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Department of Human Biodynamics, University of California, Berkeley, California 94720-4480
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
ACKNOWLEDGEMENTS
FOOTNOTES
REFERENCES
ABSTRACT 
Ferris, Daniel P., and Claire T. Farley. Interaction of
leg stiffness and surface stiffness during human hopping.
J. Appl.
Physiol. 82(1): 15-22, 1997.
When mammals run,
the overall musculoskeletal system behaves as a single linear "leg
spring." We used force platform and kinematic measurements to
determine whether leg spring stiffness
(kleg) is
adjusted to accommodate changes in surface stiffness
(ksurf) when
humans hop in place, a good experimental model for examining
adjustments to
kleg in bouncing
gaits. We found that
kleg was greatly
increased to accommodate surfaces of lower stiffnesses. The series
combination of
kleg and
ksurf
[total stiffness
(ktot)]
was independent of
ksurf at a given
hopping frequency. For example, when humans hopped at a frequency of 2 Hz, they tripled their
kleg on the least
stiff surface
(ksurf = 26.1 kN/m; kleg = 53.3 kN/m) compared with the most stiff surface
(ksurf = 35,000 kN/m; kleg = 17.8 kN/m). Values for
ktot were not
significantly different on the least stiff surface (16.7 kN/m) and the
most stiff surface (17.8 kN/m). Because of the
kleg adjustment,
many aspects of the hopping mechanics (e.g., ground-contact time and
center of mass vertical displacement) remained remarkably similar
despite a >1,000-fold change in
ksurf. This study
provides insight into how
kleg adjustments
can allow similar locomotion mechanics on the variety of terrains
encountered by runners in the natural world.
running; spring-mass model; biomechanics; motor control
INTRODUCTION WHEN HUMANS AND OTHER ANIMALS run, they literally
bounce along the ground using muscles, tendons, and ligaments to store
and return elastic energy (1, 8). During hopping, trotting, and
running, the actions of the body's numerous musculoskeletal springs
are combined so that the overall musculoskeletal system behaves as a
single linear spring. As a result, the mechanics of running gaits can
be described by a simple spring-mass model. This model consists of a
single linear "leg spring" and a point-mass equivalent to the mass of the body (4, 20). The stiffness of the leg
spring represents the stiffness of the integrated musculoskeletal system during locomotion. This stiffness governs the mechanics of the
interaction between the musculoskeletal system and the external
environment during the ground-contact phase of locomotion.
Experimental evidence has shown that the stiffness of the leg spring is
independent of forward speed during bouncing gaits (14, 18). This
constant leg spring stiffness at all forward speeds has been observed
in all mammals studied to date, including running humans, hopping
kangaroos, and trotting horses and dogs (14, 18). In each of these
animals, the spring-mass system is adjusted for higher speeds by
increasing the angle swept by the leg during the stance phase, thus
reducing the vertical movements of the center of mass during the stance
phase at higher speeds (14, 18).
Although leg stiffness remains nearly the same at all running speeds,
it is possible for the stiffness of the leg spring to be adjusted. When
humans hop in place, the stiffness of the leg can be increased by more
than twofold to accommodate increases in hopping frequency or increases
in hopping height at a given frequency (13). Furthermore, recent
evidence reveals that the stiffness of the leg spring can be increased
by more than twofold during forward running at a given speed to allow a
range of stride frequencies (15). A stiffer leg spring allows humans to
run with a higher stride frequency at the same forward speed.
The purpose of the present study was to determine whether leg stiffness
is adjusted to accommodate surfaces with different properties. This
study is part of our long-term research goal of understanding the
effects of surface properties on the biomechanics of locomotion. Most
locomotion biomechanics research has examined locomotion on hard smooth
laboratory floors. Humans and other animals run on a wide variety of
surfaces in the natural world. As a first step toward understanding the
effects of surface properties on locomotion, this study examines the
effects of surface stiffness on bouncing gaits.
Several studies have focused on the influence of surface stiffness on
single events, such as a drop jump or a landing from a jump in humans
(16, 23, 24, 28, 29). In these single events, there is less angular
displacement of the ankle, knee, and hip when a subject lands on a
compliant surface than on an extremely stiff surface. These results
suggest that humans make their legs stiffer when they land on a
compliant surface, thus decreasing the energy absorption by their
musculoskeletal system and increasing the energy absorption by the
surface. However, there are differences between these single-impact
events and locomotion that make it difficult to predict whether the
same strategy will be used for both. Locomotion is a cyclic activity
that is sustained for long periods of time. As a result, minimizing
metabolic energy cost is likely to be important in determining the
strategy used for locomotion on surfaces of different stiffnesses. By
contrast, avoidance of injury may be most important in landing from a
jump, and maximizing jump height is most important in a drop jump.
Because of these differences, the musculoskeletal adjustments for
surfaces of different stiffnesses may be different for locomotion than for single-impact events.
Locomotion experiments have shown that surface stiffness does affect
maximum running speed (21). Humans can sprint faster on a slightly
compliant surface than on an extremely stiff surface like concrete
(21). This observation was used to design the tuned indoor running
tracks currently used at Harvard and Yale Universities (10, 21).
Although this earlier work examined the effect of surface stiffness on
top speed, it did not examine the mechanics of submaximal running at a
given speed (21). Various studies have examined the effect of cushioned
running shoes on the mechanics of running at a given speed. These
studies have shown that compliant running shoes reduce the impact force
associated with lower limb deceleration immediately after the foot hits
the ground during running (9, 26). However, because running shoes are
much stiffer than the leg spring, running shoe elastic properties do
not have a substantial effect on the kinetics of running after the
initial impact with the ground.
The purpose of this study was to determine whether the stiffness of the
leg spring is adjusted to accommodate changes in surface stiffness
during bouncing gaits. Several aspects of the mechanics of bouncing
gaits, including peak ground reaction force, stride frequency, and
ground-contact time, depend on leg spring stiffness (4, 13, 15, 20).
When animals run on a compliant surface, the surface acts as a second
spring in series with the leg spring. In this case, the mechanics of a
bouncing gait depend on the combined stiffness of the leg spring and
the surface spring. We hypothesized that the leg spring stiffness would
be increased to accommodate compliant surfaces, thus offsetting the
effects of the compliant surface on the mechanics of locomotion. This
idea is supported by the single-impact studies, in which leg stiffness
appeared to increase on compliant surfaces (16, 23, 24, 28, 29). It is
important to point out that it is not mechanically required for leg
stiffness to be increased for bouncing gaits on compliant surfaces. An
alternative strategy would be to keep the leg stiffness the same for
all surfaces, thus allowing the ground-contact time to increase on less
stiff surfaces. To test our hypothesis, we used hopping in place as our
experimental model. Hopping in place is an ideal model because it
follows the same basic mechanics and spring-mass model as forward
running (13) yet has simpler kinematics. We compared the stiffness of
the leg spring during hopping in place on surfaces with a wide range of
stiffnesses.
METHODS
The surface stiffness was determined by using static load tests in which weights were placed on the surface and the displacement of the surface was measured. The force-displacement curve for each surface configuration was linear to within 3% over the range of forces that occurred during hopping. Loaded free-vibration tests showed that the effective mass of the surface was 1.5 kg. This low effective mass was possible due to the use of lightweight aluminum and fiberglass construction materials. The damping characteristics of the sprung surface were measured from the logarithmic decrement of free vibration and were found to be negligible (damping ratio <0.01). The entire surface was bolted to the top of two force platforms. Calculation of leg spring stiffness and total stiffness on hard force platform surface. The spring-mass model consists of a single point-mass equivalent to the body mass and a single linear compression spring, the leg spring (Fig. 2A) (4, 6, 13-15, 20). The leg spring represents the overall stiffness of the multijointed leg during locomotion. Because two legs were used for hopping, the leg spring stiffness was equal to the combined stiffness of both legs. When subjects hopped on the hard surface (i.e., the force platform surface), the maximum vertical displacement of the center of mass (COM) of the body during the ground-contact phase (
ytot) was equal to
the maximum displacement of the leg spring
(L; Fig. 2A). The average stiffness of the
leg spring
(kleg) during
the ground-contact phase was calculated by taking the ratio of the peak
vertical ground reaction force
(Fpeak) to the
L at the instant that the leg
spring was maximally compressed (Eq. 1). Because of the springlike nature of the leg, the
peak ground reaction force and the peak leg spring displacement both
occurred simultaneously at the middle of the ground-contact phase
|
(1) |
L
was calculated by double integration of the vertical acceleration of
the COM as calculated from the vertical ground reaction force. This
technique has been used extensively and is described in detail
elsewhere (5, 7). When the subjects hopped on the hard surface, the leg
spring stiffness was equal to the total stiffness.
L), total stiffness is
equal to leg stiffness. B: when humans
hop on an elastic compliant surface, surface spring is in series with
leg spring. Displacement of point mass
(ytot) is
equal to sum of L and surface
spring displacement. Total stiffness is equal to series combination of
leg stiffness and surface stiffness.
Calculation of leg spring stiffness and total stiffness on the elastic surface. When subjects hopped on the elastic surface, the vertical movements of the COM during the ground-contact phase depended on the stiffness of the leg spring and the stiffness of the surface (Fig. 2B). The stiffness of these two springs in series will be referred to as the "total stiffness" (ktot). The average ktot of the system was defined as the ratio of Fpeak to
ytot at the instant of the ground-contact phase when the COM reached its lowest point
|
(2) |
ytot
was calculated by integrating the vertical acceleration twice (5, 7).
ytot comprised
two components, L and the vertical
displacement of the surface
(ysurf)
|
(3) |
ysurf was
calculated from the ratio of the peak vertical ground reaction force to
the surface stiffness. The value for
L was then calculated from
ytot and
ysurf by using Eq. 3. Subsequently, leg spring
stiffness was calculated by using Eq. 1.
There were two approximations used in the calculation of leg spring
stiffness for hopping on the elastic surfaces. First, we approximated
that the force in the leg spring was equal to the ground reaction
force. This approximation is reasonable because our measurements showed
that the inertial force due to surface acceleration was very small
(Fig. 3). The inertial force due to surface
acceleration during a hop is equal to the product of the acceleration
and effective mass (1.5 kg) of the surface. To determine the surface
acceleration, we videotaped the surface at 200 Hz (JC Labs, Mountain
View, CA) while a subject hopped on the surface with the range of
hopping frequencies and surface stiffnesses used in this study. The
kinematic data were filtered by using a fourth-order zero-lag
Butterworth low-pass filter (Peak Performance Technologies) with an
optimal cutoff frequency (15 Hz) as determined by residual analysis
(32). Peak surface acceleration during a hop was between 5 and 33 m/s2, depending on surface
stiffness and hopping frequency. The peak inertial force was always
<2% of the peak vertical ground reaction force (Fig. 3). These
experimental tests showed that the approximation that the force in the
leg spring is equal to the vertical ground reaction force led to a
maximum of 1.5% overestimation of the leg spring stiffness. Thus we
concluded that it was reasonable to use the vertical ground reaction
force as an approximation of the force in the leg spring for the
calculation of leg spring stiffness.
The second approximation used was that
ytot, as
calculated by integrating the vertical ground reaction force twice, was
equal to the sum of L and
ysurf
(Eq. 3). Integrating the vertical ground reaction force
twice gives the vertical displacement of the COM of the entire system
of masses that are moving on the force platform, including both the
subject mass and the surface mass. Because the surface's COM and the
subject's COM move relative to each other during the ground-contact
phase, the leg spring displacement calculated from force platform
measurements will be slightly lower than the actual leg spring
displacement. The potential error due to this approximation was
calculated from actual data for the surface effective mass (1.5 kg),
the average mass of a subject (63.4 kg), and the distance between the
two COMs (i.e., the length of the leg spring). The length of the leg spring at the instant of touchdown was estimated as the distance from
the ground to the subject's greater trochanter (mean = 0.9 m). We
calculated that the COM of the system, including both the subject and
the surface, was 0.0225 m below the subject's COM at the instant of
touchdown. Because the leg spring compressed during the first half of
the ground-contact phase, the COM of the entire system moved upward
relative to the COM of the subject. The maximum upward movement of the
system's COM relative to the COM of the subject was 0.003 m (hopping
frequency of 2 Hz, ksurf = 50.1 kN/m), causing a
3.8% underestimation of maximum displacement of the leg spring and a
3.7% overestimation of leg spring stiffness. Because this error is
small compared with the adjustment of leg spring stiffness by as much
as 3.6-fold when subjects hopped on surfaces of different stiffnesses,
we concluded that it was reasonable to use this approximation in our
calculation of leg spring stiffness.
RESULTS
Typical force-displacement curves for the leg spring are shown in Fig.
4 for a subject hopping at 2 Hz on the most
stiff and least stiff surfaces. A single ground-contact phase is shown, including both the landing and takeoff curves. At the instant before
the subject first touched the ground, the vertical ground reaction
force and leg spring displacement were both zero. The force and the leg
spring displacement both increased during the first half of the
ground-contact phase. At the middle of the ground-contact phase, the
force reached its maximum value at the same time as the leg spring was
maximally compressed. During the second half of the contact phase, the
force and displacement both decreased, reaching zero as the subject
left the ground. During both landing and takeoff, the slope of the
force-displacement curve gradually increased at low levels of force and
displacement and became approximately linear at moderate and high
levels of force and displacement. The average slope of the leg spring
force-displacement curve during the ground-contact phase was the
average leg spring stiffness. This average slope and thus the leg
spring stiffness were much greater for hopping on the least stiff
surface than for hopping on the most stiff surface.
When the subjects hopped at a frequency of 2 Hz on surfaces with a
range of stiffnesses, the peak vertical ground reaction force decreased
as surface stiffness decreased (P < 0.0005; Fig. 5A). The
peak force decreased by 20% from 3.94 BW on the most stiff surface to
3.14 BW on the least stiff surface. The displacement of the leg spring
also decreased as surface stiffness decreased but to a much greater
extent (71%) than the peak force (P < 0.0001; Fig. 5B). The leg spring
displacement was 0.138 m on the most stiff surface and 0.043 m on the
least stiff surface. This decrease in displacement of the leg spring
was due to a nearly threefold increase in leg spring stiffness when
subjects hopped on the least stiff surface
(P < 0.005; Fig.
5C). Leg spring stiffness increased from 17.8 kN/m on the most stiff surface to 53.3 kN/m on the least stiff surface. Although there were significant differences in leg
spring stiffness among subjects (P < 0.005), all subjects increased their leg stiffness as surface stiffness
decreased
(subject-ksurf interaction, P = 0.56).
L decreased substantially on less
stiff surfaces (P < 0.0001).
C: leg spring stiffness
(kleg) was
greater during hopping on less stiff surfaces
(P < 0.005). Line,
kleg value
required to maintain a constant total stiffness equal to value for
hopping on hard surface of force platform
(ksurf = 35,000 kN/m). 
, Means for all subjects (n = 5) in all parts. Error bars, SE.
As a result of the adjustment to leg spring stiffness, the total
stiffness and the ground-contact time remained the same regardless of
surface stiffness (Fig. 6). The total
stiffness was 17.8 kN/m during hopping on the most stiff surface and
16.7 kN/m during hopping on the least stiff surface
(P = 0.60; Fig.
6A). The constant total stiffness
allowed the subjects to use the same ground-contact time regardless of
surface stiffness, ranging from 0.287 s on the least stiff surface to
0.268 s on the most stiff surface (P = 0.17; Fig. 6B).
In the second experiment, subjects hopped at a range of frequencies on
an elastic compliant surface
(ksurf = 50.1 kN/m) and on a very stiff surface
(ksurf = 35,000 kN/m). The leg spring stiffness was significantly greater on the
compliant surface than on the stiff surface at every hopping frequency
(P < 0.0001; Fig. 7A). At
a hopping frequency of 2.0 Hz, the stiffness of the leg spring was
1.65-fold greater on the compliant surface than on the stiff surface
(17.8 and 29.4 kN/m, respectively). The increase in leg spring
stiffness on the compliant surface was even greater at higher
frequencies. At a hopping frequency of 3.2 Hz, leg spring stiffness
increased by 3.6-fold from 31.6 kN/m on the stiff surface to 112.7 kN/m
on the compliant surface.
, Means for
all subjects (n = 5) on stiff surface.
, Means for all subjects on compliant surface. Errors bars, SE.
Because subjects increased their leg stiffness for hopping on the compliant surface, the total stiffness was the same at each hopping frequency on both surfaces (P = 0.44; Fig. 7B). At a hopping frequency of 3.2 Hz, the total stiffness was 34.0 kN/m on the stiff surface and 31.6 kN/m on the compliant surface. As a result of the total stiffness being the same on both surfaces, the ground-contact time was <10% greater on the compliant surface than on the stiff surface at every hopping frequency (P = 0.011; Fig. 7C).
DISCUSSION
Although the actual musculoskeletal system is a complex combination of muscles, tendons, and ligaments, a simple spring-mass model accurately describes the mechanics of running, hopping, and trotting (4, 6, 13-15, 18, 20). This model represents the springlike characteristics of the overall musculoskeletal system as a single linear spring (the leg spring). The stiffness of the leg spring remains nearly the same at all forward speeds in each of the animals studied to date, including running humans (14, 18). In addition, leg stiffness remains constant when humans run at reduced gravity levels (18). The only situations in which leg stiffness has been observed to change are when humans are asked to alter their preferred pattern for hopping in place or forward running by changing their hopping height or stride frequency (13, 15). These observations have led to speculation that the leg stiffness chosen during normal locomotion is strongly dependent on fundamental properties of the musculoskeletal system, such as tendon stiffnesses and reflex properties (18, 20).
The present study examined whether humans choose to adjust their leg spring stiffness to accommodate changes in terrain. When humans and other animals run in the natural world, they encounter a variety of terrains. However, we know very little about the biomechanics of locomotion on substrates other than hard and smooth laboratory floors. This study represents a first step toward understanding the role of musculoskeletal stiffness in the biomechanics and control of locomotion across a range of terrains.
Our findings support the hypothesis that humans adjust their leg spring stiffness to accommodate different surface stiffnesses. The stiffness of the leg spring is increased by as much as 3.6-fold to accommodate decreases in surface stiffness. As a result of the adjustment to the leg stiffness, the total stiffness of the series combination of the leg and the surface is nearly the same on all surfaces. This constant total stiffness makes it possible for the center of mass mechanics to be remarkably similar on surfaces with a wide range of stiffnesses. For example, the constant total stiffness allows the ground-contact time at a given hopping frequency to be nearly unaffected when surface stiffness is changed by as much as 1,000-fold (Fig. 6). If the leg spring stiffness had not been adjusted for different surfaces, the ground-contact time would have increased substantially on lower stiffness surfaces. For example, when the subjects hopped at 2 Hz on the least stiff surface, the ground-contact time would have been ~70% longer (0.499 vs. 0.287 s) if the leg spring stiffness had been the same as on the hard surface.
It should be emphasized that the leg stiffness adjustments and the constant total stiffness are not mechanically required to maintain a given hopping frequency. The mechanical behavior of a bouncing spring-mass system depends on its natural frequency. The natural frequency (f in Eq. 4) is determined by the ktot of the system and the mass (m)
|
(4) |
It would have been mechanically possible for the subjects to hop at 2 Hz on all of the surfaces when using the leg spring stiffness normally used on a hard surface (17.8 kN/m). On the least stiff surface (26.1 kN/m), this would have produced a total stiffness of 10.6 kN/m and a natural frequency of 2.06 Hz. This natural frequency is above the lowest possible natural frequency of 2 Hz. Our findings demonstrate that humans prefer to increase the stiffness of their leg spring to accommodate decreases in surface stiffness. For example, when subjects hopped at 2 Hz on the least stiff surface, they tripled the stiffness of their leg spring to 53.3 kN/m, keeping the total stiffness and the natural frequency nearly the same as on the hard surface. The constant total stiffness allowed the ground-contact time and the aerial time to remain nearly the same at a given hopping frequency regardless of surface stiffness. This strategy represents a choice and not a mechanical necessity. Additionally, related observations from our laboratory indicate that when subjects are allowed to freely choose their preferred hopping frequency on a range of surface stiffnesses, their preferred frequency is remarkably similar on surfaces with different stiffnesses. However, the leg spring stiffness at the preferred frequency increases by almost threefold when humans hop on the least stiff surface compared with the hard surface (n = 3; ksurf = 35,000 kN/m, preferred frequency = 2.2 Hz, kleg = 18.9 kN/m; and ksurf = 26.1 kN/m, preferred frequency = 2.0 Hz, kleg = 53.3 kN/m, respectively).
Running surfaces used by humans and other animals have a wide range of stiffnesses. Typical running tracks have much lower surface stiffnesses than the force platforms used for most locomotion biomechanics studies (track stiffnesses = 100-875 kN/m (21); force platform stiffness = 35,000 kN/m). When humans run on a very stiff surface, the most important parameter in determining the movements of the COM of the body and the ground-contact time is the vertical stiffness of their spring-mass system (14, 15, 18, 20). The vertical stiffness ranges from 20 kN/m at the lowest running speeds (18) to >100 kN/m at the highest running speeds (21). Thus the stiffness of some running tracks ranges from 1 to 8.7 times the vertical stiffness of the runner. Because the track stiffness is in the same range as the vertical stiffness during running, it may have a substantial effect on running mechanics if the vertical stiffness of the runner is not adjusted to accommodate the surface. During forward running, the vertical stiffness can be adjusted either by changing the leg spring stiffness or by changing the angle swept by the leg spring during the ground-contact phase (14, 18, 20). Our current research is examining stiffness adjustments for different surfaces in running humans.
It is interesting to note that the effect of surface stiffness on
mammalian bouncing gaits is likely to vary with body size. Recent
research has shown that the simple spring-mass model used to describe
human hopping in place and human running also describes the
biomechanics of bouncing gaits in a variety of hopping and trotting
mammals. Both leg spring stiffness and vertical stiffness increase
dramatically with body mass (M) in
mammals (kleg 
M0.67;
vertical stiffness M0.61) (14).
For example, the leg and vertical stiffnesses in a trotting horse are
~100 times greater than in a trotting rat (14). As a result, for a
surface of a given stiffness, the ratio of the surface stiffness to the
vertical stiffness will be 100-fold higher for the rat than for the
horse. This means that a surface of a given stiffness is much less
likely to affect the mechanics of locomotion in a rat than in a horse.
A surface would have to be extremely compliant
(ksurf = <5
kN/m) to require a substantial adjustment in the vertical stiffness of
a trotting rat in order to maintain a constant total stiffness.
The increased stiffness of the leg spring on compliant elastic surfaces may lead to a lower energetic cost compared with hopping or running on hard surfaces. The metabolic energy cost of locomotion is thought to be determined by a combination of the cost of performing mechanical work and the cost of generating muscular force (2, 19). When a person hops on a compliant elastic surface, part of the mechanical work required for hopping is supplied by the musculoskeletal system and part is supplied by storage and recovery of elastic energy in the surface. By increasing leg stiffness on a compliant elastic surface, the human reduces the mechanical work done by the leg and increases the mechanical work done by the surface. The second factor important in determining the energetic cost of locomotion is the cost of generating muscular force (19). With increased leg stiffness on compliant elastic surfaces, there is reduced flexion of the leg joints during the ground-contact phase. This is likely to result in a better mechanical advantage for the locomotor muscles (3). As a result, the average muscle force required for hopping or running would also be reduced. Because both the amount of work done by the person and the amount of force generated by the muscles would be reduced, the energetic cost of hopping or running is likely to be lower on a compliant elastic surface than on a hard surface.
Although it is clear that humans adjust their leg stiffness to accommodate changes in surface stiffness during hopping, the physiological mechanisms for this adjustment are not yet known. The actual leg comprises multiple joints, with muscles, tendons, and ligaments acting about each joint. The overall stiffness of the leg undoubtedly depends on a combination of the geometry of the joints and the torsional stiffness of the joints. For example, running with flexed knees increases the moment arm of the ground reaction force about the knee and greatly decreases leg stiffness (22). Many motor control studies have shown that the stiffness of a joint is highly adjustable when it is subjected to externally driven displacements and depends on both muscle activation and the modulation of reflexes (12, 17, 27, 30, 31). However, data on human locomotion suggest that reflexes do not play a large role in the control of leg stiffness. When humans have their lower limb reflexes temporarily blocked by ischemia, they run in place with a ground-contact time that is nearly the same as with active reflexes, suggesting that leg stiffness is unchanged (11). Future research should explore the link among limb stiffness, joint stiffness, and muscle activation in locomotion.
Present studies in our laboratory are examining the mechanisms by which leg spring stiffness is adjusted and how surface stiffness affects leg stiffness during forward running. The findings from this research could aid in the construction of athletic surfaces designed to reduce locomotion-related injuries and have implications for the design of spring-based prosthetic legs and legged robots intended to traverse a wide variety of terrains. Although humans and other animals run on a huge variety of terrains in the natural world, much of the locomotion biomechanics research to date has focused on locomotion across hard and smooth laboratory floors. Our results provide important insight into how the behavior of the musculoskeletal system is controlled to accommodate different surface properties.
ACKNOWLEDGEMENTS
This research was supported by National Aeronautics and Space Administration graduate fellowship NGT-51416 (to D. P. Ferris) and National Institute of Arthritis and Musculoskeletal and Skin Disease Grant R29 AR-44008 (to C. T. Farley).
FOOTNOTES
Address for reprint requests: D. Ferris, 3060 Valley Life Sciences Building, Univ. of California, Berkeley, CA 94720-3140 (E-mail: dferris{at}uclink2.berkeley.edu).
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