Research Article
Developing a Low-Cost Force Treadmill via Dynamic Modeling
Chih-Yuan Hong,1 Lan-Yuen Guo,2 Rong Song,3 Mark L. Nagurka,4 Jia-Li Sung,1 and
Chen-Wen Yen1,5
1Department of Mechanical and Electromechanical Engineering, National Sun Yat-sen University, Kaohsiung, Taiwan
2Department of Sports Medicine, Kaohsiung Medical University, Kaohsiung, Taiwan
3School of Engineering, Sun Yat-sen University, Guangzhou, China
4Department of Mechanical Engineering, Marquette University, Milwaukee, WI, USA
5Department of Physical Therapy, Kaohsiung Medical University, Kaohsiung, Taiwan
Correspondence should be addressed to Chen-Wen Yen; cmurobot@gmail.com
Received 2 January 2017; Accepted 2 April 2017; Published 4 June 2017
Academic Editor: Emiliano Schena
Copyright © 2017 Chih-Yuan Hong et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
By incorporating force transducers into treadmills, force platform-instrumented treadmills (commonly called force treadmills) can
collect large amounts of gait data and enable the ground reaction force (GRF) to be calculated. However, the high cost of force
treadmills has limited their adoption. This paper proposes a low-cost force treadmill system with force sensors installed
underneath a standard exercise treadmill. It identiﬁes and compensates for the force transmission dynamics from the actual
GRF applied on the treadmill track surface to the force transmitted to the force sensors underneath the treadmill body. This
study also proposes a testing procedure to assess the GRF measurement accuracy of force treadmills. Using this procedure in
estimating the GRF of “walk-on-the-spot motion,” it was found that the total harmonic distortion of the tested force treadmill
system was about 1.69%, demonstrating the eﬀectiveness of the approach.
1. Introduction
In walking and running, the inertial force acting on the
human body is equal to the sum of the ground reaction force
(GRF) exerted by the ground on the foot and the gravita-
tional force of the body weight. Many important gait param-
eters can be derived from the GRF. These include temporal
features such as the time instants of heel strike and toe oﬀ
and the time durations of stance and swing phases as well
as the step frequency. As a result, GRF can provide important
information about gait behavior.
GRF data have been used to investigate gait symmetry
[1], calculate leg stiﬀness [2], quantify impacts [3], under-
stand propulsion and braking [4], compute muscle forces,
joint forces and moments [5, 6], explain running economy
[7, 8], and top running speeds [9]. GRF data have also been
used to assess the eﬀects of health-related conditions that
can inﬂuence gait. These conditions include knee replacement
[10], hip arthroplasty [11], aging eﬀect [12], knee arthrosis
[13], Parkinson’s disease [14], peripheral arterial disease [15,
16], patellofemoral pain syndrome [17], osteoarthritis [18],
cerebral palsy [19], multiple sclerosis [20], lower extremity
muscle fatigue [21], stroke [22, 23], weighted walking [24],
and hemiplegia [25].
To measure GRF during gait, most previous studies
have relied on a force platform-embedded walkway. The
most common conﬁguration of a force platform consists
of a metal plate mounted on load cells that give an electri-
cal output proportional to the force applied to the plate.
Typically, only a few steps of gait data are collected in each
experimental trial. The necessity of proper foot placement
on the force platform also complicates the experimental
process. In addition, intentional behavior is likely to change
the GRF and alter the gait pattern. This problem is par-
ticularly pronounced in testing individuals who exhibit
gait diﬃculty. It is very diﬃcult to perform constant
Hindawi
Journal of Healthcare Engineering
Volume 2017, Article ID 9875471, 9 pages
https://doi.org/10.1155/2017/9875471
speed walking or running studies using ﬂoor-mounted
force platforms.
Since it has been found that the diﬀerences between
treadmill and overground locomotion are small [26–28]
and can be negligible after only a few minutes of treadmill-
walking practice [29], treadmills have been employed exten-
sively to study gait. To enhance the utility of treadmills, force
platform-instrumented treadmills (commonly called force
treadmills) have been used to quickly and continuously collect
large amounts of GRF data during gait. These force treadmills
oﬀer several advantages over conventional walkway-based
measurement systems. First, force treadmills reduce the time
and space requirements substantially. Second, with a tread-
mill, controlling the speed of locomotion becomes a straight-
forward task. Third, body weight support modules can be
added to the treadmills to ensure safety. Fourth, it is easier to
integrate complementary measurement devices (such as elec-
tromyographic systems and oxygen consumption-measuring
instruments) in the treadmill design in comparison to using
a walkway-based system.
Treadmill training is frequently prescribed as a treatment
option for patients with gait abnormalities. By using a force
treadmill to quantitatively analyze gait patterns and detect
gait abnormalities, medical therapists can adjust the intensity
of treadmill training on an individual basis. In addition, pre-
vious studies have shown that the feedback of auditory,
vibrotactile, and visual gait information can alter or improve
gait features such as walking speed [30, 31], gait coordination
[32], trunk sway [33], stride length [31], hip mechanics [34],
cadence [31], step length symmetry [35], knee movement
[36], gait cycle length [37], duration of gait [37], and swing
phase speed [37]. With the capability of generating many
important gait features, force treadmills represent an ideal
platform for implementing such biofeedback systems.
Based on the location of the force transducers, force
treadmills can be divided into two categories: direct measure-
ment force treadmills (DMFTs) and indirect measurement
force treadmills (IMFTs). By incorporating force platforms
internally, DMFTs can measure GRF directly without con-
sidering the structural dynamics of the treadmill body
[38–42]. Typically, DMFTs were built by installing force
platforms under the track surface of the treadmill. This con-
ceptually simple setup, however, requires complex mechan-
ical design and a tedious assembly and calibration process
in order to prevent erroneous force components generated
by the moving parts (the motor and mechanism) of the
treadmill [39, 42–44].
In contrast, by mounting the treadmill on top of force
transducers, IMFTs simplify the mechanical design of force
treadmills [45–49]. The friction forces generated by the mov-
ing components (such as belt, motor, and rollers) of the
treadmill become internal forces and are not measured by
the force sensors attached externally to the treadmill frame.
The tradeoﬀ of such a simpliﬁed design is the potential inﬁ-
delity of the GRF measurements. Unless the treadmill frame
can be made rigid, forces transmitted to the force transducers
of the IMFT are generally not the same as the actual GRF
applied to the treadmill track surface. To resolve this prob-
lem, current IMFTs are designed to possess a very high
natural frequency to prevent the GRF from exciting the
dynamics of the treadmill structure. This high structural
natural frequency speciﬁcation can only be achieved when
the treadmill body is light and rigid. As a result, one needs
to use low-density, high-stiﬀness materials in a specially
designed mechanical structure for the treadmill frame.
These requirements inevitably increase the manufacturing
cost. The other reason for the high price of current force
treadmill systems is that, due to their special design require-
ments, these treadmills are typically custom made or manu-
factured in very small quantities. In comparison, standard
exercise treadmills are mass produced and, as such, much
more aﬀordable.
Considering the utility of force treadmills and the fact
that their high cost has limited their adoption, the goal of this
study is to introduce a systematic approach to convert a stan-
dard exercise treadmill into a force treadmill via a straightfor-
ward system identiﬁcation method. A distinct feature of the
proposed approach is that it relaxes the high structural natu-
ral frequency requirement for the treadmill frame. As a
result, the construction cost of the force treadmills can be
reduced considerably. This work also proposes an experi-
mental procedure to assess the GRF measurement accuracy
of force treadmills.
2. Methods
2.1. The Dynamic Modeling Method. This subsection iden-
tiﬁes the dynamic speciﬁcations that need to be satisﬁed by
conventional IMFTs. Furthermore, it introduces the basic
idea of the proposed approach by addressing the problems
caused by such speciﬁcations. Denoting the force applied to
the IMFT track surface as x t and the force transmitted to
the force transducers placed under the IMFT body as y t ,
this study assumes that the GRF transmission dynamics of
transmitting the force from x t to y t can be modeled as
a linear time-invariant single-input single-output (SISO)
system. In particular, with x t as the input and y t as the
output, the GRF transmission dynamics of the IMFT are
represented by the following frequency-domain transfer
function H f :
H f = Y f
X f ,
1
where f denotes the frequency (Hz) and X f
and Y f
rep-
resent the Fourier transforms of x t and y t , respectively.
Since an IMFT can only measure y t , to ensure that the
actual GRF signal x t can be approximated closely by y t ,
conventional IMFTs were designed to behave like a distor-
tionless transmission system in the low-frequency range.
An SISO system is a distortionless transmission system if it
satisﬁes the following condition:
y t = kx t − td ,
2
where t is the time variable, k is an arbitrary constant, and td
is the time delay of this distortionless transmission system.
Therefore, the transmission is considered to be distortionless
if the input and the output have identical wave shapes with a
2
Journal of Healthcare Engineering
proportionality constant k. A delayed output that retains the
input waveform is also considered distortionless. These spec-
iﬁcations of distortionless transmission can be converted into
the frequency domain by taking the Fourier transform of (2)
which yields
Y f = kX f e−j2πf td
3
Therefore, the corresponding amplitude response is
H f
= k,
4
and the phase response is
∠H f = −td2πf
5
Hence, a distortionless transmission system must have a
constant amplitude response and a phase response that
declines linearly with frequency f . By modeling the GRF
transmission dynamics of an IMFT as a linear time-
invariant second-order system with natural frequency f n
and a damping ratio ξ, its amplitude and phase responses
can be expressed, respectively, as [50]
H u
=
1
1 − u2 2 + 4ξ2u2
6
and
∠H u = −tan−1
2ξu
1 − u2 ,
7
where the dimensionless frequency variable u = f /f n. If f is
much smaller than f n, the amplitude and phase responses
of this standard second-order system can be approximated
by
H u
≈ 1
8
and
∠H u ≈ − 2ξu
9
Therefore, a linear time-invariant second-order system
behaves like a distortionless transmission system when
f << f n. This is the reason why the structural natural fre-
quency of a conventional IMFT needs to be considerably
higher than the bandwidth of the GRF signal.
Experimental studies have found that, on average, 99% of
the vertical direction GRF signal power was contained under
12.75 Hz when walking at a comfortable speed [12]. Never-
theless, human GRF contain frequency components as high
as 60 Hz for walking [51] and 100 Hz for running [52]. To
quantitatively demonstrate the importance of high structural
natural frequency of the treadmill structure, we assume that
the natural frequency f n to be 45 Hz (Kram et al. [45] indi-
cated that the vertical direction structural natural frequencies
of the six force treadmills that they reviewed are all lower
than 45 Hz). With f =12.75 Hz, the corresponding dimen-
sionless frequency u is 12.75/45 ≈0.283. By using (6) with
u= 0.283 and ξ= 0, it can be shown that H u
≈ 1 087 which
represents an 8.7% deviation from the desired speciﬁcation of
H u
= 1. To reduce such a deviation, two more recently
developed IMFTs increase their structural natural frequen-
cies to 160 Hz [45] and 219 Hz [46], respectively. At
f =12.75 Hz, the corresponding H u
improves to 1.006
and 1.003, respectively.
When modeled as a linear time-invariant second order
system, it is well known that the structural natural frequency
f n of the treadmill can be determined from
f n = 1
2π
k
m ,
10
where k (N/m) is the stiﬀness and m (kg) is the mass of the
treadmill. Clearly, f n can be increased by reducing the weight
of the treadmill. This is the reason why previous force tread-
mills often removed parts such as side handrails, front rails,
and the control panel to make the treadmill lighter. However,
these changes also degraded the functionality and safety of
the treadmill system. The natural frequency f n can also be
increased by using higher strength materials to increase the
stiﬀness. The lightweight and high strength material require-
ments inevitably increase the cost of the treadmill.
To relax the high natural frequency requirement for the
IMFT structure, this study tries to compensate for the eﬀect
of the GRF transmission dynamics of the treadmill by identi-
fying its transfer function model. In particular, by applying
an excitation force x t
to the treadmill track surface and
measuring the resulting x t
and y t , we can identify the
transfer function from x t
to y t
from (1). Using the
inverse dynamic model of the identiﬁed transfer function,
we can then estimate the actual GRF from
xc t = F−1
̂H
−1 f Y f
,
11
where ̂H f
represents the identiﬁed transfer function of the
treadmill GRF transmission dynamics. In the remaining
parts of the manuscript, x t , y t , and xc t will be referred
to as the actual, the uncompensated, and the compensated
GRF signals, respectively. The experimental procedure for
implementing the proposed approach will be described in
the following subsection.
2.2. The Experimental Procedure. Figure 1 illustrates the con-
ﬁguration of the experimental system which consists of two
subsystems, namely, a force treadmill and a force platform.
The treadmill (7355, Fit Plus, Taiwan) has bed dimensions
of 1.5 m length and 70 cm width. The speed control system
provides a range from 0 to 22 km/hr with a minimum incre-
ment of 0.1 km/hr. The weight of the treadmill is 150 kg. To
convert this standard exercise treadmill into a force treadmill,
this study installed four load cells (Sensolink SLP-1 with
maximum capacity of 100 kg) into the legs that support the
treadmill body. The four circles shown in Figure 2 specify
the location of the force transducers.
As shown in Figure 1, to measure the actual GRF signal
x t , a force platform is placed at the center of the treadmill
track surface. Similar to a commercially available force plat-
form, the force platform built here is a rectangular plate with
force transducers located at its four corners. The force
3
Journal of Healthcare Engineering
treadmill and the force platform employed in this study use
the same load cell unit. The size of the platform is 40 cm by
40 cm. We have carefully compared the measurements
obtained by this force platform and a commercial force
platform (Kistler 9286AA) to verify comparable repeatability
and accuracy.
After ampliﬁcation, analog voltage signals obtained by
the four load cells of the force treadmill are converted to dig-
ital signals via a four channels, 24 bit DAQ (data acquisition)
card (NI 9234). The voltages generated by the load cells of the
force platform are also processed by an independent but
identical set of voltage ampliﬁers and a DAQ card. The
digitized force signals were sent to a PC using a USB chassis
(NI cDAQ-9174) and low pass ﬁltered by a distortionless
phase 20th-order Butterworth ﬁlter with a cutoﬀ frequency
of 150 Hz. The sampling frequency was set to 1024 Hz.
The experimental system used the graphical programming
environment NI LabVIEW (National Instrument, Austin,
TX, USA) for performing system control, signal processing,
and graphical user interface (GUI) functions.
The experimental work consists of two phases. The ﬁrst
phase identiﬁes the GRF transmission dynamics of the tread-
mill by ﬁnding its transfer function model. A dead blow ham-
mer with a nonmarring head was used to strike the center of
the force platform. By measuring the resulting x t and y t
with the force platform and force treadmill, respectively,
the transfer function of the GRF transmission dynamics
was determined from (1). The second phase of the exper-
imental work was to assess the accuracy of the estimated
GRF signals. The test input signals were produced by
asking ten male subjects (age 24.20 ±3.29 years, weight
73.09 ±15.42 N) to walk “on the spot” for 20 seconds when
standing on the force platform which was placed on the
center of the treadmill track surface. The ﬁdelity of the
estimated GRF was evaluated quantitatively by its total
harmonic distortion (THD), deﬁned as
THD = ∫
T
0 x t − x t
2
dt
∫
T
0 x2 t dt
,
12
where ̂x t and x t represent the estimated and actual GRF
signals, respectively. In this study, the duration for each of
the walk-on-the-spot tests was T = 20s. Note that, by deﬁning
the distorted signal as the diﬀerence between ̂x t and x(t),
the THD represents the ratio of the energy of the GRF esti-
mation error signal to the energy of the actual GRF signal.
3. Results and Discussions
Figure 3 plots the amplitude spectrum of the identiﬁed trans-
fer function of the treadmill GRF transmission dynamics
obtained in the ﬁrst phase of the experimental study. As
shown in Figure 3, the amplitude response of the identiﬁed
transfer function is very diﬀerent from that of a distortionless
transmission system. Speciﬁcally, its amplitude response is
relatively ﬂat only in the low-frequency range of 0 to 5 Hz
and becomes highly oscillatory in the higher frequency
region. This clearly reveals the importance of compensating
for the eﬀect of GRF transmission dynamics to improve
GRF measurement accuracy for an IMFT.
To demonstrate the eﬃcacy of the proposed approach,
based on the data obtained in the second phase of the
Treadmill system
Amplifcation circuits
Data acquisition
Force platform
Voltage amplifer
Voltage amplifer
Treadmill load cells
DAQ
USB
chassis
DAQ
PC
Figure 1: Conﬁguration of the experimental system.
Rear
750 mm
Right
Lef
1500 mm
2100 mm
880 mm
Front
1650 mm
Track surface
Motor & transmission system
Figure 2: Top view of the treadmill surface.
4
Journal of Healthcare Engineering
experimental study, the THDs were computed by using the
uncompensated and the compensated GRF signals as the
estimated GRF signal. The resulting THDs for the 20 partic-
ipants of the walk-on-the-spot experiment are plotted in
Figure 4. As shown in Figure 4, the THDs obtained by the
compensated GRF are considerably smaller than the THDs
of the uncompensated GRF. In particular, for the uncompen-
sated GRF, the mean and standard deviation of the THDs are
9.64% and 6.3%, respectively. In comparison, by using the
compensated GRF as the estimated GRF, the proposed
approach reduces the mean of the THDs to 1.69% and the
standard deviation of the THDs to 1.38%. Such improve-
ments can also be observed from Figure 5 that plots the time
responses of the actual, the compensated, and the uncom-
pensated GRF signals for a typical 2 s period of the walk-
on-the-spot experiment. As shown by Figure 5, the time
responses of the actual and compensated GRF signals are
relatively close. In contrast, the uncompensated GRF signal
tends to oscillate around the actual GRF signal and often
overshoots the actual GRF signal, particularly at the sharp
corners of the actual GRF time response proﬁle.
To compare the eﬃcacy of the proposed approach to the
conventional IMFT design, the IMFT was modeled as a
second-order linear system whose frequency spectra can be
represented by (6) and (7). With the actual GRF signal of
the walk-on-the-spot experiment as the input and the corre-
sponding output of the second order linear system of (6) and
(7) as the estimated GRF, the THDs can be determined for
the IMFT mathematical model. The resulting mean THDs
of the twenty participants are plotted in Figure 6 as a function
of f n for ξ =0.01, 0.05, and 0.1. As expected, THD decreases
with the increasing f n. Since Kram et al. [45] indicated that
the vertical direction natural frequencies of the six force
treadmills that they reviewed are all lower than 45 Hz, we ﬁrst
inspect the THDs for ωn= 45 Hz. Based on the results of
Figure 6, when ωn = 45Hz, the THDs are 7.07%, 3.59%, and
2.07% for ξ =0.05, 0.1, and 0.2, respectively. Note that the
solid line of Figure 6 corresponds to the mean THD obtained
by the proposed approach which is 1.69%. In order to reduce
THD to be smaller than 1.69%, the natural frequency has to
increase to 88Hz, 65 Hz, and 60 Hz for ξ =0.01, 0.05, and
0.1, respectively.
As shown in Figure 6, THDs vary from person to per-
son. Although accurate prediction of individually dependent
THDs does not seem possible, it is still valuable to under-
stand factors that can inﬂuence the accuracy of the esti-
mated GRF. Considering the potential inﬂuences of noise
on the system identiﬁcation process in the high-frequency
range, it is hypothesized that the THD is positively corre-
lated with the bandwidth of the GRF signals. Due to
unavailability of the actual GRF signal during the normal
treadmill operations, this study investigates the association
between the bandwidth of the compensated GRF signal
and its THD. In particular, by specifying the 98% bandwidth
as the portion of the signal spectrum in the frequency
domain
which
contains
98%
of
the
signal
energy,
Figure 7 depicts the scatter diagram of THD versus 98%
bandwidth of the compensated GRF signal. With a p value
of 1.41 ×10−7, the value of the corresponding correlation
coeﬃcient is 0.891. Such a strong correlation demonstrates
that the inaccuracy of the compensated GRF signal increases
with its bandwidth. To the best of our knowledge, such an
association between GRF frequency content and the GRF
measurement accuracy has never been studied systematically.
Such knowledge can help us estimate the degree of inaccu-
racy of the GRF measurements in dealing with GRF signals
with diﬀerent frequency contents.
The experimental results presented in this work demon-
strate the feasibility of the proposed approach. However,
the success of the approach relies on the linear system
assumption of (1). For a poorly constructed treadmill, this
assumption of linearity may not be valid. It is also possible
that the GRF transmission dynamics of the treadmill are
too complex to be compensated accurately. Therefore, choos-
ing a treadmill with a relatively solid structure should be an
important consideration in implementing the proposed
approach.
Since increasing the structural natural frequency of an
IMFT tends to increase its cost and an IMFT with poor rigid-
ity may be too diﬃcult to be compensated accurately, a pos-
sible compromise between cost and performance of an IMFT
is to build a relatively rigid but inexpensive IMFT with a less
than ideal structural natural frequency and then improve its
GRF measurement accuracy with the proposed approach. A
possible future work is to systematically study the tradeoﬀs
between the cost and accuracy for such a hybrid hardware-
software force treadmill design. For the existing IMFTs, the
proposed approach can be used to examine the frequency
responses of their GRF transmission dynamics. This can help
us better understand the dynamic behaviors of the existing
IMFTs since their frequency responses have rarely been
investigated systematically. The proposed approach can also
be applied to quantify the accuracy of the existing IMFTs
by computing the distortions of their GRF signals. If neces-
sary, the proposed approach can also be used to improve
their GRF measurement accuracy by compensating the eﬀect
of the GRF transmission dynamics.
0
50
100
150
‒60
‒50
‒40
‒30
‒20
‒10
0
10
20
30
Frequency (Hz)
Amplitude (dB)
Figure 3: The amplitude spectrum of the identiﬁed transfer
function.
5
Journal of Healthcare Engineering
4. Conclusion
The goal of this work is to reduce the cost and extend the
applicability
of
force
platform-instrumented
treadmills
(force treadmills). By identifying the inﬂuences of treadmill
structural dynamics on ground reaction force (GRF) mea-
surements and by installing force transducers underneath
the treadmill body, a standard exercise treadmill can be con-
verted to a force treadmill. A previous work showed that
treadmill structures need to be highly rigid in order to ensure
that the resultant force measured by these force sensors
closely approximates the actual GRF applied to the track sur-
face. The high cost for building such treadmills has limited
their adoption.
To relax the requirement of high structural rigidity, the
proposed approach adopts a system identiﬁcation approach
to model the GRF transmission dynamics from the treadmill
track surface to the force sensors underneath the treadmill.
Actual GRF
Uncompensated GRF
Compensated GRF
700
710
720
730
740
750
760
770
780
790
800
GRF signals (N)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Time (s)
Figure 5: GRF signal time responses of a typical 2-second period for the walk-on-the-spot experiment.
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
0
5
10
15
20
25
30
Participants
Harmonic distortion (%)
Compensated GRF
Uncompensated GRF
Figure 4: Total harmonic distortions of the estimated GRF signals for the walk-on-the-spot experiment.
6
Journal of Healthcare Engineering
By using the inverse dynamic model of the identiﬁed transfer
function, the approach can be used to estimate the actual
GRF by compensating for the eﬀect of the GRF transmission
dynamics of the treadmill.
In addition to developing a compensation method to
enhance the GRF measurement accuracy, this work intro-
duces an experimental procedure to assess the accuracy of
the estimated GRF signals. As shown by the test results
obtained from the walk-on-the-spot experiment, the mean
total harmonic distortion of the estimated GRF signals is only
1.69%. This study also found that the inaccuracy of the esti-
mated GRF signal increases with its bandwidth. In addition
to converting standard exercise treadmills to force treadmills,
the proposed approach can be used to assess and improve the
GRF measurement accuracy of existing force treadmills.
Conflicts of Interest
The authors declare that they have no competing interest.
Acknowledgments
This research was partly supported by the Ministry of
Science and Technology in Taiwan, under Grant MOST
104-2221-E-110-010.
0
1
2
3
4
5
6
7
5
10
15
20
25
30
35
Harmonic distortion (%)
Bandwidth (Hz)
Figure 7: The scatter diagram of the total harmonic distortion and the 98% bandwidth of the compensated GRF.
fn (Hz)
30
40
50
60
80
90
100
0.1
1
1.69
10
100
Harmonic distortion (%)
 
Proposed approach
70
훇: 0.1
훇: 0.05
훇: 0.01
Figure 6: The total harmonic distortion of a second-order IMFT model for the walk-on-the-spot experiment.
7
Journal of Healthcare Engineering
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9
Journal of Healthcare Engineering

Developing a Low-Cost Force Treadmill via Dynamic Modeling.
Hong, Chih-Yuan,Guo, Lan-Yuen,Song, Rong,Nagurka, Mark L,Sung, Jia-Li,Yen, Chen-Wen