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Energetics and mechanics of human running on surfaces of different stiffnesses

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Abstract and Figures

Mammals use the elastic components in their legs (principally tendons, ligaments, and muscles) to run economically, while maintaining consistent support mechanics across various surfaces. To examine how leg stiffness and metabolic cost are affected by changes in substrate stiffness, we built experimental platforms with adjustable stiffness to fit on a force-plate-fitted treadmill. Eight male subjects [mean body mass: 74.4 +/- 7.1 (SD) kg; leg length: 0.96 +/- 0.05 m] ran at 3.7 m/s over five different surface stiffnesses (75.4, 97.5, 216.8, 454.2, and 945.7 kN/m). Metabolic, ground-reaction force, and kinematic data were collected. The 12.5-fold decrease in surface stiffness resulted in a 12% decrease in the runner's metabolic rate and a 29% increase in their leg stiffness. The runner's support mechanics remained essentially unchanged. These results indicate that surface stiffness affects running economy without affecting running support mechanics. We postulate that an increased energy rebound from the compliant surfaces studied contributes to the enhanced running economy.
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Energetics and mechanics of human running on surfaces
of different stiffnesses
Harvard Division of Health Sciences and Technology, and
Artificial Intelligence Laboratory,
Massachusetts Institute of Technology, Cambridge 02138;
Concord Field Station, Museum of
Comparative Zoology, Harvard University, Bedford 01730;
Division of Engineering and Applied
Sciences, Harvard University, Cambridge 02138;
United States Army Research Institute for
Environmental Medicine, Natick 01760; and
Department of Physical Medicine and Rehabilitation,
Harvard Medical School, Spaulding Rehabilitation Hospital, Boston, Massachusetts 02114
Received 12 December 2000; accepted in final form 24 September 2001
Kerdok, Amy E., Andrew A. Biewener, Thomas A.
McMahon, Peter G. Weyand, and Hugh M. Herr. Ener-
getics and mechanics of human running on surfaces of dif-
ferent stiffnesses. J Appl Physiol 92: 469478, 2002; 10.1152/
japplphysiol.01164.2000.—Mammals use the elastic compo-
nents in their legs (principally tendons, ligaments, and mus-
cles) to run economically, while maintaining consistent sup-
port mechanics across various surfaces. To examine how leg
stiffness and metabolic cost are affected by changes in sub-
strate stiffness, we built experimental platforms with adjust-
able stiffness to fit on a force-plate-fitted treadmill. Eight
male subjects [mean body mass: 74.4 7.1 (SD) kg; leg
length: 0.96 0.05 m] ran at 3.7 m/s over five different
surface stiffnesses (75.4, 97.5, 216.8, 454.2, and 945.7 kN/m).
Metabolic, ground-reaction force, and kinematic data were
collected. The 12.5-fold decrease in surface stiffness resulted
in a 12% decrease in the runner’s metabolic rate and a 29%
increase in their leg stiffness. The runner’s support mechan-
ics remained essentially unchanged. These results indicate
that surface stiffness affects running economy without affect-
ing running support mechanics. We postulate that an in-
creased energy rebound from the compliant surfaces studied
contributes to the enhanced running economy.
biomechanics; locomotion; leg stiffness; metabolic rate
IN THEIR GROUNDBREAKING work, McMahon and Greene
(29) investigated the effects of surface stiffness (k
on running mechanics. Their study sought to deter-
mine whether it was possible to build a track surface
that would enhance performance and decrease injury.
Their work showed that a range of k
values existed
over which a runner’s performance was enhanced by
decreasing foot-ground contact time (t
), decreasing the
initial spike in peak vertical ground reaction force
), and increasing stride length. Tracks built
within this enhanced performance range at Harvard
University, Yale University, and Madison Square Gar-
den have been shown to increase running speeds by
23% and to decrease running injuries by 50% (29).
Despite the success of these “tuned tracks,” the mech-
anisms underlying the performance enhancement are
not clearly understood.
A major assumption of McMahon and Greene’s (29)
was that the running leg and surface could be repre-
sented as a simple spring and mass (Fig. 1). McMahon
and Cheng (27) subsequently described the leg spring
as having two stiffnesses: k
and k
. The k
is the
actual leg stiffness describing the mechanical behavior
of the leg’s musculoskeletal system during the support
phase and is calculated from the ratio of f
to the
compression of the leg spring (l, defined in Eq. B4)
In distinction, k
is the effective vertical stiffness of
the runner. This stiffness serves as the mechanism by
which the direction of the downward velocity of the
body is reversed during limb contact (27, 30). There-
fore, k
describes the vertical motions of the center of
mass during the ground contact phase (27, 30). The
can be calculated from the ratio of f
to the
maximum vertical displacement of the center of mass
during contact (y
), measured from the onset of
limb contact (heel-strike) to midstep
Farley et al. (12) and He et al. (19) determined that, for
a given ground stiffness, k
changes little with speed.
Later experiments showed that k
changes when an-
imals run on surfaces of different stiffnesses (16, 18). It
was specifically shown that human hoppers’ k
justments were mainly due to changes in both ankle
joint stiffness and leg posture (14). However, Aram-
patzis et al. (3) provided evidence that the knee joint is
Deceased 14 February 1999.
Address for reprint requests and other correspondence: A. E.
Kerdok, Harvard University, 29 Oxford St., Pierce Hall G-8, Cam-
bridge, MA 02138 (E-mail:
The costs of publication of this article were defrayed in part by the
payment of page charges. The article must therefore be hereby
marked ‘‘advertisement’’ in accordance with 18 U.S.C. Section 1734
solely to indicate this fact.
J Appl Physiol 92: 469478, 2002;
8750-7587/02 $5.00 Copyright
2002 the American Physiological Society 469
the main determinant of k
as a function of speed in
human running. In addition, modeling efforts and ex-
periments on humans have shown that a runners
center of mass deections (y
) remain nearly con
stant, independent of k
, and that this may be a
general principle of running mechanics (16, 29). In
other words, by adjusting their leg springstiffness to
adapt to different k
values, a runner may be able to
maintain apparently uniform support mechanics.
Representations of the running leg as a simple
spring have described the mechanics of a running leg
remarkably well (2, 11, 12, 15, 16, 18, 19, 2527). It has
been shown that the physical musculoskeletal elastic
components of the leg (tendons, ligaments, and mus-
cles) are used to minimize metabolic cost while running
(1, 2, 810). However, no one, to date, has related the
performance enhancements of running on surfaces of
different stiffnesses to metabolic cost. In this paper, we
assume that the leg can be represented by an un-
damped, linear spring and examine how the energetics
and mechanics of running vary on surfaces of different
The goal of this study is to relate human running
biomechanics to energetics on surfaces of different
stiffnesses. We expect that differences in the metabolic
cost of running on various surfaces are likely related to
the k
variations observed by Farley et al. and Ferris
et al. (13, 17, 18). Specically, we expect a less exed
knee to account for a reduction in metabolic cost (30),
as well as an increase in k
(3, 18).
In this study, we investigate the energetics and me-
chanics of running on surfaces having a stiffness range
from 75 to 945 kN/m. This range of stiffnesses was
selected to incorporate the range of McMahon and
Greenes tuned track (29) and to extend the work of
similar recent studies (1618). We hypothesize that
the metabolic cost of forward human running reaches a
minimum when the k
of the runner is maximized on
surfaces of decreased stiffness. We expect a cost reduc-
tion to result from a change in leg posture, whereby the
knee is less exed or straighter during stance (30).
Running with a straighter leg should improve the
limbs mechanical advantage, thereby reducing the
amount of muscle force and muscle volume recruited to
support body weight (5). We also anticipate that a
reduction in metabolic cost could result from an in-
creased energy return to the runner from the more
compliant surfaces (14). Last, we expect that the run-
ners support mechanics will remain virtually unaf-
fected across the above-dened range of k
General procedures. Eight healthy male subjects [body
mass: 74.4 7.1 (SD) kg; leg length: 0.96 0.05 m] ran at 3.7
m/s on a level treadmill, tted with track platforms of ve
different stiffnesses (see descriptions below). All subjects
wore the same at-soled running shoes. Approval was
granted from Harvard Universitys Committee on the Use of
Human Subjects in Research, and subjects provided signed,
informed consent before participation. Subjects ran for 5 min
on each track platform stiffness in a mirrored fashion (run-
ning on stiffest to least stiff and then least stiff to stiffest).
Beaded strings hung from the ceiling to give the runner a
tactile sign as to where he needed to run so that his midstep
corresponded with the fore-aft center of the track platform.
Video was also used to ensure that the runner was both
centered and lateral enough not to be stepping on both sides
of the track simultaneously. If a runner was unable to avoid
the seam between tracks, he was asked to move laterally and
run on one track or the other. We recorded ground reaction
force (1,000 Hz) using a force plate (model OR65-1, Ad-
vanced Medical Technology, Newton, MA) mounted within
the treadmill (22). Kinematic data were collected at 60 Hz
using an infrared motion analysis system (MacReex by
Qualysis), and oxygen uptake was measured using a closed
gas-collection Douglas bag setup. Oxygen and carbon dioxide
contents of the collected gas samples were analyzed using
Ametek (Pittsburgh, PA) S-3A O
and CD-3A CO
equipped with an Ametek CO
sensor (P-61B) and ow con
troller (R-2). The analyzers were calibrated before each run
with gas by pumping several balloons of known gas mixture
(16.23% O
and 4.00% CO
medical gas mixture; AGA Gas,
Billerica, MA) through them. Force-plate and kinematic data
were obtained simultaneously, and oxygen consumption
) data were sampled during the fourth and fth minutes
of running to ensure that the subject was at a steady state.
Subjects participated in two separate trials so that they ran
on each platform stiffness four times. Averages were taken
on each day and then averaged together for all variables
Experimental platform design. We built platforms with an
adjustable stiffness for our running surface. Because the
experiments were conducted on a treadmill, the running
surface was limited to platforms that would t within the size
limitations of the treadmill. We used a treadmill tted with
an AMTI force plate (22) that was accessible to the Douglas
bag oxygen analysis setup.
We tested ve k
based on ranges found in the literature
(14, 16, 18, 29). The McMahon and Greene (29) tuned track
stiffness range is between 50 and 100 kN/m. Because of size
limitations of the existing treadmill and earlier work done by
Farley and Morgenroth (15) and Ferris et al. (17), we de-
signed our variable stiffness track platforms to span from
Fig. 1. Spring-mass model representing a runners leg in contact
with a compliant surface. l
, Uncompressed leg length; m
, mass of
the runner represented as a point mass located at the hip; y
maximum vertical displacement of the center of mass; l, maximum
compression of the leg spring; , angle of the leg spring at rst
ground contact; k
, spring constant of the runners leg; m
effective mass of the running surface; d
, amount the running
surface deects; k
, spring constant of the running surface; and f
vertical ground reaction force.
J Appl Physiol VOL 92 FEBRUARY 2002
75.4 kN/m to stiffnesses of 97.5, 216.8, 454.2, and 945.7
kN/m. The indoor track at Harvard University has a k
190 kN/m, allowing for a 9-mm deection for a 75-kg
runner (assuming a runner exerts roughly 2.3 times body
weight at midstance). For a similar runner, our track would
result in 22.4-, 17.4-, 7.8-, 3.7-, and 1.8-mm deections [sur-
face deections (d
)], respectively, according to the follow
ing equation
2.3 m
where m
is the mass of the runner, g is the gravitational
constant, and k
is the stiffness of the track. The factor 2.3
is an estimate of how much the f
exceeds body weight
during a running step.
The platform design is shown in Fig. 2. Garrolite (G-10,
Current, East Haven, CT) was chosen as the material for the
track platforms because it met all of the design criteria
described below and in
APPENDIX A and could be easily ma-
chined. The design consisted of two G-10 planks (1.22
0.254 0.014 m) rigidly supported in the front and simply
supported in the rear by 0.016-m-thick acrylic. By moving the
treadmill rollers in at either end of the belt surface, enough
slack was provided to t the platforms under the belt directly
on top of the force plate. Rollers were added to the existing
treadmill to reroute the treadmill belt over the platforms,
and a frame was built (not shown) to hold the platform in
place on top of the force plate during testing. The rear
support was movable so that, by simply adjusting it in closer
to or farther away from the front support, the stiffness of the
running surface was increased or decreased, respectively.
Once installed, the stiffness of each platform was cali-
brated by applying static loads to a person and measuring
force (f
, from the force plate) and deection (d
; from an
LVDT cable extender 0.25%, Celesco Transducer Products)
(Eq. 3).
As described in
APPENDIX A, the inertial effects of the run-
ning platform motion compared with the forces exerted by
the runners leg can be considered negligible if the effective
mass of the platform is 17% of the m
(11.43 kg for the
smallest runner studied). The effective masses (6.88, 8.88,
4.94, 2.65, and 5.39 kg) gave inertial forces of 41.43,
30.41, 10.04, 3.33, and 0.42 N, respectively. These
forces were 2.5% of the peak forces exerted by the runner
and so were ignored.
Given that the running surface was a compliant surface
having the potential to return energy to the runner, we also
calculated the energy return of our variable-stiffness track
platform. We did this by using the track deection to derive
the potential energy at each track stiffness (E
Multiplying this energy by two times the stride frequency
results in the mechanical power delivered from the track to
the runner. This was then related to a measurement of the
metabolic power (E
) consumed by the runner at each
track stiffness.
Force-plate measurements. A runners support mechanics,
dened as f
, t
, duty factor, stride frequency, step length,
one-half of the angle swept by a runners leg during ground
contact (), and the total vertical displacement of the center
of mass, can be calculated from the force-plate data and the
assumption that the leg can be represented by an undamped,
linear spring (22). These parameters can then be indirectly
used to calculate the mass-spring characteristics of the run-
ners leg. Custom LabVIEW (version 4.0.1) software was used
to acquire the force-plate data. The force plate was calibrated
by applying known loads to the plate before and after each
set of running trials and sampling its output using the same
software. The derivation of all of the above parameters is
described in
Kinematic measurements. To obtain information on the
posture of the limb in contact with the ground, we used an
infrared camera system (MacReex; Qualysis) to follow
markers that were specically placed on the subjects. Mark-
ers were positioned on the skin overlying the greater trochan-
ter, the lateral epicondyle of the femur, and the lateral
malleolus, so that the angle that the lower leg made with the
upper leg (knee angle) could be determined.
Kinematic data were collected simultaneously and syn-
chronized with the force-plate data (using an infrared light-
emitting diode in the cameras eld of view that gave a
voltage pulse that was recorded when the light-emitting
diode was switched on). Kinematic data were analyzed using
the Maxdos software from MacReex (Qualysis) and incorpo-
rated into a Matlab (version 4.0) program to calculate the
knee angle at midstep. The program also calculated the
series minimum height points of the greater trochanter
marker for several strides over the 10-s collection period.
This marker was used to estimate the position of a runners
center of mass, and its minimum trajectory was used to
dene the midpoint of each step when force application
reached its peak (13, 19, 26).
Fig. 2. Side view (A) and top view (B) of a schematic of
the experimental compliant track treadmill. The run-
ners foot strikes the treadmill belt (7) (note that this is
cut away on top view to show underlying structures and
also that the belt is longer than depicted) and exerts a
vertical force (F) on the compliant running platforms
(6) below. The vertical force is transmitted from the
platforms via the supports (2 and 8) to the force plate
(1). The stiffness of the running surface is adjusted by
moving the movable support (8) in and out. The force
plate (1) and entire treadmill apparatus are supported
by the treadmill base (5). By moving the treadmill
rollers (3) closer together, enough slack is recovered in
the belt (7) to insert the track platforms (6). The belt is
then redirected over the track platforms with the redi-
rection rollers (4).
J Appl Physiol VOL 92 FEBRUARY 2002
Measuring metabolic cost. To quantify the metabolic cost of
human running, we used the indirect calorimetry method, as
described previously. After the runners ran for 3 min, we
collected the expired air for 2 min using two Douglas bags (1
per minute), a mouthpiece, and a nose clip, which were
attached to the runner via a special headpiece equipped with
a one-way valve. The rate of V
(ml/min) was then calcu
lated using the volume of the expired air (from a dry-gas
volume meter; Parkinson-Cowan), room and vapor pressure
corrections, and the percentage of CO
and O
values. We
converted the rate of V
into energy consumption using an
energy equivalent of 20.1 J/ml O
(6) and divided by 60 s/min
to obtain E
in watts.
Kram and Taylor (23) dene the rate of metabolic con-
sumption (E
) in terms of a cost coefcient, C
where C
is an empirical measure of the metabolic cost of
applying ground force to support the bodys weight (F
) (4,
31). For this investigation, the C
is computed to determine
the effect of k
on the energetics of supporting the runners
body weight.
Statistical methods. A1 5 ANOVA with a Scheffe´ post
hoc test of condition means was used to assess the effect of
on the parameters of interest: t
, peak vertical force,
stride time, stride frequency, step length, , y
, displace
ment of the limb with respect to the track displacement,
, C
, k
, k
, l, overall system stiffness, and knee
angle. P values 0.05 were considered signicant for all
The runners support mechanics were nearly invari-
ant across the 12.5-fold change in k
of the experi
mental treadmill platform (Fig. 3), whereas their met-
abolic rate dropped dramatically with k
(Fig. 6).
The results of the Scheffe´ post hoc test revealed that,
in virtually every case, the support mechanics re-
mained essentially unchanged over the four stiffest
surfaces tested. The basis for a signicant difference in
the ANOVA results reported below was found to be due
to the data recorded for the lowest stiffness track
As shown in Fig. 3, the effect of k
on t
0.0001, F 8.7), duty factor (P 0.0001, F 18.45),
step length (P 0.0001, F 8.51), stride frequency
(P 0.0001, F 15.35), (P 0.0001, F 8.44), and
(P 0.009, F 4.19) were signicant. However,
the data across these support mechanics showed only a
small difference between the two stiffness extremes.
The source of the difference occurred at the lowest
stiffness, with the remaining four stiffnesses being
essentially the same.
Fig. 3. When subjects ran at a con-
stant speed (3.7 m/s) over 5 different
surface stiffnesses (74945 kN/m),
their support mechanics remained es-
sentially unchanged. As conrmed by
the Scheffe´ post hoc test, the differ-
ences observed were due to the lowest
surface stiffness only. The time that
the foot is in contact with the ground
[y 0.0017 ln(x) 0.204, R
(A); the duty factor [y 0.0063 ln(x)
0.265, R
0.58] (B); the step length
(right foot to left foot) [y 0.0065
ln(x) 0.76, R
0.22] (C); the stride
(right foot to right foot) frequency [y
0.019 ln(x) 1.31, R
0.87] (D); the
angle swept by the runners leg [y
0.221 ln(x) 23.44, R
0.24] (E), and
the peak vertical ground reaction force
[y ⫽⫺41.4 ln(x) 2163.2, R
(F) were all virtually constant. Values
are means SD. T
, period of foot-
ground contact; T
, period of foot in air.
J Appl Physiol VOL 92 FEBRUARY 2002
In particular, when the support mechanics means
are compared, there was a 4% decrease in t
, step
length, and between the stiffest and least stiff sur-
faces studied. A 7% decrease in duty factor, 3% de-
crease in stride frequency, and a 5% increase in f
were also observed between these stiffness extremes.
The post hoc test revealed that the runners also
maintained a nearly constant total leg plus track plat-
form stiffness (k
) over the observed range of condi
tions (P 0.0207, F 3.45) (Fig. 4C). To achieve this,
the runners k
increased by 29% with decreasing k
(P 0.0001, F 23.76) (Fig. 4A). Given that the
did not change greatly over the substrate
stiffness range (Fig. 3F), the observed increase in the
runners k
most likely resulted from a decrease in the
amount that his leg spring was compressed (P
0.0001, F 33.93) (Eq. 1, Figs. 1 and 4D). The l is a
function of leg length, , and vertical displacement of
the runner relative to the displacement of the track
surface (y
)(Eq. B4). Because leg length and re
mained essentially constant, the decrease in the l was
likely due to the observed decrease in y
(P 0.0001,
F 94.05) (Fig. 5B, Eq. B5).
We achieved the ve different k
by allowing the
simply supported track to displace beneath the runner.
Therefore, d
increased 12.5-fold from the stiffest to
the least stiff surface (Fig. 5A). This substantial in-
crease in surface displacement was mostly offset by
so that y
was minimally changed between the
extremes (0.8 cm) (P 0.0001, F 16.28).
Again, the change in y
was only signicant at the
lowest k
studied (Fig. 5C). Our nding that the k
(Fig. 4B) remained virtually constant (P 0.0001, F
11.77) over the four stiffest surfaces further supports
the fact that the runners y
changed minimally, as
is a function of f
and y
.(Eq. 2).
We also found a 12% decrease in the runners rate of
as k
decreased (P 0.0001, F 71.95) (Fig.
6A). The runners mean E
decreased from 896 to
792 W as k
decreased from 945 to 75 kN/m. Refer
ring to Eq. 5 and recalling that t
remained essentially
unchanged (Fig. 3A), the observed decrease in meta-
bolic rate suggests that the C
dened by Kram and
Taylor (23) also decreased with decreasing k
0.0001, F 32.54) (Fig. 6B).
In an attempt to evaluate limb mechanical advan-
tage, we used the kinematic data, together with the
vertical ground reaction force, to calculate the limbs
knee angle at midstep for running over all surfaces
(Fig. 7). Knee angle increased 2.5% as k
(P 0.0001, F 16.35). Thus only a slight straight-
ening of the leg was observed.
Last, to test our hypothesis that the track itself may
return signicant energy to the runner, we calculated
the track platforms mechanical power (E
, Eq. 4)at
each k
and compared this with the reduction in
of the runner (Eq. 5) (Fig.
8). The results show
that, for every watt of mechanical power returned from
the track platform, there exists the possibility of a
1.8-W E
savings to the runner (R
Our results support the hypothesis that the meta-
bolic cost of running at an intermediate speed is pro-
gressively reduced and that the spring stiffness of the
leg is progressively increased as k
is decreased from
945.7 to 75.4 kN/m. However, in contrast to our hy-
pothesis that a change in limb posture is the principal
factor underlying a change in both k
and metabolic
cost, we found that only small changes in knee angle
were associated with the observed 29% increase in k
and 12% decrease in E
. Our data do not provide
Fig. 4. When subjects ran at a con-
stant speed (3.7 m/s) over 5 different
surface stiffnesses (74945 kN/m),
there was a 29% change in their leg
stiffness [y ⫽⫺1.37 ln(x) 22.4, R
0.87] (A) and a 16% decrease in leg
compression [y 0.008 ln(x) 0.091,
0.86] with decreasing surface
stiffness (D). The overall stiffness of
the system [y ⫽⫺0.175 ln(x) 14.46,
0.4] (C) and the effective vertical
stiffness of the runner [y 0.81 ln(x)
29.31, R
0.66] (B) remained essen
tially unchanged. Values are means
J Appl Physiol VOL 92 FEBRUARY 2002
any additional insight into the mechanism for k
adjustment but do suggest that a reduction in meta-
bolic cost occurs as the elastic rebound provided by a
more compliant surface replaces that otherwise pro-
vided by a runners leg.
Previous work indicated that runners adjust the
stiffness of their limbs to maintain virtually constant
support mechanics on surfaces of different stiffnesses
(3, 14, 16, 18, 28). Although these studies provide
insight into the mechanics of human running, they did
not specically examine the metabolic cost of running
on compliant surfaces. One study (30) looked at deep-
knee-exed running and its effect on k
and V
did not incorporate k
or compliant surfaces. Our goal
was to expand on these earlier studies and examine
how changes in limb-substrate stiffness interactions
affect the metabolic cost of running. Consequently, we
Fig. 5. A: as designed, the vertical displacement of the compliant
running surface increased with decreasing surface stiffness [y
0.01 ln(x) 0.064, R
0.91]. B: the vertical displacement of the
runners center of mass relative to the tracks vertical displacement
decreases with surface stiffness [y 0.0065 ln(x) 0.011, R
This limb displacement is used to dene the leg compression (Fig. 4,
Eq. B4), which in turn denes the leg stiffness of the runner (Fig. 4,
Eq. 1). C: the total vertical displacement of the runners center of
mass (com) measured from midstep to take-off using the vertical
displacement of the hip marker is essentially unchanged over the
surface stiffnesses [y ⫽⫺0.003 ln(x) 0.076, R
0.84]. This value
is used to dene the effective vertical stiffness (Fig. 4, Eq. 2). Values
are means SD.
Fig. 6. A: the runners metabolic rate decreased with surface stiff-
ness [y 41.17 ln(x) 622.31, R
0.97] over the 12.5-fold change
in surface stiffness (74945 kN/m) when running at a constant speed
(3.7 m/s). B: because the contact time remained essentially constant
(Fig. 3), the cost coefcient must also decrease with surface stiffness
[y 0.0142 ln(x) 0.171, R
0.91] per Eq. 5 [E
, where E
is the rate of metabolic consumption, C
is an
empirical measure of the metabolic cost of applying ground force to
support the bodys weight (F
), and t
is the period of foot-ground
contact]. Values are means SD.
Fig. 7. The angle formed between the runners upper and lower legs
was dened from markers placed at the greater trochanter, lateral
epicondyle of the femur, and lateral malleolus. This knee angle
increased 2.5% as surface stiffness decreased [y ⫽⫺1.25 ln(x)
137.29, R
0.97], giving rise to a slightly straighter leg on the softer
surfaces studied. Values are means SD.
J Appl Physiol VOL 92 FEBRUARY 2002
adopted a similar mechanical and experimental ap-
proach to that of these studies, focusing on the knee
joint and assuming that the leg behaves as a massless,
undamped linear spring.
Using this simple model of the human leg, our nd-
ings generally support those of Farley et al. (11, 13
15), indicating that human runners alter their leg
spring stiffness to compensate for changes in k
out altering their overall support mechanics. McMahon
and Greene (29), Farley et al. (14), and Ferris et al. (17)
have commented that an observer looking only at the
upper body of a runner would be unable to discern
when the runner experienced a change in ground stiff-
ness. This suggests that runners compensate for vari-
able ground stiffness without affecting the uctuations
in the motion of their center of mass. This is consistent
with our ndings that d
is offset by y
, thus
resulting in the minimal 0.8-cm change observed in
. Hence, utilizing preferred support mechanics
might represent a general principle of running.
Kram and Taylors (23) analysis suggests that the
mass-specic metabolic rates of running animals are
determined by the rate of ground-force application (1/
), regardless of the speed and size of the animal. Their
analysis assumes that animals maintain a uniform
limb mechanical advantage over a range of running
speeds and gaits. This assumption is supported by
previous studies of animals moving at steady speeds
over a constant (high) stiffness substrate (5). As a
result, the cost of force generation and the volume of
muscle that must be activated to support a given unit
body weight also appear to remain constant (21). How-
ever, we found a reduction in metabolic rate with
virtually no change in the t
(Figs. 3A and 6A). Thus
the energetic cost of applying a ground force to support
the runners body weight can be reduced at a given rate
of ground force application (1/t
) when running on more
compliant surfaces.
The close relationship between the reductions in
metabolic rates and the increased mechanical power
returned by the track to the runner in the latter por-
tion of foot-ground contact (Fig. 8) offers a straightfor-
ward explanation. This close relationship strongly sug-
gests that, when a greater share of the elastic rebound
elevating the center of mass in the latter portion of the
contact phase is provided by the elastic recoil of the
running surface rather than the biological springs in
the runners leg, the metabolic cost of running is re-
duced. We believe that these reductions in the meta-
bolic cost of operating leg springs are probably ex-
plained by decreases in the mechanical work and
shortening velocity performed by the muscles active
during foot-ground contact.
Although we had hypothesized that reductions in
metabolic cost and increases in k
would be achieved
predominantly via changes in knee angle, it seems
evident that this mechanism cannot fully account for
these changes. The change in k
is likely due to a
combination of local joint stiffness variation and over-
all limb posture adjustment (15). Whereas our study
provided some indication that the leg becomes
straighter at midstep on less stiff surfaces (Fig. 7), the
change at the knee was small and would require a
large sensitivity to have an effect on externally devel-
oped knee torque. Therefore, this small change in knee
angle could only account for a minority of the reduc-
tions in metabolic cost and increases in k
that we
observed on more compliant surfaces.
Our hypothesis also anticipated that the decrease in
might well be explained by an enhanced energy
return from the more compliant track platforms. The
elastic surface could actually be assisting the runner
by assuming some of the cost necessary to operate the
leg spring, reducing the amount of mechanical work
required, and thereby allowing the leg muscles to op-
erate more isometrically. Reductions in relative short-
ening velocities would reduce metabolic cost in two
ways. First, the increased force per unit area of active
muscle would reduce the volume of muscle required to
support the bodys weight. Second, the E
sumed per unit of active muscle is also reduced when
the muscles shorten through a lesser distance (20).
To lend support for these ideas, experiments were
conducted to characterize the track-runner interaction.
The dynamic calibration of the four most compliant
experimental track platforms showed a linear relation-
ship between force and displacement (R
0.96, 0.97,
0.95, and 0.94 from least to most stiff) with little
hysteresis (damping ratio 0.1). Hence, the track can
indeed be considered an elastic substrate capable of
storing and returning mechanical energy. Also, by cal-
culating the resonant period of the track-plus-runner
system at the least stiff surface (0.2 s) and comparing
the result to the contact times of the runners at this
same stiffness (0.21 0.02 s), we conclude that the
track has sufcient time to return its stored energy to
the runner. Last, our results show a consistent linear
Fig. 8. Change in the runners metabolic power (E
) as a function
of the change in mechanical power delivered from the track plat-
forms (E
) from the stiffest surface (K
). The power delivered from
the compliant track is derived from the mechanical energy due to the
track spring (Eq. 4) multiplied by the runners stride frequency. For
every watt delivered from the track platforms, there exists a poten-
tial 1.8-W reduction in metabolic power (y 1.80x, R
Values are means SD. K
, surface stiffness where n 1, 2, 3, 4.
J Appl Physiol VOL 92 FEBRUARY 2002
relationship between the reduction in E
and track
mechanical power output across all surfaces studied
(Fig. 8). These results suggest that the track has the
capacity to save the runner 1.8 W of E
for every
watt of mechanical power that it returns.
Although our results support the fact that running
on a decreased k
results in a reduction of metabolic
cost and an increase in k
without affecting support
mechanics, future studies need to be done to nd a true
metabolic minimum. Our measurements were de-
signed to examine surfaces that were within a stiffness
range that had already demonstrated an enhanced
running performance (29). However, support mechan-
ics are progressively altered to accommodate extreme
decreases in k
. As mentioned above, our results
support our hypothesis that these support mechanics
would remain fairly constant over the 12.5-fold change
in k
but also show a signicant change in these
variables at the lowest k
studied. This raises the
possibility of a trend in data as k
goes even lower.
McMahon and Greenes (29) work supports this spec-
ulation. We also anticipate that, as k
decreases even
further and the virtual consistency of the support me-
chanics seen at the higher stiffnesses is lost, there
would exist a true metabolic minimum. Studies that
looked at running on surfaces with extremely low stiff-
ness, such as a trampoline and pillows (30) or sand
(24), which also have high damping ratios, indicate
that runners likely increase the amount of center-of-
mass work that they perform and thus substantially
increase their cost of locomotion (24). We propose that
a study be done to examine lower k
values than
were studied here to determine at what substrate stiff-
ness a true metabolic minimum exists as a relation of
speed. We believe that there exists an optimal ratio of
to surface resonant period that can be used for the
future design of tracks and even running shoes to
minimize the cost of running.
Summary. Our study sought to link the mechanics
and energetics of human running on surfaces of differ-
ent stiffnesses. The results show that both metabolic
cost and k
change when k
is manipulated. The
metabolic reduction is largely due to the tracks elastic
energy return assisting the runners leg spring. Al-
though the mechanism for k
adjustment still re
mains unclear, our results support the hypothesis that
human runners adjust k
to maintain consistent sup
port mechanics across different surfaces.
This study has served to link previous studies on
animal locomotion and to open the door to future in-
vestigations on locomotory mechanics and energetics.
Understanding how metabolism, speed, and k
to substrate mechanics will not only lead to advances
in running shoe technology and track design, but may
also motivate the development of highly adaptive or-
thotic and prosthetic leg devices that change stiffness
in response to speed and ground surface variations,
enabling the physically challenged to move with
greater ease and comfort.
Experimental Track Platform Design
The design of the variable-stiffness track platform was
based on simply supported, two-point bending beam theory.
Pilot studies showed that this conguration would work well
within the size limitations of the treadmill (0.102-m maxi-
mum height from the force plate to beneath the belt, 1.22-m
long 0.457-m wide force plate, and 0.5 2.64-m overall belt
surface). Materials and dimensions were chosen based on the
maximum deection (y
) of the center of the beam accord
ing to the factor of safety (FS) associated with the loads that
would be applied in running (F) or
where L is the length of the beam, E is Youngs modulus, I is
the area moment of inertia,
is the ultimate stress of the
material, and
is the maximum allowable stress of the
Another design criterion was that the track platform mass
needed to be small enough so that the inertial forces due to
the movement of the platform would be negligible compared
with the forces exerted by the runners leg. By modeling the
leg and platform surface as a two-mass and two-spring sys-
tem with a damper, we found that the effective mass of the
platform had to be 12 kg (or 17% of the m
) in order for the
platforms inertia to represent 10% of the peak force devel-
oped by a 72-kg runner. Therefore, given that the masses of
the actual runners were from 67.3 to 81.5 kg, the effective
mass of the track platforms (m
) had to be 11.413.9 kg
to meet this criterion.
The inertial effects of the track platforms on measure-
ments obtained from the force plate could be obtained by
calculating the effective mass of the platforms. The m
was estimated by treating the track as a harmonic oscillator
and nding the damped frequency (
). The
was measured
by striking the platform and plotting the displacement vs.
time for the free vibration of the track surface (14). This was
accomplished by mounting the LVDT cable extender at the
center edge of the platform for each stiffness conguration,
with the platform resting in position on top of the AMTI force
plate and under the treadmill belt. The
was computed
from the period of vibration (T
The equation describing the envelope of the free vibration
curve can be used together with the damped natural fre-
quency of the track to obtain the natural frequency and the
damping ratio of the track surfaces
x Ae
where x denes the envelope of free vibration, A is the
amplitude of free vibration,
is the natural frequency, and
t is time. With the use of Eqs. A4 and A5, the natural
frequency of the platform was calculated to be 105 rad/s, thus
resulting in a negligible damping ratio of ␰⬇0.07. Hence the
was estimated from the k
and the
J Appl Physiol VOL 92 FEBRUARY 2002
The m
was then used, together with the second deriva
tive of the displacement curves (to obtain acceleration), to
estimate the inertial force (F
) of the track platforms
Derivation of the Force-Plate Parameters
LabVIEW (version 4.0.1) was used to acquire the force-
plate data and output the parameters of the runners support
mechanics (f
, t
, stride time, stride frequency, step length,
, and the vertical displacement of the center of mass).
Because of the vibrational noise from the treadmill belt,
motor, and track (22), we ltered the force data using a
low-pass, third-order Butterworth double-reverse lter. The
smoothed curve for the ground reaction force was used for
analysis. The f
is the force at midstep and was taken to be
the maximum value of this curve. The duration of the force
provided a measure of the t
as well as total stride (right foot
to right foot) time (t
, where t
is the period the
foot is in the air and dur
is total duration) that were then
used to calculate the stride frequency (freq) and step length
(SL) (distance traveled by the center of mass during one t
SL t
where u
is the horizontal (forward) velocity. With the addi
tional input of the runners leg length (l
) measured from the
runners greater trochanter to the oor while standing
straight legged, we calculated (see Fig. 1) from
Because the ground reaction force is equal to the runners m
times his acceleration, we were able to calculate the y
the runner by twice integrating the vertical acceleration of
the center of mass over time (7).
To account for the displacement of the variable-stiffness
surfaces (d
) in relation to the runners y
, we calcu
lated d
from the calibrated values obtained for k
the forces obtained from the force plate (Eq. 3, where 2.3
from force plate).
The above variables were then used to calculate the mass-
spring characteristics of the runners leg. The maximum l
was calculated by using the runners l
, , and the actual
(18, 26)
l y
1 cos ␪兲 (B4)
Because the f
occurs at the same time that the center of
mass is at its lowest height, the stiffness of the leg spring
) was calculated using the ratio of f
to maximum leg
compression (13, 19, 26) (Eq. 1). Similarly, the effective
vertical spring stiffness was calculated using the peak force
and the total displacement of the center of mass of the system
(Eq. 2).
The total displacement is used in calculating k
than the actual displacement of the runner alone, because, on
less stiff surfaces, k
is affected by the displacement of the
surface (18). If the actual (or relative) displacement is used,
the possibility exists that vertical stiffness could assume a
negative value (the runner moves in the opposite direction at
midstep in an effort to maintain a constant displacement of
the systems center of mass), which is nonsensical.
Overall stiffness of the system (k
) was calculated as the
sum of the k
and the track platform stiffness (k
The authors thank Claire Farley and Roger Kram from the Uni-
versity of California at Berkeley for helpful discussions, as well as
Robert Wallace from the United States Army Research Institute for
Environmental Medicine for statistical analysis.
This research was supported in part by a graduate fellowship from
the Whitaker Foundation and the Division of Engineering and Ap-
plied Sciences, Harvard University.
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... Une autre étude se concentrant sur la force de réaction au sol sur l'axe antéro-postérieur a montré qu'un sol moins raide et « coulissant » permettait de réduire la vitesse de montée en force et la fréquence de l'impact (Chen et al., 2019). Cependant le lien entre la force de réaction au sol et la raideur du sol fait l'objet de controverses car certaines études ne reportent pas de changement du pic passif (Kerdok et al., 2002). Bien que la raideur du sol soit modifiée, la raideur effective du coureur reste inchangée, cela étant dû à une adaptation de la raideur de la jambe qui vient se compresser de manière plus importante (diminution de raideur) lorsque le sol est très raide (Kerdok et al., 2002). ...
... Cependant le lien entre la force de réaction au sol et la raideur du sol fait l'objet de controverses car certaines études ne reportent pas de changement du pic passif (Kerdok et al., 2002). Bien que la raideur du sol soit modifiée, la raideur effective du coureur reste inchangée, cela étant dû à une adaptation de la raideur de la jambe qui vient se compresser de manière plus importante (diminution de raideur) lorsque le sol est très raide (Kerdok et al., 2002). En conséquence, le sol sportif a un potentiel pour modifier la raideur de la jambe, et donc, les caractéristiques des vibrations des tissus mous (Boyer, 2006). ...
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La course à pied et les différentes pratiques sportives induisent des chocs et des vibrations transitoires au niveau des tissus mous à chaque impact. Ces impacts et vibrations peuvent générer un stress mécanique important, qui accroit le risque de fatigue et de blessure de sur-sollicitation. Le premier objectif de la thèse était consacré au développement de méthodes de traitement du signal d’accélération et d’analyse statistique afin de mieux caractériser les impacts et vibrations subies par le sportif. Le second objectif était de définir les facteurs externes, tels que le type de mouvement, le matériel sportif, ou la fatigue neuromusculaire, qui faisaient varier le comportement vibratoire en pratique écologique. Avec le développement de méthodes de traitement du signal (transformée en ondelettes continue) et statistiques (Statistical Parametric Mapping), nous avons montré que la vibration des tissus mous était différente de la vibration musculaire. Ainsi, les accéléromètres ne permettaient de caractériser que partiellement la vibration du muscle par rapport à une échographe ultra rapide. De plus, l’augmentation de la vitesse de course et les mouvements effectués lors de la pratique de sports collectifs génèrent des impacts à plus grande amplitude et à plus haute fréquence, ainsi que des vibrations des tissus mous plus amples que la course en ligne droite. Parmi le matériel sportif évalué, seul un revêtement sportif coulissant a permis de réduire l’amplitude de l’impact au sol. Une identification du type de mouvement a été rendu possible grâce à la mesure des impacts et l’usage d’un réseau de neurones convolutifs, permettant de franchir une première étape dans l’évaluation de la dose vibratoire subie par un sportif lors de sa pratique. Enfin, une étude réalisée lors des courses de l’UTMB a permis d’observer une stratégie de protection de l’organisme après des efforts de type trail en diminuant l’amplitude et la fréquence des vibrations des muscles les plus sollicités. Il reste nécessaire d’améliorer la caractérisation de la vibration musculaire avec des accéléromètres fixés sur la peau et de déterminer l’effet de l’exposition répétée à des vibrations transitoires sur le système neuromusculaire et musculo-squelettique.
... Frontiers in Sports and Active Living | exist including leg stiffness, vertical stiffness and joint stiffness, previous research has demonstrated that oxygen consumption and running economy are related to lower extremity stiffness values (McMahon and Cheng, 1990;Latash and Zatsiorsky, 1993;Kerdok et al., 2002;Butler et al., 2003;Beck et al., 2016;Moore et al., 2019). It is widely accepted that greater lower extremity stiffness is associated with improved running economy (Kerdok et al., 2002;Butler et al., 2003;Beck et al., 2016;Moore et al., 2019) due to the greater utilization of stored energy in passive, elastic tissues (Latash and Zatsiorsky, 1993). ...
... exist including leg stiffness, vertical stiffness and joint stiffness, previous research has demonstrated that oxygen consumption and running economy are related to lower extremity stiffness values (McMahon and Cheng, 1990;Latash and Zatsiorsky, 1993;Kerdok et al., 2002;Butler et al., 2003;Beck et al., 2016;Moore et al., 2019). It is widely accepted that greater lower extremity stiffness is associated with improved running economy (Kerdok et al., 2002;Butler et al., 2003;Beck et al., 2016;Moore et al., 2019) due to the greater utilization of stored energy in passive, elastic tissues (Latash and Zatsiorsky, 1993). One measure of stiffness that been associated with improved mechanical and metabolic performance during a running task is lower limb and knee joint stiffness (Latash and Zatsiorsky, 1993;Butler et al., 2003;Beck et al., 2016;Powell and Williams, 2018;Moore et al., 2019). ...
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IntroductionBreast pain is a major barrier to running for women. While breast support through the use of sports bras reduces breast-related discomfort, the effect of breast support on running performance is less understood. Therefore, the purpose of the current study was to evaluate the effect of greater breast support on oxygen consumption and running economy during a treadmill running task.Methods Fifteen female recreational runners performed a 10-min treadmill running task at their preferred running speed in each of two sports bra conditions: low support and high support. Participants ran on an instrumented treadmill (1,200 Hz, Bertec) while indirect calorimetry was performed using a metabolic measurement system (100 Hz, TrueOne, ParvoMedics). Average VO2 (absolute and relative) from the third to 10th minutes was used to evaluate oxygen consumption. Running economy was calculated as the distance traveled per liter of oxygen consumed. Paired samples t-tests were used to compare mean oxygen consumption and running economy values between breast support conditions. Correlation analysis was performed to evaluate the relationship between breast size and change in running performance.ResultsGreater breast support was associated with reductions in absolute (p < 0.001) and relative oxygen consumption (p < 0.001; LOW: 30.9 ± 7.1 ml/kg/min; HIGH: 28.7 ± 6.7 ml/kg/min). Greater breast support was associated with increases in running economy (p < 0.001; LOW: 88.6 ± 29.1 m/L O2; HIGH: 95.2 ± 31.1 m/L O2). No changes in temporospatial characteristics of running were observed including cadence (p = 0.149), step length (p = 0.300) or ground contact time (p = 0.151). Strong positive linear correlations were observed between the change in running performance metrics and breast size (Oxygen Consumption: p < 0.001, r = 0.770; Relative Oxygen Consumption: p < 0.001, r = 0769; Running Economy: p < 0.001, r = 0.807).Conclusions Greater breast support was associated with reduced oxygen consumption and increased running economy. These findings demonstrate that greater breast support is not only associated with improved comfort but also improved running performance.
... change in gait to facilitate higher speeds [87]), extrinsic factors (e.g. moving over a deformable substrate/changeable grade [86,88]), tag placement [65] and collar roll [89,90], thereby altering the relationship between VeDBA and mechanical power (and thus speed) [86,91]. ...
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The combined use of global positioning system (GPS) technology and motion sensors within the discipline of movement ecology has increased over recent years. This is particularly the case for instrumented wildlife, with many studies now opting to record parameters at high (infra-second) sampling frequencies. However, the detail with which GPS loggers can elucidate fine-scale movement depends on the precision and accuracy of fixes, with accuracy being affected by signal reception. We hypothesized that animal behaviour was the main factor affecting fix inaccuracy, with inherent GPS positional noise (jitter) being most apparent during GPS fixes for non-moving locations, thereby producing disproportionate error during rest periods. A movement-verified filtering (MVF) protocol was constructed to compare GPS-derived speed data with dynamic body acceleration, to provide a computationally quick method for identifying genuine travelling movement. This method was tested on 11 free-ranging lions ( Panthera leo ) fitted with collar-mounted GPS units and tri-axial motion sensors recording at 1 and 40 Hz, respectively. The findings support the hypothesis and show that distance moved estimates were, on average, overestimated by greater than 80% prior to GPS screening. We present the conceptual and mathematical protocols for screening fix inaccuracy within high-resolution GPS datasets and demonstrate the importance that MVF has for avoiding inaccurate and biased estimates of movement.
... Mechanical energy is also lost to branch displacement, energy that cannot then be used to move the animal forward. Humans engaging in ballistic forms of locomotion, like running and hopping, have been shown to recoup some of that energy as the support oscillations and footfalls are phased to allow the rebounding support to do work on the CoM, increase energetic efficiency (Farley et al., 1991Ferris et al., 1998;Kerdok et al., 2002;McMahon & Greene, 1979). There is mixed evidence that jumping frogs may exploit a similar strategy, and the degree to which mechanical energy recuperation can be exploited during jumping may be limited by the range of substrate compliance in the wild (Astley et al., 2015;Reynaga et al., 2019). ...
Arboreal environments require overcoming navigational challenges not typically encountered in other terrestrial habitats. Supports are unevenly distributed and vary in diameter, orientation, and compliance. To better understand the strategies that arboreal animals use to maintain stability in this environment, laboratory researchers must endeavor to mimic those conditions. Here, we evaluate how squirrel monkeys (Saimiri boliviensis) adjust their locomotor mechanics in response to variation in support diameter and compliance. We used high-speed cameras to film two juvenile female monkeys as they walked across poles of varying diameters (5, 2.5, and 1.25 cm). Poles were mounted on either a stiff wooden base ("stable" condition) or foam blocks ("compliant" condition). Six force transducers embedded within the pole trackway recorded substrate reaction forces during locomotion. We predicted that squirrel monkeys would walk more slowly on narrow and compliant supports and adopt more "compliant" gait mechanics, increasing stride lengths, duty factors, and an average number of limbs gripping the support, while the decreasing center of mass height, stride frequencies, and peak forces. We observed few significant adjustments to squirrel monkey locomotor kinematics in response to changes in either support diameter or compliance, and the changes we did observe were often tempered by interactions with locomotor speed. These results differ from a similar study of common marmosets (i.e., Callithrix jacchus, with relatively poor grasping abilities), where variation in diameter and compliance substantially impacted gait kinematics. Squirrel monkeys' strong grasping apparatus, long and mobile tails, and other adaptations for arboreal travel likely facilitate robust locomotor performance despite substrate precarity.
Background Nike ZoomX Vaporfly (NVF) improves running economy and performance. The biomechanical mechanisms of these shoes are not fully understood, although thicker midsoles and carbon fiber plates are considered to play an important role in the spring-like leg characteristics during running. Leg stiffness (kleg) in the spring-mass model has been commonly used to investigate spring-like running mechanics during running. Research question Does kleg during running differ between NVF and traditional (TRAD) shoes? Methods Eighteen male habitual forefoot and/or midfoot strike runners ran on a treadmill at 20 km/h with NVF and TRAD shoes, respectively. kleg, vertical oscillation of the center of mass (∆CoM), spatiotemporal parameters, and mechanical loading were determined. Results kleg was 4.8% lower in the NVF shoe condition than in the TRAD condition, although no significant difference was observed. ∆CoM was not significantly different between shoe conditions. Spatiotemporal parameters and mechanical loading were also not significantly different between shoe conditions. Significance The NVF shoe is well known as improving the running economy and running performance for the cause by characteristics of better spring function. Contrary to expectation, kleg and other parameters were not significantly different during running in the NVF compared to TRAD shoe at 20 km/h. These findings indicate that well-trained runners’ spring-like running mechanics would not alter even if wearing the NVF shoes.
This book reports on advanced topics in the areas of wearable robotics research and practice. It focuses on new technologies, including neural interfaces, soft wearable robots, sensors and actuators technologies, discussing industrially and medically-relevant issues, as well as legal and ethical aspects. It covers exemplary case studies highlighting challenges related to the implementation of wearable robots for different purposes, and describing advanced solutions. Based on the 5th International Symposium on Wearable Robotics, WeRob2020, and on WearRacon Europe 2020, which were both held online on October 13-16, 2020, the book addresses a large audience of academics and professionals working in for the government, in the industry, and in medical centers, as well as end-users alike. By merging together engineering, medical, ethical and industrial perspectives, it offers a multidisciplinary, timely snapshot of the field of wearable technologies.
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Shoes are generally designed protect the feet against repetitive collisions with the ground, often using thick viscoelastic midsoles to add in-series compliance under the human. Recent footwear design developments have shown that this approach may also produce metabolic energy savings. Here we test an alternative approach to modify the foot–ground interface by adding additional stiffness in parallel to the plantar aponeurosis, targeting the windlass mechanism. Stiffening the windlass mechanism by about 9% led to decreases in peak activation of the ankle plantarflexors soleus (~ 5%, p < 0.001) and medial gastrocnemius (~ 4%, p < 0.001), as well as a ~ 6% decrease in positive ankle work (p < 0.001) during fixed-frequency bilateral hopping (2.33 Hz). These results suggest that stiffening the foot may reduce cost in dynamic tasks primarily by reducing the effort required to plantarflex the ankle, since peak activation of the intrinsic foot muscle abductor hallucis was unchanged (p = 0.31). Because the novel exotendon design does not operate via the compression or bending of a bulky midsole, the device is light (55 g) and its profile is low enough that it can be worn within an existing shoe.
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Muscle, bone, and tendon forces; the movement of the center of mass, and the spring properties of the body during terrestrial locomotion can be measured using ground-mounted force platforms. These measurements have been extremely time consuming because of the difficulty in obtaining repeatable constant speed trials (particularly with animals). We have overcome this difficulty by mounting a force platform directly under the belt of a motorized treadmill. With this arrangement, vertical force can be recorded from an unlimited number of successive ground contacts in a much shorter time. With this treadmill-mounted force platform it is possible to accurately make the following measurements over the full range of steady speeds and under various perturbations of normal gait: 1) vertical ground reaction force over the course of the contact phase; 2) peak forces in bone, muscle, and tendon; 3) the vertical displacement of the center of mass; and 4) contact time for the limbs. In our treadmill-force platform design, belt forces and frictional forces cause no measurable cross-talk problem. Natural frequency (160 Hz), nonlinearity (less than 5%), and position independence (less than 2%) are all quite acceptable. Motor-caused vibrations are greater than 150 Hz and thus can be easily filtered.
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Moving about in nature often involves walking or running on a soft yielding substratum such as sand, which has a profound effect on the mechanics and energetics of locomotion. Force platform and cinematographic analyses were used to determine the mechanical work performed by human subjects during walking and running on sand and on a hard surface. Oxygen consumption was used to determine the energetic cost of walking and running under the same conditions. Walking on sand requires 1.6-2.5 times more mechanical work than does walking on a hard surface at the same speed. In contrast, running on sand requires only 1.15 times more mechanical work than does running on a hard surface at the same speed. Walking on sand requires 2.1-2.7 times more energy expenditure than does walking on a hard surface at the same speed; while running on sand requires 1.6 times more energy expenditure than does running on a hard surface. The increase in energy cost is due primarily to two effects: the mechanical work done on the sand, and a decrease in the efficiency of positive work done by the muscles and tendons.
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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 (k(leg)) is adjusted to accommodate changes in surface stiffness (ksurf) when humans hoop in place, a good experimental model for examining adjustments to k(leg) in bouncing gaits. We found that k(leg) was greatly increased to accommodate surfaces of lower stiffnesses. The series combination of k(leg) 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 k(leg) on the least stiff surface (ksurf = 26.1 kN/m; k(leg) = 53.3 kN/m) compared with the most stiff surface (ksurf = 35,000 kN/m; k(leg) = 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 k(leg) 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 k(leg) adjustments can allow similar locomotion mechanics on the variety of terrains encountered by runners in the natural world.
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The work done during each step to lift and to reaccelerate (in the forward direction) and center of mass has been measured during locomotion in bipeds (rhea and turkey), quadrupeds (dogs, stump-tailed macaques, and ram), and hoppers (kangaroo and springhare). Walking, in all animals (as in man), involves an alternate transfer between gravitational-potential energy and kinetic energy within each stride (as takes place in a pendulum). This transfer is greatest at intermediate walking speeds and can account for up to 70% of the total energy changes taking place within a stride, leaving only 30% to be supplied by muscles. No kinetic-gravitational energy transfer takes place during running, hopping, and trotting, but energy is conserved by another mechanism: an elastic "bounce" of the body. Galloping animals utilize a combination of these two energy-conserving mechanisms. During running, trotting, hopping, and galloping, 1) the power per unit weight required to maintain the forward speed of the center of mass is almost the same in all the species studied; 2) the power per unit weight required to lift the center of mass is almost independent of speed; and 3) the sum of these two powers is almost a linear function of speed.
The goals of this study were to examine the following hypotheses: (a) there is a difference between the theoretically calculated (McMahon and Cheng, 1990. Journal of Biomechanics 23, 65-78) and the kinematically measured length changes of the spring-mass model and (b) the leg spring stiffness, the ankle spring stiffness and the knee spring stiffness are influenced by running speed. Thirteen athletes took part in this study. Force was measured using a "Kistler" force plate (1000 Hz). Kinematic data were recorded using two high-speed (120 Hz) video cameras. Each athlete completed trials running at five different velocities (approx. 2.5, 3.5, 4.5, 5.5 and 6.5 m/s). Running velocity influences the leg spring stiffness, the effective vertical spring stiffness and the spring stiffness at the knee joint. The spring stiffness at the ankle joint showed no statistical difference (p < 0.05) for the five velocities. The theoretically calculated length change of the spring-mass model significantly (p < 0.05) overestimated the actual length change. For running velocities up to 6.5 m/s the leg spring stiffness is influenced mostly by changes in stiffness at the knee joint.
A mathematical model for terrestrial running is presented, based on a leg with the properties of a simple spring. Experimental force-platform evidence is reviewed justifying the formulation of the model. The governing differential equations are given in dimensionless form to make the results representative of animals of all body sizes. The dimensionless input parameters are: U, a horizontal Froude number based on forward speed and leg length; V, a vertical Froude number based on vertical landing velocity and leg length, and KLEG, a dimensionless stiffness for the leg-spring. Results show that at high forward speed, KLEG is a nearly linear function of both U and V, while the effective vertical stiffness is a quadratic function of U. For each U, V pair, the simulation shows that the vertical force at mid-step may be minimized by the choice of a particular step length. A particularly useful specification of the theory occurs when both KLEG and V are assumed fixed. When KLEG = 15 and V = 0.18, the model makes predictions of relative stride length S and initial leg angle θ0 that are in good agreement with experimental data obtained from the literature.
A model of running is proposed in which the leg is represented as a rack-and-pinion element in series with a damped spring. The rack-and-pinion element emphasizes the role of descending commands, while the damped spring represents the dynamic properties of muscles and the position and the rate sensitivity of reflexes. This model is used to predict separately the effect of track compliance on step length and ground contact time. The predictions are compared with experiments in which athletes ran over tracks of controlled spring stiffness. A sharp spike in foot force up to 5 times body weight was found on hard surfaces, but this spike disappeared as the athletes ran on soft experimental tracks. Both ground contact time and step length increased on very compliant surfaces, leading to moderately reduced running speeds, but a range of track stiffness was discovered which actually enhances speed.