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special communication
Force treadmill for measuring vertical
and horizontal ground reaction forces
RODGER KRAM, TIMOTHY M. GRIFFIN, J. MAXWELL DONELAN, AND YOUNG HUI CHANG
Department of Integrative Biology, University of California, Berkeley, California 94720-3140
Kram, Rodger, Timothy M. Griffin, J. Maxwell
Donelan, and Young Hui Chang. Force treadmill for
measuring vertical and horizontal ground reaction forces. J.
Appl. Physiol. 85(2): 764–769, 1998.—We constructed a force
treadmill to measure the vertical, horizontal and lateral
components of the ground-reaction forces (F
z
,F
y
,F
x
, respec-
tively) and the ground-reaction force moments (M
z
,M
y
,M
x
),
respectively exerted by walking and running humans. The
chassis of a custom-built, lightweight (90 kg), mechanically
stiff treadmill was supported along its length by a large
commercial force platform. The natural frequencies of vibra-
tion were .178 Hz for F
z
and .87 Hz for F
y
, i.e., well above
the signal content of these ground-reaction forces. Mechani-
cal tests and comparisons with data obtained from a force
platform runway indicated that the force treadmill recorded
F
z
,F
y,
M
x
and M
y
ground-reaction forces and moments
accurately. Although the lowest natural frequency of vibra-
tion was 88 Hz for F
x
, the signal-to-noise ratios for F
x
and M
z
were unacceptable. This device greatly decreases the time
and laboratory space required for locomotion experiments
and clinical evaluations. The modular design allows for
independent use ofboth treadmill and force platform.
biomechanics; locomotion; force platform
OUR GOAL was to construct an improved force treadmill
(FTM) for measuring the forces and moments exerted
on the ground by walking and running humans. Previ-
ousforce-measuringtreadmilldeviceshave beenshown
to reduce substantially data-collection time for locomo-
tion experiments, to allow for feedback to subjects
and/or patients, and to enable experiments to be con-
ducted that are not otherwise possible (9, 11–13, 16).
However,previous designs couldsatisfactorilymeasure
only the vertical force component. We sought to build a
FTM that can record all three components of the
ground-reaction force: vertical (F
z
), horizontal (F
y
), and
lateral (F
x
), as well as the moments (M
z
,M
y
, and M
x
).
These measurements are necessary for measuring the
mechanical work performed on the center of mass, for
determining the point of force application, and for
calculating joint moments.
Various combinations of force platforms or force
transducers with treadmills have been constructed in
the past, but each of the designs had limitations.
Several laboratories have mounted a force platform
inside a treadmill (15, 17, 19) or built a treadmill
around a ground-mounted force platform (8, 10). These
devices could record the vertical ground-reaction force
and the moments around the lateral and anterior-
posterior axes with excellent fidelity, but they could not
measureF
y
,F
x
,orM
z
.Otherinvestigatorshave mounted
a treadmill on top of multiple force sensors (4, 14, 18,
20, 22). Although these designs could measure F
y
in
addition to F
z
,M
x
, and M
y
, they have done so with
unsatisfactoryfidelity.Frequency-responsecharacteris-
tics and signal-to-noise ratios were beyond limits nor-
mally considered acceptable. For example, the natural
frequencies of F
z
for all these designs have all been ,45
Hz. These previous attempts were hampered by three
factors: large treadmill mass, inadequate overall stiff-
ness,and vibrations inducedby the motororrollers. We
have developed a FTM that is a hybrid of these two
basic designs.
METHODS
A1-in. (2.5 cm)-thick aluminum plate was firmly affixed to
the laboratory floor with epoxy glue, bolts, and concrete
anchors. We mounted a large 71 3 24 in. (180 3 60 cm)
commercial strain-gauged multicomponent force platform
[model ZBP-7124–6–4000;Advanced Mechanical Technology
(AMTI), Watertown, MA] to the aluminum plate. The tread-
mill chassis was bolted to threaded metal inserts in the top
surface of the force platform. The main chassis of the tread-
millwasbuiltfrom4-in.(10-cm)6061aluminum I-beams that
were connected by eight cross-members made of 2-in. (5-cm)
aluminum channel. The bed of the treadmill was made of
0.25-in. (6-mm)-thick 6061 aluminum plate with a thin Teflon
sheet to reduce belt-bed friction.
Therollerswere custom-made on a lathe from a single piece
ofsteel toachieveexcellent balanceandthus tominimizeinduced
vibrations(F. & G. WilliamsMachine and Tool,Hatboro, PA). The
rollers hada diameter of 3in. (8cm) and aface width of 14in. (35
cm).Therollershadaslighttapercrownforbetterbelttracking.A
custom-made lead screw device allowed for tensioning of the belt
bymoving thenondrive rolleralongthe horizontallong axisofthe
chassis.A2-hp(1,500-W) variable-speedalternating-current elec-
tric motor (Leeson Electric, Grafton, WI) was mounted on the
mainchassis.Atimingpulleyon themotor shaftwas connectedto
a larger pulley on the drive roller by means of a standard rubber
timing belt. With the use of two different timing-pulley combina-
tions, treadmill speeds of0.5–7.0 m/swere easilyachieved.
In addition, a flywheel mounted on the drive roller shaft
helped to maintain a nearly constant belt speed during
operation. We have found that a very large timing pulley
works adequately asa flywheel, althougha custom-machined
balanced flywheel would be preferable. For safety, the drive
pulleys and flywheel were covered with a plywood box that
did not touch any of the drive parts or the force platform. For
safety in mounting and dismounting, handrails were at-
8750-7587/98 $5.00 Copyright
r
1998 the American Physiological Society764 http://www.jap.org
tached to the surrounding laboratory floor. We monitored the
speed with a tachometer that detected the revolution rate of
the drive roller. Theoverall design is shown in Fig. 1.
It is important to recognize that the entire treadmill
(motor, drive pulleys, rollers, chassis, and so forth) was
supported by the force platform. This was an essential design
feature. If the motor were not mounted on the force platform,
we would have had to measure the forces and torques
imparted by the motor on the force platform. The chassis was
supported in a distributed manner along its entire length.
Some previous FTM designs have been ‘‘simplysupported’’(3)
at four points by force transducers; thus they were much less
stiff, particularly in the vertical direction. The total mass of
our treadmill was 90 kg. A rough breakdown of the major
components of this mass was as follows (in kg): I-beam
chassis, 20; treadmill bed, 3; motor, 17; flywheel, 19; and two
rollers, 14 each. High-frequency response is desirable in any
force-transducing system. The natural frequency of vibration
for any object can be increased by decreasing the mass. The
most obvious treadmill components that could be lightened
are the flywheel and therollers.An ideal flywheel wouldhave
its mass concentrated on the rim to maximize the inertia-to-
mass ratio. Rollers made of aluminum rather than steel would
save nearly 20 kg. Titanium components would provide further
mass reduction but at considerably greater expense. One advan-
tageofourdesignwasthatthetreadmillcouldbereadilyremoved
from the force platform, so that both pieces of equipment
could be used independently for other experiments.
RESULTS
We performeda battery of static and dynamic teststo
evaluate the fidelity ofthe FTM.
Linearity. We found it convenient to ‘‘tare’’ the force
platform in the vertical direction; that is, we balanced
the amplifier bridge circuit to give zero voltage output
when the treadmill was mounted on the force platform.
To ensure that this did not cause any distortion of the
signal, we performed a static-force calibration with the
treadmill mounted on the force platform. When we
applied known loads, the output voltage response was
linear to within 0.2% over a range of applied forces up
to 2,300 N (R
2
. 0.99).
Point of force application. To verify that the position
of force application did not affect the vertical-force
output, we applied the same static load (700 N) at
different locations. As expected from the manufactur-
er’sspecifications, the recorded voltage output from the
amplifiers varied ,0.7% from the mean, regardless of
the location of force application. To determine the
accuracy with which we could locate the point of force
application, we placed a known static load at various
known positions along the length and width of the
treadmill (6). The position of static-force application
could be resolved to within 0.5 cm for the y-axis and 0.6
cm along the x-axis.
To calculate joint moments or torques during locomo-
tion, it is necessary to locate the point of force applica-
tion dynamically.AMTI force platforms provide a direct
measure of the moment around the mediolateral axis.
However, the moment is referenced to an axis that is
midway along the length of the platform and slightly
below the top surface of the force platform. In the
manual, this distance below the top surface is referred
to as the origin; for our particular platform, the dis-
tance was 0.053 m. The treadmill elevated the point of
force application by a distance 0.107 m above the
surface of the force platform. As a result, both the
vertical-force component (F
z
) and the horizontal shear
force (F
y
) exerted by the subject contributed to the
measured M
x
. If the point of force application occurs at
distance a along the length of the force platform from
the M
x
axis, then the equationfor the moment is
M
x
5 (F
z
·a) 1 [F
y
·(0.107 1 0.053)]
By recording M
x
,F
z
, and F
y
, it was simple to calculate a
and thus locate thepoint of force application.
Using the following procedure, we verified that we
could locate dynamically the point of force application.
First, weaffixed a smalldot of reflective tape onthe end
of a sturdy wooden stick. With the treadmill belt in
motion, a person standing on the side of the FTM
pressed on the treadmill belt with the stick, applying a
varying force with both vertical and horizontal compo-
nents. The end of the stick naturally moved backward
with the treadmill belt.As the force was applied via the
stick, we recorded the force signals and simultaneously
recorded videotape at 200 fields/s, synchronized with
theforce-datacollection. Severaladditionalsmallreflec-
tive dots identified the midpoint along the length of the
platform and also provided a scale. Using the above
equation, we calculated the point of force application.
We also analyzedthe videotape with a Peak 5 digitizing
system. The video and force-platform data methods
consistently identified nearly the same point of force
application. Above a vertical-force threshold of 50 N,
the two methods had a difference of ,1 cm. The results
from a sample calibrationtrial are shown in Fig. 2.
Fig. 1. Schematic view of force-tread-
mill (FTM) design. Handrailsand gear-
box cover are omitted from this draw-
ing.
765FORCE TREADMILL
Natural frequency. Before proceeding to dynamic
locomotion trials, we determined the unloaded natural
frequencies of the FTM for F
z
,F
y
, and F
x
. Using a
woodenmallet, we gavethe treadmill asharp rap inthe
appropriate direction and collected the force signal at 1
kHzbyusing aMacintoshQuadra 650,NationalInstru-
ments analog-to-digital board, and LabView4 software.
To calculate the natural frequencies, we simply noted
the time elapsed for 10 cycles of the ensuing ‘‘ringing’’
observed in the force traces. We found that the natural
frequencies were .178 Hz for F
z
, .87 Hz for F
y
, and
.88 Hz for F
x
. The force platform without the treadmill
had higher natural frequencies, as specified by the
manufacturer (350 Hz for F
z
, and 300 Hz for F
y
and F
x
).
The addition of the treadmill mass and the compliance
ofthe treadmill clearlydecreased theresonant frequen-
cies. Given that the natural frequency of the force
platform alone in the vertical direction is 350 Hz, the
added mass of the treadmill would theoretically reduce
the overall resonant frequency to ,200 Hz. The actual
natural frequency was 178 Hz; this indicated that the
treadmill chassis was very stiff indeed. The more
substantial drop in the natural frequencies in the
horizontal directions appeared to be caused by the
mass of the motor and the compliance in the mounting
of the motor. However, the natural frequencies of the
FTM were more than adequate for accurate recording
of the ground-reaction forcesof human locomotion.
Vibration and electrical noise. When the motor of the
FTM was not turned on, we recorded little noise (,63
N for F
z
, ,61 N for F
y
and F
x
). When the motor was
turned on (with no subject on the treadmill), we re-
corded noise amplitudes of 680 N on the F
z
and 660 N
on the F
y
and F
x
signals. However, a fast Fourier
transform (FFT) spectral power analysis of these sig-
nals revealed that 99% of this noise was at frequencies
.46 Hz (see Fig. 3). The mediolateral forces applied by
walkingor runninghumans typicallyhave peakmagni-
tudes of only 5–10% of body weight (BWt; e.g., 70 N);
thus the signal-to-noise ratio for F
x
was poor. A large
fraction of the vibration noise was due to flywheel
imbalance. If measuring F
x
were of particular interest,
it may be technically feasible to do so with a precision-
balanced flywheel.
Frequency content of ground-reaction force signals.
To determine the frequency content of the ground-
reaction force signals in a situation that is free of
externalvibrations, we hada subject walk(1.5m/s) and
run (3 m/s) over a conventional ground-mounted force
platform (model LG6–4–2000, AMTI). We measured
speed with a series of photocell beams placed along the
runway. Five acceptable trials (average speed within
60.05 m/s) were saved for both walking and running.
We considered these data to be virtually noise free. We
then performed a FFT spectral power analysis of these
force records. For walking,99% of the integrated power
content of both the F
y
and F
z
signals was ,9 Hz. These
values were similar to those reported previously (1).
For running,99% of theintegrated power content ofthe
F
z
signal was at frequencies ,10 Hz and .98% of the
FFT power of the F
y
signal was at frequencies ,17 Hz.
These spectral analyses are shown in Fig. 3. These
analyses helped us choose appropriate filtering cut-off
frequencies for processing our FTM data. We used a
Fig. 2. Accuracyof the point of force-application determination. With
treadmill running, weapplied atime-varying force to the moving belt
surfaceby using a sturdywooden stick. Wedetermined the positionof
the end of the stick by digitizing a high-speed video recording and by
using the force-platform signals, as described in
METHODS. Above a
vertical force threshold of 50 N, the 2 methods gave results within
0.01 m of each other. The mean difference betweenthe 2 methods was
0.002 6 0.006 (SD) m. The two signals were highly correlated; R
2
.
0.99.
Fig. 3. Fast Fourier transform (FFT) power-spectrum analysis for
ground-reaction force data and FTM vibration noise. Verticalground-
reaction force (F
z
) data were obtained (at 1 kHz) during overground
runningat3m/s.We considered those data to be essentially noise free
and representative of the true signal. FTM noise signals were
obtained (also at 1 kHz) while operating the treadmill at 3 m/s with
no subject running. Data were then transformed into the frequency
domain by using a FFT; 99% of the signal power was ,10 Hz, while
99% of the noise power was .46 Hz.Thus low-pass digital filtering of
FTM data, with a cut-off frequency of 25 Hz, eliminated the noise
without affecting the signal.
766 FORCE TREADMILL
fourth-order low-pass Butterworth nonrecursive filter
passedin bothdirections toeffectzero-phase shiftand a
3-dB cutoff of 25 Hz. We found that this eliminated 99%
of the noise while retaining all of the important compo-
nents of the signal.
Overall system tests. Next we performed some simple
dynamic tests of the FTM to determine the overall
accuracy of the system. The same subject walked and
ran on the FTM at 1.5 and 3 m/s, respectively, while we
collected F
z
and F
y
at 1 kHz. We filtered these data as
described above. Over an integral number of strides,
the average vertical force must be equal to BWt, and if
the subject is maintaining the speed, the braking and
propulsive ground-reaction impulses (force integrated
over time) must be equal. We measured the average
verticalforce exertedover 10successive, completesteps
to be within 1% of BWt. We also compared the inte-
grated horizontal-force signals for the first and second
halves of the stance phase for the running trials.
Averaged for 10 steps, the measured braking impulse
was within 1% of the propulsive impulse. The roller
tachometer indicated that the treadmill speed was
quite constant. With a subject walking at 1.25 m/s, the
speed fluctuated by ,0.02m/s; for running at 3.0 m/s,
fluctuations were ,0.04 m/s.
FTM vs. overground measurements. We compared
the FTM signals with the established methodology of a
traditional runway-mounted force platform. We had a
single subject run at 3 m/s on the FTM and across our
force-platform runway. A comparison of the average
values (from 10 steps) for various force magnitudes
from the FTM vs. overground revealed only small
differences caused by normal variation. The average
peak vertical force (F
z
) values were 1.78 vs. 1.83 3 BWt
for the impact peak and 2.47 vs. 2.44 3 BWt for the
active peak. The average peak braking (F
y
) forces were
20.30 vs. 20.35 3 BWt, and the average propulsive
peaks were 0.21 vs. 0.20 3 BWt. A comparison of a
typical running stride for the FTM vs. overground
force-platform records is shown in Fig. 4. The signals
obtained with the FTM were quite similar to those
obtained overground. Because some stride-to-stride
variability occurs, the traces were not identical. All of
thesevalues concurred with thosein the literature(21).
DISCUSSION
From a purely mechanical perspective, steady-speed
walkingor runningonan adequatemotorized treadmill
is identical to overground walking and running; the
only difference is the frame of reference for each
situation (23). Locomotion on a treadmill with inad-
equate power or momentum (i.e., no flywheel) does
indeed differ from overground locomotion. However, on
a treadmill with an adequate motor and flywheel,
where the belt speeddoes not vary, the kinematics (21),
ground-reaction forces (19), and metabolic cost (2) of
locomotion are nearly indistinguishable from over-
ground locomotion. As detailed above, our motor and
flywheel appear to be adequate in maintaining a con-
stant tread speed.
Fig. 4. Comparison of vertical (F
z
; top) and horizontal (F
y
; bottom)
ground-reaction force signals obtained from FTM (solid line) and a
force-platform runway (dashed line) for same subject when running
at 3 m/s. FTM data were low-pass filtered at 25 Hz.
Fig. 5. Sample FTM data for subject walking at 1.25 m/s. Signals
were low-pass filtered at 25 Hz. Dashed line, body weight.
767FORCE TREADMILL
FTMs provide many advantages over conventional
runway-mounted forceplatforms. Our new FTM design
now extends these advantages to many more studies of
locomotion because we can measure the vertical and
horizontal components of ground-reaction force and
their moments. FTMs allow ground-reaction force data
to be collected far more rapidly than do traditional
runway studies (19). Furthermore, a large number of
successive steps can be averaged to determine more
representative values, thereby increasing statistical
power. To adequately study running mechanics with a
ground-mounted force platform system, a long labora-
tory or hallway space must be available. With a FTM,
high-speed running studies can be conducted in very
small laboratories. The modular design of the FTM
allows the force platform and treadmill to be used
independently of each other. That is an important
point, because each itemhas considerable expense.
In addition to time and space savings, a FTM allows
for experiments and treatments not possible with con-
ventional runway-mounted force platforms. For ex-
ample, with a FTM, it is possible to study the biome-
chanics of gait transitions (13), adjustments to
perturbations of stability (5), and locomotion in simu-
lated reduced gravity (16) or even microgravity (9).
Furthermore, a FTM allows for simultaneous collection
of biomechanical and other data (for example, rate of
oxygen consumption or electromyography) without the
use of telemetry. Dingwell et al. (11) have found that a
FTM can provide useful feedback of vertical ground-
reaction forces during rehabilitation of clinical patients
who have amputations below the knee. In our own
research, we find that the FTM is very useful as an
ergometer that allows us to measure the mechanical
work performed on the center of mass during locomo-
tion (7). This is possible because the FTM records the
summed ground-reaction force fromboth feet.
In Fig. 5, we show a typical force recording from the
FTM for the same subject walking at 1.25 m/s. When
humans walk, both feet are on the ground for at least
part of the stride cycle. For some purposes, it is
necessary to know the force under each individual foot.
Davis and Cavanagh (8) and Dingwell et al. (11) have
developed clever algorithms to separate the individual
foot vertical forces for use with a FTM. These calcula-
tions rely on the location and velocity of the center of
pressure to determine the time of single and double
support. The same algorithms can be used with the
present FTM design. Unfortunately, an equivalent
algorithm cannot separate the horizontal forces for
the individual feet in walking. This is because, during
the double-support period, it is not possible to locate
the pointof force application (center of pressure) forthe
individual feet along the y-axis of the treadmill. Note
that it is possible to locate very accurately the point of
force application, and thus joint moments, during run-
ningand the single-support phaseof walking. TheFTM
designof Belliet al.(4)uses twoparallel treadmills,one
for each foot. This allows for separate measurement of
the individual foot horizontal forces, but it requires the
subject to walk with an unnaturally wide stance. Thus
aperfectlyacceptable methodofmeasuring thehorizon-
tal forces exerted by the individual feet during the
double-support phase of walking for repeated strides
remains elusive.
In conclusion, the FTM described here can facilitate
many types of biomechanical studies of human locomo-
tion. Our device can accurately record the vertical (F
z
)
and horizontal (F
y
) ground-reaction forces as well as
the moments M
x
and M
y
. Induced vibrations prevented
satisfactory measurements of F
x
and M
z
with the
present device. This device can greatly decrease the
timeand laboratory spacerequired forstandard experi-
ments and clinical evaluations.
The authors appreciate the design and machining assistance of
Bruce Cannon.
This project was supported by the University of California, Berke-
ley, Committee on Research and National Institute of Arthritis and
Musculoskeletal and Skin Diseases Grant R29AR-44688-01.
Address for reprint requests: R. Kram, Dept. of Integrative
Biology, Univ. of California, Berkeley, 3060 VLSB, Berkeley, CA
94720-3140 (E-mail:rkram@socrates.berkeley.edu).
Received 15 December 1997; accepted in final form 21April 1998.
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769FORCE TREADMILL
