running and acceleration, but they operate at different
shortening velocities. This conclusion is based upon a comparison of
accelerative and steady-speed steps at a single running velocity. The increase
in joint excursion over approximately the same contact time from steady-speed
running to acceleration suggests that muscle shortening velocity,
V/Vmax, increases with acceleration. This is
consistent with the behavior of a model of muscle-tendon unit action during
acceleration, where a doubling of the volume of muscle recruited to accelerate
a load resulted in a large increase in muscle shortening velocity and only a
small increase in muscle force (Roberts,
2002). Measurements of individual muscle function suggest that a
similar mechanism explains the increase in muscle work from level to uphill
running. Muscle work, shortening and integrated EMG all increase as a function
of incline in the lateral gastrocnemius muscle of running turkeys, while the
peak force produced remains unchanged
(Roberts et al., 1997
). This
change in muscle shortening and work output may be facilitated by elastic
mechanisms. Together, these results support the idea that steady speed, level
running can be characterized as a low mechanical power activity, where muscles
operate effectively at low V/Vmax values, whereas
acceleration may be characterized as a high-power activity, where muscles
operate at intermediate V/Vmax values favorable
for muscle power production.
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Acknowledgments |
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Footnotes |
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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. Philos. Trans. Roy. Soc. Lond. B. Biol. Sci. 353,1607 -1620.
Alexander, R. McN. (1974). The mechanics of jumping by a dog (Canis familiaris). J. Zool. Lond. 173,549 -573.
Alexander, R. McN. (1988). Elastic Mechanisms in Animal Movement. Cambridge: Cambridge University Press.
Alexander, R. McN. (1995). Leg design and jumping technique for humans, other vertebrates and insects. Philos. Trans. Roy. Soc. Lond. B. Biol. Sci. 28,235 -248.
Biewener, A. A. (1989). Scaling body support in mammals: limb posture and muscle mechanics. Science 245, 45-48.[Medline]
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., Huijing, P. A. and van Ingen Schenau, G. J. (1986). An estimation of power output and work done by the human triceps surae muscle-tendon complex in jumping. J. Biomech. 19,899 -906.[Medline]
Carrier, D. R., Heglund, N. C. and Earls, K. D. (1994). Variable gearing during locomotion in the human musculoskeletal system. Science 265,651 -653.[Medline]
Cavagna, G. A., Saibene, F. P. and Margaria, R. (1964). Mechanical work in running. J. Appl. Phys. 19,249 -256.[Medline]
Clark, J. and Alexander, R. McN. (1975). Mechanics of running by quail (Coturnix). J. Zool. Lond. 176,87 -113.
Daley, M. A. and Biewener, A. A. (2003). Muscle
force-length dynamics during level versus incline locomotion: a comparison of
in vivo performance of two guinea fowl ankle extensors. J. Exp.
Biol. 206,2941
-2958.
Gabaldon, A. M., Nelson, F. E. and Roberts, T. J.
(2004). Mechanical function of two ankle extensors in wild
turkeys: shifts from energy production to energy absorption during incline
versus decline running. J. Exp. Biol.
207,2277
-2288.
Gatesy, S. M. (1999). Guineafowl hind limb function. I: cineradiographic analysis and speed effects. J. Morph. 240,115 -125.[CrossRef]
Jacobs, R., Bobbert, M. F. and van Ingen Schenau, G. J. (1993). Function of mono- and biarticular muscles in running. Med. Sci. Sports Exerc. 25,1163 -1173.[Medline]
Ker, R. F., Alexander, R. McN. and Bennett, M. B. (1988). Why are mammalian tendons so thick? J. Zool. Lond. 216,309 -324.
Nelson, F. E., Gabaldon, A. M. and Roberts, T. J. (2004). Force-velocity properties of two avian hind limb muscles. Comp. Biochem. Physiol. A 137,711 -721.
Peplowski, M. M. and Marsh, R. L. (1997). Work
and power output in the hind limb muscles of cuban tree frogs Osteopilus
septentrionalis during jumping. J. Exp. Biol.
200,2861
-2870.
Rall, J. A. (1985). Energetic aspects of skeletal muscle contraction. Exerc. Sport Sci. Rev. 13, 33-74.[Medline]
Roberts, T. J. (2002). The integrated function of muscles and tendons during locomotion. Comp. Biochem. Physiol. A 133,1087 -1099.
Roberts, T. J. and Marsh, R. L. (2003). Probing
the limits to muscle-powered accelerations: lessons from jumping bullfrogs.
J. Exp. Biol. 206,2567
-2580.
Roberts, T. J. and Scales, J. A. (2002).
Mechanical power output during running accelerations in wild turkeys.
J. Exp. Biol. 205,1485
-1494.
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.
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.
Taylor, C. R. (1994). Relating mechanics and energetics during exercise. In Advances in Veterinary Science and Comparative Medicine, vol. 38A (ed. J. H. Jones), pp. 181-215. San Diego: Academic Press.[Medline]
van Ingen Schenau, G. J., Boots, P. J. M., Groot, G. d., Snackers, R. J. and van Woensel, W. W. L. M. (1992). The constrained control of force and position in multi-joint movements. Neuroscience 46,197 -207.[CrossRef][Medline]
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