Journal of Applied Biomechanics, 2013, 29, 481-489
© 2013 Human Kinetics, Inc.
An Official Journal of ISB
www.JAB-Journal.com
ORIGINAL RESEARCH
Changes in Kinematics, Metabolic Cost, and External Work
During Walking With a Forward Assistive Force
Christopher A. Zirker, Bradford C. Bennett, and Mark F. Abel
University of Virginia
We examined how the application of a forward horizontal force applied at the waist alters the metabolic cost,
kinematics, and external work of gait. Horizontal assist forces of 4%, 8% and 12% of a subject’s body weight
were applied via our testing apparatus while subjects walked at comfortable walking speed on a level treadmill.
Kinematic and metabolic parameters were measured using motion capture and ergospirometry respectively
on a group of 10 healthy male subjects. Changes in kinematic and metabolic parameters were quantified and
found similar to walking downhill at varying grades. A horizontal assist force of 8% resulted in the greatest
reduction of metabolic cost. Changes in recovery factor, external work, and center of mass (COM) movement
did not correlate with changes in metabolic rate and therefore were not driving the observed reductions in cost.
The assist force may have performed external work by providing propulsion as well as raising the COM as it
pivots over the stance leg. Assist forces may decrease metabolic cost by reducing the concentric work required
for propulsion while increasing the eccentric work of braking. These findings on the effects of assist forces
suggest novel mobility aids for individuals with gait disorders and training strategies for athletes.
Keywords: gait, treadmill walking, energy, kinematics
During walking, the body adapts to maintain stability
and efficiency under a variety of circumstances. There
is an expanding body of research examining the energy
required for locomotion under different environmental
conditions and the underlying biomechanical adaptations.
Changes in energy requirements during locomotion have
been studied extensively on different surfaces such as
grass and sand,1,2 uphill and downhill gradients,3–5 and
at different speeds.6 One interesting walking condition
occurs when an external force is applied in the horizontal
direction such that the propulsion required for locomotion
is reduced. Prior work found that an assistive horizontal
force could reduce metabolic energy consumption during
walking by up to 47% when 10% of a subject’s body
weight pulled forward at the waist.7 Such reductions
suggest that this type of assistance could be helpful in
assistive devices for individuals such as those with cerebral palsy where the high metabolic cost of ambulation
limits their participation in society. However, to date there
is no research into the kinematics or mechanical work of
Christopher A. Zirker (Corresponding Author) is with the
Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA. Bradford C. Bennett is
with the Department of Mechanical and Aerospace Engineering,
and with the Department of Orthopaedic Surgery, University
of Virginia, Charlottesville, VA. Mark F. Abel is with the
Department of Orthopaedic Surgery, University of Virginia,
Charlottesville, VA.
walking with a horizontal assist force that would aid in
understanding the reduction in metabolic energy use and
inform us as to whether a device (eg, a powered walker)
would be an appropriate aid.
Other groups have examined the relationship
between gait and energy during normal walking but not
during assisted walking. An inverted pendulum model
can describe the energy exchange between kinetic energy
and gravitational potential energy of the body center of
mass (COM) and how this can reduce cost during level
walking.8 Expanding upon this model, one can calculate
the external work performed on the COM and the energy
exchange between kinetic and potential energy can be
quantified.9 The mechanical work for step-to-step transitions is an important determinant of metabolic cost10
and the energetic cost of raising the COM during this
transition is significant.11 However, it has been shown that
healthy human subjects do not demonstrate a reduction in
metabolic cost when movement of the COM is reduced12
and that changes in mechanical work do not explain
higher metabolic costs in the young13 or elderly.14 Therefore external work and metabolic cost are not always
covariant, and the causes of changes in the metabolic
cost of gait are unclear. Studying the kinematics, work,
and energy of human locomotion with an assistive force
may add further insights into the relationship between
the mechanics and energetics of walking.
We hypothesized that a horizontal assist force (HAF)
in the direction of walking will result in a decrease in metabolic cost and that an optimal assist force exists to create
481
482 Zirker, Bennett, and Abel
the greatest reduction in cost. Secondly, since external
work and metabolic cost are positively correlated in both
healthy15 and disabled populations16 we hypothesized that
some of the reduction in metabolic cost with assist force
is due to a decrease in external work due to an increase
in recovery factor. Finally, since walking downhill creates a forward force similar to a HAF, we hypothesized
that kinematics changes of the lower extremities would
resemble those of downhill walking.
Methods
Subjects
Kinematic and metabolic data were collected and analyzed in a convenience sample of 10 healthy adult males
without known musculoskeletal, neurological, cardiac, or
pulmonary pathology [age = 32.8 ± 13.2, height = 1.8 ±
.07 m, mass = 77.5 ± 12.0 kg]. All tests were conducted
in the Motion Analysis and Motor Performance Laboratory at the University of Virginia. Subject consent was
approved by the University of Virginia’s Human Investigation Committee and was obtained for all subjects.
Protocol
Throughout this protocol, subjects walked at a selfselected comfortable walking speed. Subject walking
speed was determined in two steps. First, the treadmill
was started at a slow “barely walking” speed then accelerated by the investigators in increments of 0.2 km/hr as
requested by the subject until the subject indicated it was
the desired speed. Next, the treadmill speed was increased
to a rapid “close to running” pace and decelerated in
a similar method until the subject again indicated the
desired speed. The two indicated speeds were averaged
to determine walking speed; mean walking speed was
1.29 ± 0.08 m/s.
Testing began with subjects sitting at rest until two
minutes of baseline resting steady state metabolic rate
was recorded. Subjects rested while seated rather than
standing because subtracting the standing from the total
rates tends to underestimate the total effort of walking.17
In addition, this allowed the protocol to be repeated in
future studies by individuals with disabilities that use
assistive devices and have difficulty standing as has been
done in other studies.18–20 Next, subjects performed a
“warm up” baseline walking trial on the treadmill without
any assist force until two minutes after steady state was
achieved. This cycle of sitting and walking was repeated
with a HAF of 4%, 8%, and 12% of the subject’s body
weight. These assist forces were chosen to bracket the
10% HAF that produced the maximum metabolic reduction in the work of Gottschall and Kram7 with a lower 4%
assist force for use in future studies including subjects
with disabilities who struggle with higher forces. This
required at least seven minutes of walking but no more
than eleven minutes of walking per condition. Trial order
was randomized for assist force trials. After a rest period,
subjects completed a fifth “cool down” repeated baseline
trial with no assist force. Subjects were then asked to fill
out a brief questionnaire providing a qualitative description of their experiences of walking with an assist force.
Assistive Force Apparatus
A constant HAF was applied through a belt strapped
around each subject’s waist and the desired load was
applied via hanging weights on a pulley system (Figure
1). A spring was used to filter the motion artifacts between
the subject and the weights. A spring stiffness of 2.8 N/
cm was used so that the natural frequency of the springmass system was different from gait cadence to avoid
resonance. No damping was added to the system. The
length of the horizontal section of the pulley system was
maintained at greater than 60 cm resulting in a variation
from the horizontal of the assist force vector was less
than less than 2° for all trials. Forces between the subject
and the spring were recorded using a load cell and were
maintained on average within 8.0 ± 1.4% for 4% HAF,
6.0 ± 0.9% for 8% HAF and 5.3 ± 1.0% for 12% HAF
of the desired force, which is a variation of less than 10
N for even the highest assist forces measured. Variations
in the assist force were oscillatory and did not produce
a systematic bias toward greater or weaker assist forces.
The assist force apparatus did not interfere with subject
movement and allowed unrestricted treadmill walking.
Data Collection
After 4 minutes of walking steady state metabolic rate
was confirmed by monitoring real-time VO2/kg consumption visually. All resting and walking trials were
conducted until two minutes of steady state metabolic
data were recorded. Three-dimensional kinematic data
were collected using an eight camera Vicon Motion
Analysis System (Oxford Metric; Oxford, UK) at 120 Hz.
A full-body Vicon Plug-in Gait set of 37 markers21 and
Figure 1 — Schematic of the experimental setup. A rope was
attached to a waist belt worn by the subject and connected in
series to a load cell, spring, rope, and weights. The subject wore
a set of 38 markers and an oxygen consumption measuring
device which included a vest and mask (not shown).
Walking with a Forward Assistive Force 483
the Oxycon Mobile apparatus (Viasys Healthcare; San
Diego, CA) were attached to the subjects after anthropometric measurements were taken. For each walking task,
kinematic data were collected for at least five trials of ten
complete strides each. Trials were collected at least one
minute apart after the first two minutes of walking during
each task. Assist force data were collected by a single
degree of freedom load cell (ATI Industrial Automation;
Apex, North Carolina) at 1080 Hz through Vicon.
Data Processing
For each assist force level, the normalized net metabolic
rate was calculated by subtracting the average resting
steady state VO2 L∙min–1 from the average walking steady
state VO2 L∙min-1. This value was then divided by the
subjects mass to obtain VO2 L∙min–1∙kg–1. Metabolic
cost, VO2 L∙m–1∙kg–1, was obtained by dividing the rate
by the walking velocity. Marker trajectory data were
exported from Vicon and processed using MATLAB
(Mathworks; Natick, Massachusetts). Gait events were
determined using validated methods22 and used to calculate average stride length and duration of swing phase
and stance. Joint kinematics of the ankle, knee, and hip
were determined using the Vicon Plug-in Gait model.
Previously described energy and work measures23 were
calculated based on the COM position found using a validated full-body kinematic model.23 COM position data
were then filtered using a bidirectional low-pass second
order Butterworth filter with a cutoff frequency of 8 Hz
to remove signal noise without introducing a phase shift.
Work and energy values calculated include the kinetic and
gravitational potential energy of the COM, external work
(Wext), external work assuming no energy exchange (Wne),
recovery factor (R), and the relative phase angle between
kinetic and potential energy curves. Recovery factor is
the percentage of mechanical energy recovered through
energy exchange between the kinetic and potential energy
of the movement of the COM.
Subject Questionnaire
After testing, subjects were asked to fill out a brief questionnaire. The questionnaire asked the subjects to rank
the trials by effort required, inquired if walking during
the assist force trials “felt natural,” and requested for subjects to provide their own qualitative comments about the
experiment and walking with an assist force. All subjects
responded to the questionnaire in full.
Comparison with Downhill Walking
When walking downhill there exists a component of
force normal to the ground and a component parallel
to the ground (ie, direction of travel); this force is what
allows passive dynamic walking robots to walk down a
slight grade.24 The component parallel to the direction of
travel can be found as the sine of the angle of inclination
times downward force or body weight. Thus the angle
that creates a desired force parallel to the ground can be
computed. Slopes of 2.3°, 4.6°, and 6.9° create forces
parallel to the ground that are 4%, 8%, and 12% of body
weight, respectively.
Statistics
Differences between variables were determined using
repeated-measures ANOVA with Tukey’s post hoc test.
Significance was determined at P < .05. Because no significant differences were found between the “warm-up”
and “cool-down” baseline trials for any measure, data
from the two were averaged to create “normal” or “0%
HAF” condition. Correlations were determined using a
Pearson correlation.
Results
Application of a HAF reduced metabolic cost such that
the lowest cost was observed at 8% HAF (P < .001). The
metabolic costs differed with assist level (P < .001) with
all three levels of assist force resulting in a reduction in
metabolic cost relative to normal walking (P < .001).
During assisted trials, the metabolic cost of walking at
comfortable walking speed was shown to reduce by 23.7
± 6.3% of normal walking for 4% HAF, 34.7 ± 6.9% for
8% HAF, and 19.1 ± 12.8% for 12% HAF (Figure 2).
Eight of the ten subjects demonstrated the pattern shown
while the remaining two had the lowest metabolic cost
at 12% HAF followed by 8%, then 4% while the highest
cost was always measured during normal walking. When
asked to rank the trials in order of preference, subjects
preferred the unassisted “warm up” condition followed
by 4% HAF, unassisted “cool down,” 8% HAF, and lastly
12% HAF. Eight out of ten subjects rated the 12% HAF
trial as requiring the most effort. All subjects stated that
walking with an assist force “felt unnatural” especially
at the higher force levels, although the 4% HAF trial
was generally regarded as “easy” or “tolerable.” Many
subjects, either verbally or in writing, commented that
the sensation of walking with an assist force was similar
to walking downhill.
Recovery factor did not necessarily increase
nor did external work decrease with an assist force
(Table 1). Wext differed from the normal condition only
at 12% assist where it was 33% larger (P < .02). Wne
increased with every assist level (P < .005). The recovery
factor increased with the 4% HAF (P < .04) but was not
different from the normal condition at the higher assist
levels. The recovery factor for normal walking of 64.7
changed to 72.0 for 4%, (P < .03), 70.5 for 8% (P < .11)
and 64.4 for 12% HAF (P < .99). The relative phase
increased at each assist level (P < .001), nearly 180°
out of phase at 4% HAF, but increasing at 8% and 12%
HAF. There were significant changes in all dependent
measures except the ratio of potential to kinetic energy
(Figure 3). The main effects for the relative phase, Wext,
Wne, and excursions of the potential and kinetic energies
were at the P < .001 level, while the recovery factor had
a level of P < .005.
484 Zirker, Bennett, and Abel
Figure 2 — Measured metabolic rates as a percentage of normal unassisted walking (mean ± standard deviation). The curve is a
second-order polynomial least squares fit, y = 9.8x2 – 55.9x + 146.8, R2 = .98.
Table 1 Summary of data
Average Value
% Reduction in Metabolic Cost
Normal
4%
8%
12%
0
23.7*
34.7*
19.1*
Stride Length (cm)
143
138*
135*
130*
Stride Duration (s)
1.1
1.06*
1.04*
1.00*
% of Stride in Double Support
18.5
17.5*
16.7*
16.0*
Max Hip Flexion (deg)
33.1
30.8*
29.2*
29.5*
Max Hip Extension (deg)
–14.5
–12.7
–11.2*
–6.0*
Max Knee Flexion (deg)
66.9
68.2
69.8*
71.6*
Max Knee Extension (deg)
0.1
–1.4*
–1.7*
–0.9
Max Dorsiflexion (deg)
10.7
10.1
11.3
12.8*
Max Plantar Flexion (deg)
–21.4
–19.4
–15.4*
–12.2*
Hip Excursion (deg)
47.6
43.5*
40.4*
35.5*
Knee Excursion (deg)
66.8
69.6*
71.5*
72.5*
Ankle Excursion (deg)
32.1
29.5*
26.7*
25.0*
Relative Phase (deg)
159
181*
197*
213*
Recovery Factor
64.7
72.0*
70.5
64.4
Wext (J∙kg–1∙m–1)
0.64
0.56
0.66
0.85*
Wne (J∙kg–1∙m–1)
1.80
2.01*
2.23*
2.36*
Kinetic Energy Excursion (J∙kg–1∙m–1)
0.224
0.250
0.278*
0.294*
Potential Energy Excursion (J∙kg–1∙m–1)
0.238
0.256
0.287*
0.300*
Potential Energy / Kinetic Energy
1.16
1.12
1.11
1.09
*Indicates P < .05 compared with normal.
Walking with a Forward Assistive Force 485
Figure 3 — Demeaned kinetic and potential energies of the center of mass over half a stride, where 0% is the maximum kinetic
energy. Shifting peaks of the potential energy curves show the changing relative phase while varying amplitudes correspond with
changes in external work.
As with changing downhill grades, changes in assist
force resulted in changes in gait kinematics (Table 1).
There were main effects for maximum hip and knee flexions, hip extension, and ankle dorsiflexion, and all angle
excursions (P < .001) as well as for maximum knee extension and ankle plantar flexion (P < .01). Maximum hip
flexion and extension decreased. In addition, maximum
knee flexion in stance increased and ankle plantar flexion
decreased with increasing HAF. Excursions of the hip and
ankle decreased while knee excursion increased. Stride
length shortened with increasing assistance (P < .001) and
all values differed from each other (P < .02). For stride
duration there was also a main effect (P < .001) and all
assist values were shorter than the normal condition but
did not differ from each other. The relative percentage
of time of each stride spent in double support decreased
with increasing assist force (P < .01); normal to 4%: P
< .04, normal to 8% and normal to 12%: P < .001. This
reduced time in double support can be seen in the altered
phasing of joint angles of the lower extremities between
assist force levels (Figure 4).
Discussion
The metabolic results supported our hypothesis that an
assist force would reduce the cost of walking in healthy
adults. However, we reject our hypothesis that this
reduction in metabolic cost is the result of a reduction of
external work performed as the same trend was not seen
in Wext and Wne. In fact, there was a significant increase in
Wne with increasing assist force. This increase in Wne was
the result of increases in excursions of both the potential
and kinetic energies. While there was an increase in the
recovery factor at 4% HAF reflecting improved phasing
of the energies, this could not overcome the increases
in the energy excursions to decrease the overall Wext
performed. Therefore our hypothesis that the reduced
metabolic consumption would be accompanied by
reduced mechanical work and improved energy recovery
was not substantiated.
Our measured reductions in metabolic cost are lower
in magnitude but with a similar trend as the data of Gottschall and Kram7 and both sets of data suggest the maximum reduction in metabolic cost occurs between 8% and
10% HAF. The different percentages in reductions found
in the two studies is most likely due to their use of standing for the resting metabolic state instead of the sitting
values used in this study; subtracting a larger “resting”
value results in any changes being a larger percentage of
the unassisted data. As mentioned previously, we chose
sitting as our rest condition to be consistent when working
with populations that have difficulty standing. In addition,
some researchers believe using standing resting values
tends to underestimate the cost of walking as it removes
the effort to stand.17 Recent work measured a standing
metabolic rate as 16% greater than sitting,17 but other
researchers have found greater differences in the cost
of maintaining a standing posture.25 Another difference
between the two studies was that subjects in the present
work walked at their own comfortable walking speed
486 Zirker, Bennett, and Abel
Figure 4 — Joint kinematics of the lower extremities for various levels of assist forces. Flexion at the hip and knee and dorsiflexion
of the ankle are defined as positive. Heel strike occurs at 0% of the stride.
rather than a uniform speed. Since comfortable walking
speed typically results in the most efficient gait, subjects
walking at an arbitrary speed may have higher costs that
allow for a greater reduction with assist force.
Despite observing the highest recovery factor, most
energetically efficient relative phase, and lowest Wext at
4% HAF, the greatest reduction of metabolic cost was
seen at 8% HAF. This result indicates that while changes
in recovery factor, total external work and COM motion
can contribute to reduction of metabolic cost, they are
not the sole cause and other mechanisms must be considered. Although the assist force was only applied
in the horizontal direction, it may have been able to
contribute to elevating the COM. Considering gait
as an inverted pendulum, the forward leg acts as a
pivot which guides the COM through its trajectory.8
Between toe off and midstance of the contralateral foot,
the COM rises as it moves in the forward direction,
increasing its potential energy. During unassisted walking, this energy comes from either metabolic expenditure
or transfer from kinetic energy, but during assisted walking it may be provided by the assist force as the COM is
pulled forward while it travels upwards to its peak height
during midstance.
Walking with a Forward Assistive Force 487
While the inverted pendulum model may provide
a simple and insightful means of analyzing mechanical
energy during walking, it is not the only relevant tool
for explaining the associated metabolic cost. In addition
to both recovery factor and relative phase showing the
greatest improvement at 4% HAF instead of 8% HAF,
Wne increased as assist force increased. This discrepancy
between the work performed by the subject, work performed by the assist force device, and the overall metabolic cost indicates that additional factors may need to be
considered when comparing mechanical and metabolic
energy costs of walking.
During normal walking, forward speed is not constant and involves propulsion by the trailing leg during
toe off and braking by the lead leg during heel strike.
This individual limb work during double support has
been shown to be an important determinant of metabolic
cost.10 The peak anterior/posterior ground reaction force
for propulsion during normal walking at comfortable
walking speed is around 2 N/kg and supplies up to 85%
of the power in walking.26 For our conditions, this would
result in a nominal impulse of 0.6 Ns/kg per stride. The
percentage of this impulse provided by a 4%, 8% and 12%
HAF is 67%, 133% and 200%, respectively, reducing the
work requirements for forward propulsion but increasing
the requirements of braking. This can also be viewed from
the perspective of the work performed. The virtual work
values of the assist forces relative to the treadmill belt
on the subjects are 68%, 110% and 140% of the Wext at
4%, 8% and 12% HAF, respectively. Once the required
propulsion and work is supplied, any additional energy
must be dissipated. Thus it may be natural that the greatest
reduction in metabolic cost occurs at a point where the
added impulse and virtual work are close to the no assist
values. While the combined leg work computed here is
less than would be computed using the individual limb
method,10 we still see an increased Wext and metabolic
cost at 12% HAF relative to 8% HAF where the added
impulse and work were beyond what was needed for
propulsion. For lower assist levels, the fact that negative
(eccentric) work is more metabolically efficient than positive (concentric) work27 results in reduced cost despite the
increase in braking force for lower assist levels.
Several changes in the kinematics of the lower
extremities were noteworthy. At the hip joint, flexion
during heel strike and extension during toe off are both
reduced significantly (Figure 4, Table 1) as assist force
increased reflecting the shortened stride. Our data also
suggests that the source of the increased COM and potential energy excursion was increased flexion of the knee
during stance. The maximum flexion of the knee during
stance increased with assist force most likely because
of the increased braking during double support7 similar
to what is seen in walking downhill. This braking could
also contribute to the increase in kinetic energy variation.
There is also a significant decrease in plantar flexion
accompanying toe off. This suggests that one effect of
the HAF was to reduce the power requirements at the
ankle, an effect suggested in earlier work by decreased
EMG activity in the medial gastrocnemius.7 Because
the plantar flexors are responsible for the majority of the
propulsive work at the ankle during toe off,28 it is intuitive
that plantar flexion angles should decrease dramatically
as assist force increases. This finding is in agreement
with previous findings of decreased horizontal ground
reaction forces during the propulsive phase when walking
with an assist force.7
Walking with a horizontal assist force can be compared with downhill walking where a component of gravity acts parallel to the walking surfaces. Unsurprisingly,
many of the kinematic and energetic changes observed
with a HAF are similar to those reported in downhill
walking studies and could explain why some subjects
noted the similarities between the two activities. While
studies have found a reduction in stride duration at slopes
with grades of 10% and 15%,29 we found a reduction at all
levels of assist. The increased knee flexion during stance
with increased assist force is qualitatively similar to the
increases in knee flexion angles seen in walking down
a ramp.30 Decreased stride length with increased assist
force may result from the increased shear ground reaction
forces required for braking as is seen in downhill walking,30 but was only found for slopes greater than 17%. As
we observed in assisted walking, metabolic cost decreases
with slope angle to a point then increases again.31 The
greatest metabolic reductions happen roughly around a
–9% grade,31,32 which converts to a 9% HAF. Our findings
suggest a strong biomechanical link between walking
with a HAF and downhill walking.
There are several limitations to this study. First,
we report only the external work (the work done on
the COM) and not the internal work that is done by the
limbs relative to the COM. However, the nature of the
kinematic changes suggest there was little change in the
internal work done relative to the COM. While kinematic
changes are identified in the lower extremity with increasing HAF, it is not clear what specific aspects of these
changes contribute to changes in metabolic cost, recovery
factor and relative phase. Furthermore, while this study
demonstrates that the relationship between energetic and
metabolic cost are not directly related, it does not explain
why. This shortcoming could be addressed by incorporating dynamics to study reduction in joint moments during
gait or estimating muscle activation to show reduced
muscular effort.
This study implies possible training routines for
athletes such as hikers and mountaineers who navigate
slopes who may be able to incorporate assisted treadmill
walking into their training routines if walking downhill is
not available. Because the majority of injuries incurred
during hiking occur during descent,33 simulating downhill
walking using an assist force may provide a manner of
training to strengthen leg muscles and reduce the risk
of injury.
Perhaps more importantly these findings may have
important therapeutic implications for both rehabilitation
and the development of assistive devices. When treating
patients with disorders that cause them to fatigue rapidly,
488 Zirker, Bennett, and Abel
usage of an assist force during treadmill exercises could
increase the time patients remain active during therapy
sessions. The development of an intelligent powered
walker may be of benefit to many patients. Individuals
with conditions such as cerebral palsy often demonstrate
gait patterns with a significantly higher cost of walking34
and have reduced strength in their plantar flexors. A
powered walker which senses user feedback and intelligently provides a forward force at appropriate times (ie,
push-off and not during foot contact when negative work
is performed) may enable walker users to travel greater
distances without rest thus increasing independence and
quality of life.
This study is the first to show how work, lower limb
kinematics, and motion of the COM change with the
application of a forward horizontal assist force. The greatest reductions in metabolic cost were seen at 8% HAF.
Changes in metabolic cost, walking temporal parameters
and kinematics of the hip and knee were similar to what
is seen in downhill walking at slopes equivalent to the
assist force levels. Indeed recent work has shown that in
walking on slopes, the joints of the lower limbs are tuned
together and only a selected property is tuned to adapt
in response to the slope.35 Despite shorter stride length
and duration, shorter periods of double support, shifting
of the phase of the energies, and increases in energy
excursions with increasing HAF, the ratio of potential
energy to kinetic energy never changes and it is only at
12% HAF that the external work increases.
Future work should include collection of force
data that would allow the computation of individual leg
work to provide better understanding of the reductions
in metabolic cost. In addition, further study is needed
to fully understand our adaptation to assist forces in
walking. This data sheds light on the basic organization of walking and adds to the body of work23,36,37
that suggests that the “organization” of the gait with
respect to the COM remains an important feature of
walking under various conditions. Finally, study of
the application of intermittent assist forces is needed to
determine whether propulsion of the trailing leg can be
assisted while reducing the need for additional braking
force of the lead leg.
Acknowledgments
We would like to thank Doug Friedman and Rafat Mehdi for
their assistance with data collection and processing as well as
Shawn Russell and Jason Franz for their advice and technical
assistance.
References
1. Lejeune TM, Willems PA, Heglund NC. Mechanics and
energetics of human locomotion on sand. J Exp Biol.
1998;201(13):2071–2080. PubMed
2. Pinnington HC, Dawson B. The energy cost of running
on grass compared to soft dry beach sand. J Sci Med
Sport. 2001;4(4):416–430. PubMed doi:10.1016/S14402440(01)80051-7
3.Gottschall JS, Kram R. Mechanical energy fluctuations
during hill walking: The effects of slope on inverted pendulum exchange. J Exp Biol. 2006;209(Pt 24):4895–4900.
PubMed doi:10.1242/jeb.02584
4. Minetti AE, Moia C, Roi GS, et al. Energy cost of walking
and running at extreme uphill and downhill slopes. J Appl
Physiol. 2002;93(3):1039–1046. PubMed
5. Minetti AE, Ardigo LP, Saibene F. Mechanical determinants of gradient walking energetics in man. J Physiol.
1993;472:725–735. PubMed
6.Heglund NC, Taylor CR. Speed, stride frequency and
energy cost per stride: How do they change with body size
and gait? J Exp Biol. 1988;138(1):301–318. PubMed
7. Gottschall JS, Kram R. Energy cost and muscular activity
required for propulsion during walking. J Appl Physiol.
2003;94(5):1766–1772. PubMed
8.M o c h o n S , M c M a h o n TA . B a l l i s t i c w a l k i n g . J B i o m e ch . 1 9 8 0 ; 1 3 ( 1 ) : 4 9 – 5 7 . P u b M e d
doi:10.1016/0021-9290(80)90007-X
9. Winter DA. Biomechanics and motor control of human
movement. 1990.
10.Donelan JM, Kram R, Kuo AD. Mechanical work for
step-to-step transitions is a major determinant of the
metabolic cost of human walking. J Exp Biol. 2002;205(Pt
23):3717–3727. PubMed
11.Neptune RR, Zajac FE, Kautz SA. Muscle mechanical
work requirements during normal walking: The energetic
cost of raising the body’s center-of-mass is significant. J
Biomech. 2004;37(6):817–825. PubMed doi:10.1016/j.
jbiomech.2003.11.001
12. Ortega JD, Farley CT. Minimizing center of mass vertical
movement increases metabolic cost in walking. J Appl
Physiol. 2005;99(6):2099–2107. PubMed doi:10.1152/
japplphysiol.00103.2005
13. Frost G, Dowling J, Dyson K, Bar-Or O. Cocontraction in
three age groups of children during treadmill locomotion.
J Electromyogr Kinesiol. 1997;7(3):179–186. PubMed
doi:10.1016/S1050-6411(97)84626-3
14. Van de Walle P, Desloovere K, Truijen S, et al. Age-related
changes in mechanical and metabolic energy during
typical gait. Gait Posture. 2010;31(4):495–501. PubMed
doi:10.1016/j.gaitpost.2010.02.008
15. Cavagna GA, Kaneko M. Mechanical work and efficiency
in level walking and running. J Physiol. 1977;268(2):467–
481. PubMed
16. Detrembleur C, Dierick F, Stoquart G, et al. Energy cost,
mechanical work, and efficiency of hemiparetic walking.
Gait Posture. 2003;18(2):47–55. PubMed doi:10.1016/
S0966-6362(02)00193-5
17. Weyand PG, Smith BR, Sandell RF. Assessing the metabolic cost of walking: The influence of baseline subtractions. Conf Proc IEEE Eng Med Biol Soc. 2009;2009:68786881. doi:10.1109/IEMBS.2009.5333126.
18. Maltais DB, Pierrynowski MR, Galea VA, Bar-Or O. Physical activity level is associated with the O2 cost of walking
in cerebral palsy. Med Sci Sports Exerc. 2005;37(3):347–
353. PubMed doi:10.1249/01.MSS.0000155437.
45937.82
19. Maltais D, Wilk B, Unnithan V, Bar-Or O. Responses of
children with cerebral palsy to treadmill walking exercise
in the heat. Med Sci Sports Exerc. 2004;36(10):1674–1681.
PubMed doi:10.1249/01.MSS.0000142312.43629.D8
20.Unnithan VB, Dowling JJ, Front G, Bar-Or O. Role of
mechanical power estimates in the O2 cost of walking
in children with cerebral palsy. Med Sci Sports Exerc.
Walking with a Forward Assistive Force 489
1999;31(12):1703–1708. PubMed doi:10.1097/00005768199912000-00003
21.Vicon, 2002. Plug-in-Gait modeling instructions. Vicon
Manual, Vicon 612 Motion Systems. Oxford Metrics Ltd.,
Oxford, UK.
22.Zeni JA, Richards JG, Higginson JS. Two simple
methods for determining gait events during treadmill
and overground walking using kinematic data. Gait
Posture. 2008;27(4):710–714. PubMed doi:10.1016/j.
gaitpost.2007.07.007
23.Bennett BC, Abel MF, Wolovick A, et al. Center of
mass movement and energy transfer during walking
in children with cerebral palsy. Arch Phys Med Rehabil. 2005;86(11):2189–2194. PubMed doi:10.1016/j.
apmr.2005.05.012
24.McGeer T. Passive dynamic walking. Int J Robot Res.
1990;9(2):62–82. doi:10.1177/027836499000900206
25. Grabowski A, Farley CT, Kram R. Independent metabolic
costs of supporting body weight and accelerating body
mass during walking. J Appl Physiol. 2005;98(2):579–583.
PubMed doi:10.1152/japplphysiol.00734.2004
26. Winter DA. The biomechanics and motor control of human
gait. Univ of Waterloo Pr; 1987.
27.Abbott BC, Bigland B, Ritchie JM. The physiological
cost of negative work. J Physiol. 1952;117(3):380–390.
PubMed
28. Winter DA. Energy generation and absorption at the ankle
and knee during fast, natural, and slow cadences. Clin
Orthop Relat Res. 1983;(175)(175):147-154.
29. Hunter LC, Hendrix EC, Dean JC. The cost of walking
downhill: Is the preferred gait energetically optimal? J
Biomech. 2010;43(10):1910–1915. PubMed doi:10.1016/j.
jbiomech.2010.03.030
30. Redfern MS, DiPasquale J. Biomechanics of descending
ramps. Gait Posture. 1997;6(2):119–125. doi:10.1016/
S0966-6362(97)01117-X
31.Wanta DM, Nagle FJ, Webb P. Metabolic response
to graded downhill walking. Med Sci Sports Exerc.
1993;25(1):159–162. PubMed doi:10.1249/00005768199301000-00022
32. Margaria R. Positive and negative work performances and
their efficiencies in human locomotion. Eur J Appl Physiol.
1968;25(4):339–351. PubMed doi:10.1007/BF00699624
33. Ainslie PN, Campbell IT, MacLaren DP, Reilly T. Characteristic activities and injuries of hill-walkers. Contemporary Ergonomics; 2002:167–171.
34. Rose J, Gamble JG, Burgos A, et al. Energy expenditure
index of walking for normal children and for children with
cerebral palsy. Dev Med Child Neurol. 1990;32(4):333–
340. PubMed doi:10.1111/j.1469-8749.1990.tb16945.x
35.Funato T, Aoi S, Oshima H, Tsuchiya K. Variant and
invariant patterns embedded in human locomotion through
whole body kinematic coordination. Exp Brain Res.
2010;205(4):497–511. PubMed doi:10.1007/s00221-0102385-1
36.Bennett BC, Russell SD, Sheth P, Abel MF. Angular
momentum of walking at different speeds. Hum Mov
Sci. 2010;29(1):114–124. PubMed doi:10.1016/j.
humov.2009.07.011
37. Cavagna GA, Heglund NC, Taylor CR. Mechanical work in
terrestrial locomotion: Two basic mechanisms for minimizing energy expenditure. Am J Physiol. 1977;233(5):R243–
R261. PubMed