A wearable force plate system for the continuous measurement of triaxial ground reaction

force in biomechanical applications

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Meas. Sci. Technol. 21 (2010) 085804 (9pp) doi:10.1088/0957-0233/21/8/085804

A wearable force plate system for thecontinuous measurement of triaxialground reaction force in biomechanicalapplicationsTao Liu, Yoshio Inoue and Kyoko Shibata

Department of Intelligent Mechanical Systems Engineering, Kochi University of Technology,185 Miyanokuchi, Tosayamada-Cho, Kami-City, Kochi 782-8502, Japan

E-mail: liu.tao@kochi-tech.ac.jp

Received 18 September 2009, in final form 30 March 2010Published 6 July 2010Online at stacks.iop.org/MST/21/085804

AbstractThe ambulatory measurement of ground reaction force (GRF) and human motion underfree-living conditions is convenient, inexpensive and never restricted to gait analysis in alaboratory environment and is therefore much desired by researchers and clinical doctors inbiomedical applications. A wearable force plate system was developed by integrating smalltriaxial force sensors and three-dimensional (3D) inertial sensors for estimating dynamictriaxial GRF in biomechanical applications. The system, in comparison to existent systems, ischaracterized by being lightweight, thin and easy-to-wear. A six-axial force sensor (Nitta Co.,Japan) was used as a verification measurement device to validate the static accuracy of thedeveloped force plate. To evaluate the precision during dynamic gait measurements, wecompared the measurements of the triaxial GRF and the center of pressure (CoP) by using thedeveloped system with the reference measurements made using a stationary force plate and anoptical motion analysis system. The root mean square (RMS) differences of the two transversecomponents (x- and y-axes) and the vertical component (z-axis) of the GRF were 4.3 ± 0.9 N,6.0 ± 1.3 N and 12.1 ± 1.1 N, respectively, corresponding to 5.1 ± 1.1% and 6.5 ± 1% of themaximum of each transverse component and 1.3 ± 0.2% of the maximum vertical componentof GRF. The RMS distance between the two systems’ CoP traces was 3.2 ± 0.8 mm,corresponding to 1.2 ± 0.3% of the length of the shoe. Moreover, based on the results of theassessment of the influence of the system on natural gait, we found that gait was almost neveraffected. Therefore, the wearable system as an alternative device can be a potential solutionfor measuring CoP and triaxial GRF in non-laboratory environments.

Keywords: wearable force plate, ground reaction force, triaxial force sensor, 3D inertialsensor

(Some figures in this article are in colour only in the electronic version)

1. Introduction

In a traditional gait analysis laboratory, the stationary forceplate cannot measure more than one stride; moreover, in themeasurements of stair ascent and descent, complex multiplesystems composed of many force plates, a motion capturesystem based on high-speed cameras and a data fusion method

have been constructed [1, 2]. Therefore, these stationarymeasurement systems probably impose some constraints onour ability to measure ground reaction force (GRF) andbody orientations, and are not feasible for measurementsin everyday situations. An easy-to-use and inexpensivemeasurement system which can accurately estimate the triaxialGRF and three-dimensional (3D) body orientations and has

0957-0233/10/085804+09$30.00 1 © 2010 IOP Publishing Ltd Printed in the UK & the USA

Meas. Sci. Technol. 21 (2010) 085804 T Liu et al

less influence on natural gait is much desired for biomechanicalapplications as an alternative to conventional techniques.

In past studies of GRF sensors, many researchers havedeveloped wearable sensors attached to insoles. Pressuresensors have been widely used to measure the distributedvertical component of GRF and to analyze the loading patternon the plantar soft tissue during the stance phase of gait [3, 4],but the transverse component of GRF (friction force) could notbe estimated using these sensor systems. Fong et al proposed amethod to estimate the triaxial GRF from pressure insoles, butthe acceptable high accuracy of the sensor system is limitedto measurements on the same group of subjects with the sametype of shoes [5]. By mounting multi-axial force sensorsbeneath a special shoe, some researchers have developedinstrumented shoes for ambulatory measurements of triaxialGRF in a variety of non-laboratory environments; for example,Chateau et al applied an instrumented shoe fixed under thehorse’s hoof to GRF measurement on any track [6]. However,these sensor systems in which the adopted commercial sensorexcluding the mounting frames has a height of 15.7 mm [7]increase the height and weight of the shoe and probably affectnatural gait. Significant differences between instrumentedand normal shoes were found in the maximum GRF, and themaximum GRF averaged over all subjects differed by 56 N ina sensor system test study [8]. Moreover, these measurementsystems were limited to the specific shoes, so they could notbe easily reconstructed for a variety of subjects with differentfoot lengths. Therefore, the first problem to be resolved inour research is to make a light and thin force plate whichcan implement ambulatory triaxial GRF measurements on avariety of subjects and has less influence on their normalgaits.

Recently some inexpensive in-chip inertial sensorsincluding gyroscopes and accelerometers have gradually foundpractical applications in human motion analysis. To expand thescope of application of our wearable force plate, an ambulatory3D inertial sensor system can be integrated with the forceplate. Schepers et al proposed a combination sensor systemincluding six degrees of freedom force sensors and miniatureinertial sensors (Xsens Motion Technologies) to estimate jointmoments and powers of the ankle [9]. If 3D orientations ofthe foot can be obtained when we measure triaxial GRF duringgait, the inverse dynamic method can be used to accuratelyanalyze joint dynamics of the lower limb [10]. Therefore, inour research, the wearable force plate was integrated with 3Dinertial sensor modules to construct an ambulatory systemfor the continuous measurement of triaxial GRF, and the3D inertial sensor modules were designed using lower costinertial sensor chips including a triaxial accelerometer and agyroscope.

2. Wearable force plate system

2.1. Design of a wearable force plate

As shown in figure 1(a), a wearable force plate (weight:86 g; size: 80 × 80 × 15 mm3) was constructed usingthree small triaxial force sensors provided by Tec Gihan Co.,

(a)

15mm

Small triaxal force sensors Strengthening fiberboards

(b)

Protective rubber coat

Figure 1. (a) Prototype of a wearable force plate. (b) Coordinatesystems of the force plate.

Table 1. Main specifications of the small triaxial force sensor usedfor the wearable force plate system.

Type USL06-H5-500N-C

Rated capacity (N) X- and Y-axes 250Z-axis 500

Rated capacity (με) X- and Y-axes 900Z-axis 1700

Nonlinearity (after calibration ofcross effect)

Within 1.0%

Hysteresis (after calibration of crosseffect)

Within 1.0%

Size (mm) 20 × 20 × 5Weight (g) 15

Japan, in which two strengthening fiberboards were used astop and bottom plates to accurately fix the three sensors.The specifications of the applied small sensors are given intable 1. Each small sensor calibrated using the data providedby the manufacturer can measure triaxial forces relative tothe slave coordinate system

(∑si

)defined at the center of

the sensor, and the subscript i represents the number of thesmall sensor in every force plate (i = 1, 2 and 3). The GRFand center of pressure (CoP) measured using the developedforce plate could be expressed in a force plate coordinatesystem

(∑f

)which is located on the interface between

the force plate and the ground, and the origin of the forceplate coordinate system was the center of the force plate (seefigure 1(b)). The y-axis of the force plate coordinate systemwas chosen to represent the anterior–posterior direction ofhuman movement on the bottom plate, and the z-axis was madevertical, while the x-axis was chosen such that the resultingforce plate coordinate system would be right handed. We

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Meas. Sci. Technol. 21 (2010) 085804 T Liu et al

(a) 3D inertial sensor module

Wearable force plate system Accelerometer (Bottom)

Gyroscopes

(b)

Figure 2. (a) 3D inertial sensor module mounted on the force plate. (b) A wearable force plate system mounted beneath a shoe.

aligned the y-axis of each sensor’s slave coordinate to theorigin of the force plate coordinate system, while the threeorigins of the slave coordinates were evenly distributed on thesame circle (radius: r = 30 mm) and fixed at angles of 120◦

from each other. Fxi , Fyi and Fzi were defined as triaxialforces measured using the three triaxial sensors. Triaxial GRFand coordinates of CoP could be calculated by the followingequations:

Fx = (Fx1 + Fx3) · cos(60◦)−Fx2 − (Fy3 − Fy1) · cos(30◦) (1)

Fy = (Fy1 + Fy3) · cos(60◦)−Fy2 − (Fx1 − Fx3) · cos(30◦) (2)

Fz = Fz1 + Fz2 + Fz3 (3)

Mx = Fz2 · r − (Fz1 + Fz3) · sin(30◦) · r (4)

My = (Fz1 − Fz3) · cos(30◦) · r (5)

Mz = (Fx1 + Fx2 + Fx3) · r (6)

xCOP = My/Fz (7)

yCOP = Mx/Fz (8)

zCOP = 0, (9)

where Fx, Fy and Fz were defined as triaxial GRF (FGRF)measured using the force plate in the force plate coordinatesystem, and Mx, My and Mz indicate triaxial momentsestimated from the measurements of the three sensors, whilexCOP, yCOP and zCOP are coordinates of the CoP in the forceplate coordinate system.

2.2. Design of a 3D inertial sensor module

As shown in figure 2(a), we constructed a 3D motion sensormodule composed of a triaxial accelerometer (MMA7260Q,

supplied by Sunhayato Co.) and three uniaxial gyroscopes(ENC-03R, supplied by Murata Co.) which have been appliedto the ambulatory measurement of human body segments’orientations in our related research [11, 12]. The modulewas mounted on a developed force plate to measure triaxialaccelerations and angular velocities which could be used toestimate the 3D orientation transformation matrix. When theforce plate system is fixed under a shoe (see figure 2(b)), wecan implement an ambulatory GRF and CoP measurementduring gait.

2.3. Transformation of triaxial GRF measured by wearableforce plates

Considering the bending of a shoe sole during human walking,we adopted a mechanism similar to the structure proposed byVeltink et al [6], who mounted two small force plates beneatheach shoe to measure triaxial GRF. The maximum angles to theXY plane at the initial contact and terminal stance (toe-off) ofhuman walking are about 10◦ and 40◦, respectively. Therefore,it is important to transform the two force plate measurementson their local coordinate systems to the global coordinatefixed to the stationary force plate during the initial contactand terminal stance. In this paper, two force plate coordinatesystems fixed to the two force plates under the heel and theforefoot were defined as

∑f heel and

∑f toe, respectively. The

relative position of the two force plates was aligned using asimple alignment mechanism composed of three linear guidesand a ruler to let the origins of

∑f toe be on the y-axis of∑

f heel and to let the y-axes of the two force plate coordinatesystems be collinear before we mounted them onto a shoe. Thealignment mechanism and an alignment process are shown infigure 3. First, we can align two force plates’ centers andregulate the distance between two force plates according todifferent foot lengths. Second, the barefoot subject is asked

3

Meas. Sci. Technol. 21 (2010) 085804 T Liu et al

(1)

Alignment mechanism

Guides

Ruler

)3( )2(

(a)

(b)

Figure 3. (a) A simple alignment mechanism. (b) Alignment process for mounting the force plate system under a shoe.

(a)

(b)

R0

i

The ground

Zf_heel

Yf_heel

Xf_heel

Zf_toe

Yf_toe

Xf_toe

Zg

Yg

Xg

d=155mm

Small triaxial force sensors

Force plate under the forefoot

g

i

f_heel

i

f_toe

i+1

f_heel

i+1

f_toe

Ri

i+1

Force plate under the heel

Σ

Σ

ΣΣ

Σ

Figure 4. (a) Coordinate systems of the wearable force plate system. (b) Coordinate transformation during the movements of the forceplates.

to stand on the force plates which are fixed on the alignmentmechanism and then we band two force plates to the foot.Lastly, we release the two force plates from the alignmentmechanism and let the two force plates be worn on the footduring gait. For calculation purposes, such as estimatingjoint moments and reaction forces of the ankle during loadingresponse and terminal stance phases [13], all vectors includingthe joint displacement vector, GRF vector and gravity vectorhave to be expressed in the same coordinate system, which

is the global coordinate system(∑

g

). Moreover, the origin

and orientation of this global coordinate system are renewedfor each foot placement to coincide with the heel force platecoordinate system

(∑f heel

)when the heel is flat on the ground

(see figure 4).

The integration of the measured angular velocity vector(ω = [ωx, ωy, ωz]) in each force plate coordinate system wasdefined as C = [Cx,Cy,Cz], which could be used to calculatethe 3D orientation transformation matrix (R) between the

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Meas. Sci. Technol. 21 (2010) 085804 T Liu et al

X-Y stage

Weight loading

Linear guide and slider with low friction

(a)

Z

XZX

Reference six-axial force sensor

Developed force plate

(b)

X

Y

60mm

60mm

30mm

30mm

(c)

Figure 5. A reconfigurable platform for the test experiments. (a) Test platform for evaluating the normal force (z-axial force) and CoPmeasurements. (b) Test platform for the transverse force measurement (x- and y-axial forces). (c) 25 specific points of known coordinatesfor evaluation of the measurement of CoP with the developed force plate.

global coordinate system and a force plate coordinate systemby solving the following equations proposed by Bortz [14]:

Ci+1i = [ωx(i) + ωx(i + 1), ωy(i) + ωy(i + 1),

ωz(i) + ωz(i + 1)] · (�t/2) (10)∣∣Ci+1i

∣∣ =√(

Cxi+1i

)2+

(Cyi+1

i

)2+

(Czi+1

i

)2(11)

Ri+1i = Ci+1

i · Ci+1i

T

∣∣Ci+1i

∣∣2

(1 − cos

(∣∣Ci+1i

∣∣))

+

⎡⎣cos

(∣∣Ci+1i

∣∣) 0 00 cos

(∣∣Ci+1i

∣∣) 00 0 cos

(∣∣Ci+1i

∣∣)⎤⎦

+sin

(∣∣Ci+1i

∣∣)∣∣Ci+1i

∣∣⎡⎣ 0 −Czi+1

i Cyi+1i

Czi+1i 0 −Cxi+1

i

−Cyi+1i Cxi+1

i 0

⎤⎦ (12)

R = R0 · R10 · R2

1 · · · Ri+1i · · · (13)

where [ωx(i), ωy(i), ωz(i)] is a sample vector of the triaxialangular velocities of the force plate during a sampling interval�t, while Ci

i+1 is an angular displacement vector in a samplinginterval and R0 is an initial transformation matrix initialized asa unit matrix (|R0| = 1). We use the total acceleration of theforce plate measured using the triaxial accelerometer to detectthat the plate is on the ground, because there is almost nomovement acceleration in addition to gravity acceleration. Ifthe force plate is flat on a level ground or remains stationary offthe ground, we can update R by R = R0, and a threshold of themeasured acceleration was set to 1.01 (gravity acceleration),

because resolution of the accelerometer in our data samplingsystem is limited to 0.01 (gravity acceleration):

R0 =⎡⎣1 0 0

0 cos(Cx0) − sin(Cx0)

0 sin(Cx0) cos(Cx0)

⎤⎦

·⎡⎣ cos(Cy0) 0 sin(Cy0)

0 1 0− sin(Cy0) 0 cos(Cy0)

⎤⎦

·⎡⎣cos(Cz0) − sin(Cz0) 0

sin(Cz0) cos(Cz0) 00 0 1

⎤⎦ (14)

Cx0 = arctan(ay0

/(ax2

0 + az20

))(15)

Cy0 = arctan(ax0/az0) (16)

Cz0 = 0, (17)

where [ax0, ay0, az0] is a sample vector of the triaxialacceleration of the force plate flat on the ground orremains stationary off the ground, and C0 = [Cx0, Cy0, Cz0]is a angular displacement vector calculated using theaccelerometer tilt information.

The triaxial GRF measured by the two force plates couldbe transformed to the global coordinates and then combinedto calculate the total GRF

(F

g

FRG

)and the global coordinate

vectors of CoP ([x, y, z]g heelCOP and [x, y, z]g toe

COP ) using thefollowing equations:

Fg

FRG = Rf −heelg · F heel

FRG + Rf −toeg · F toe

FRG (18)

5

Meas. Sci. Technol. 21 (2010) 085804 T Liu et al

[x, y, z]g heelCOP = Rf heel

g · [x, y, z]heelCOP (19)

[x, y, z]g toeCOP = Rf toe

g · [x, y, z]toeCOP, (20)

where F heelFRG and F toe

FRG are triaxial GRF measured by thetwo force plates under the heel and the forefoot with theircoordinate systems, respectively; [x, y, z]heel

COP and [x, y, z]toeCOP

are coordinate vectors of CoP measured using two force platesand R

f heelg and R

f toeg are the orientation transformation

matrices of the two force plate system for transforming thetriaxial GRF measured by the two force plates in their attachedcoordinate systems into the measurement results relative to theglobal coordinate system.

3. Experiment methods

3.1. Static validation of the wearable force plate

To validate the developed force plate, a reconfigurable platformfor test experiments mainly composed of a six-axial forcesensor IFS-67M25A50-L40 (Nitta Co., Japan) and a two-dimensional X–Y stage were constructed to impose threedirectional reference forces on the force plate using theweight loading on the linear guide and slider mechanism (seefigure 5). In the static test experiment, a low-pass filter(cut-off frequency: 10 Hz) was applied for the outputs ofthe six-axial force sensor and the force plate in measuringinput forces. First, as shown in figure 5(a), we tested theaccuracy of the measurements of the normal force and CoPusing the platform. The accuracy of the CoP calculation wasevaluated by applying weight loads (100 N) on 25 specificpoints of known coordinates using the X–Y stage (see figure5(c)). For the second step, the force measurements of thetwo transverse directions referred to as the x- and y-axes weretested. As shown in figure 5(b), we applied the two directionaltransverse forces (x- and y-axes) to the sensor, respectively,and the imposed forces were measured using the small triaxialforce sensor.

3.2. Dynamic measurement accuracy

A combination system composed of a force plate EFP-S-2KNSA12 (KYOWA, Japan) and an optical motion analysissystem Hi-DCam (NAC Image Tech., Japan) was used asa reference measurement system to verify the measurementresults of the developed system (see figure 6(a)). As shownin figure 6(b), a young volunteer (age = 29 years, height =170 cm, weight = 66 kg) was required to wear the forceplate system to walk on the stationary force plate in thecapture region of Hi-DCam, and the signals from the twomeasurement systems were simultaneously sampled at a rate of100 samples s−1. The Hi-DCam can output a trig signal whencameras began to capture human motions, and the developedsystem and the reference system could be synchronized usingthe signal.

As well as verifying the accuracy of the wearableforce plate system, we also used the parameters includingstride length (SL), stride width (SW), maximum lateral footexcursion (ME), single stance time (SST), double stance

Wearable force plates

+-

-

+

+

-

Z

YX

Stationary force plate(EFP-S-2KNSA12)

(a)

(b)

Stationary force plate(EFP-S-2KNSA12)

Optical motion analysis system Hi-DCam

Figure 6. Reference measurement system (a); GRF measurementverification experiment (b).

time (DST), stride time (ST), maximum GRF (MaxF), andminimum GRF (MinF) proposed by Liedtke et al [8] toassess the influence of the wearable system on natural gait.When the subject walked across the stationary force plate withnormal shoes and walked with the wearable force plate system,respectively, we repeatedly measured foot motion and triaxialGRF using the reference measurement system ten times. Eachparameter was determined for a stride and averaged over therepeated ten walking trials by a normal shoe, and then wascompared with the results obtained by the wearable system inplace under the same conditions.

4. Results

4.1. Static measurement tests

Three directional reference loads (x-axis: 0 N, 10.1 N,20.5 N, 29.7 N, 40.1 N, 52.3 N, −9.4 N, −21.1 N,−30.6 N, −40.1 N, −51.3 N; y-axis: 0 N, 10.5 N, 20.9 N,30.1 N, 40.6 N, 51.9 N, −10.3 N, −20.3 N, −29.8 N,−40.7 N, −50.7 N; z-axis: 0 N, 98.7 N, 200.1 N,

6

Meas. Sci. Technol. 21 (2010) 085804 T Liu et al

Time (s)

Tri

axia

l ang

ular

dis

plac

emen

ts (

Deg

rees

)

(b)

Time (s)

Gro

und

reac

tion

forc

es (

N)

(a)

Figure 7. (a) GRF measurements of the two force plates. (b) Orientations of the two force plates.

291.6 N, 302.5 N, 397.2 N) which were measured by the six-axial force sensor were respectively imposed on the developedforce plate. The root mean square (RMS) difference wasdefined as

RMSD =√

1

n

∑(Fi − Fri)2, (21)

where Fi is the force measured with the developed system, Fri

is the force measured with the reference system and n is thenumber of sample data.

RMS differences for the two-axial transverse force (x- andy-axes) and the normal force (z-axis) were 2.1 N, 3.0 N and5.4 N, respectively. The RMS distance between the estimated

CoP coordinates and the known coordinates for the 25 pointswas 0.7 mm. Based on the platform for the static tests, wefinished the load range evaluation of the developed force plate,and the load ranges are rated as ±300 N for the x- and y-axesand 800 N for the z-axis.

We repeated the loading on the three directions five times,and the repeatabilities of the force plate while measuringx-, y- and z-directional forces were 2.2% rate output (RO),2.0% RO and 2.7% RO, respectively, when the maximumreference loads or rate outputs of each axial force (Fx =50 N, Fy = 50 N and Fz = 400 N) were applied to theforce plate. As shown in table 1, the uncertainties of the

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Meas. Sci. Technol. 21 (2010) 085804 T Liu et al

small sensor adopted in the force plate are all less than 1.0%RO, but the standard deviations as the uncertainty of thetriaxial measurements of the force plate are more than 2%RO. The torques induced on the small triaxial sensors mustaffect the force measurements of the sensors in the plate, sothat the measurement errors of the plate are increased. Byusing the measurement results in the repeatability test, wecould calculate nonlinearity of the developed force plate, andthe nonlinearities while measuring x-, y- and z-directionalforces were 1.4% RO, 1.9% RO and 2.2% RO, respectively.In the hysteresis test, the force plate was tested for the threedirections under two conditions: firstly that of an increasingload from zero to rate load and secondly that of a decreasingload from rate load to zero load. The hystereses of the forceplate in the x-, y- and z-directions were 2.5% RO, 2.0% ROand 3.1% RO, respectively.

4.2. Dynamic measurement test: Continuous GRFmeasurements

A group of representative experimental results of GRF andCoP measurements during gait are plotted in figure 7. Themeasurements of triaxial forces made by the small triaxialforce sensors (see figure 7(a)) in the two force plates (oneunder the forefoot and another under the heel) were used tocalculate triaxial GRF and CoP according to equations (1)–(3) and equations (7)–(9) in each force plate. Equations(18)–(20) were adopted for calculating total triaxial forcesand CoP in the global coordinate system based on the forceplate orientation measurements (see figure 7(b)). As shown infigure 8, comparisons of the three components of GRF and CoPtrajectory measured by the wearable system and the referencemeasurement systems were demonstrated in the representativewalking trial. The results show good correspondence betweenthe measurements of the wearable system and the referencedevices, which was examined by RMS difference and standarddeviation (SD) for the ten walking trials. If we never includedthe transformation by using measurements of the gyroscopesand accelerometers, the RMS differences (RMS ± SD) of thetwo transverse components (x- and y-axes) and the verticalcomponent (z-axis) of the GRF were 6.7 ± 1.2 N, 9.0 ± 2.5 Nand 13.9 ± 3.0 N, respectively. When the transformationwas applied to the estimations by using measurements of thegyroscopes and accelerometers, the RMS differences (RMS± SD) of the two transverse components (x- and y-axes)and the vertical component (z-axis) of the GRF were 4.3 ±0.9 N, 6.0 ± 1.3 N, and 12.1 ± 1.1 N, respectively,corresponding to 5.1 ± 1.1% and 6.5 ± 1% of the maximumof each transverse component and to 1.3 ± 0.2% of themaximum vertical component of GRF. The RMS distancebetween the two systems’ CoP measurements was 3.2 ±0.8 mm, corresponding to 1.2 ± 0.3% of the length of theshoe. The level of reproducibility of the ten measurementscan be evaluated using the SD. The results show that in theten gait measurements the reproducibility by SD is less than1.3 N and that the validity of the transformation using themeasurements of the inertial sensors is supported.

Y (mm)

X (

mm

)

(b)

Time (s)

Gro

und

reac

tion

forc

es (

N)

(a)

Figure 8. (a) Comparison results of the triaxial GRF measurement.(b) CoP measurements of the two systems.

Table 2. The mean and SD of the gait parameters including stridelength (SL), stride width (SW), maximum lateral foot excursion(ME), single stance time (SST), double stance time (DST), stridetime (ST), maximum GRF (MaxF) and minimum GRF (MinF)calculated over ten walking trials.

Normal shoe Wearable system

SL (mm) 1441.3 ± 1.2 1429.1 ± 2.5SW (mm) 83.1 ± 3.1 100.0 ± 5.7ME (mm) 27.4 ± 2.3 30.2 ± 2.1SST (s) 0.83 ± 0.11 0.98 ± 0.09DST (s) 0.20 ± 0.06 0.22 ± 0.10ST (s) 1.27 ± 0.2 1.31 ± 0.7MaxF (N) 700.9 ± 10.1 699.2 ± 7.9MinF (N) 554.3 ± 8.9 549.0 ± 9.0

4.3. Assessment of the effect of the system on walking gait

The parameters used to assess the effect of the wearablesystem on gait were averaged over ten trials. An overviewis presented in table 2, and none of the parameters for the twoshoe conditions showed significant differences. Stride length(SL), stride width (SW), maximum lateral foot excursion

8

Meas. Sci. Technol. 21 (2010) 085804 T Liu et al

(ME), single stance time (SST), double stance time (DST),stride time (ST), maximum GRF (MaxF), and minimum GRF(MinF) averaged over ten trials differed by 12.2 mm, 6.9 mm,2.8 mm, 0.15 s, 0.02 s, 0.04 s, 1.7 N and 5.3 N between anormal shoe and the wearable system, respectively.

5. Conclusion

By integrating small triaxial force sensors and inertial sensors,we developed a wearable force plate system for measuring CoPand triaxial GRF in a number of non-laboratory environments,and natural gait was almost never affected by the wearablesystem during the ambulatory GRF measurements. Significantdifferences (56 N) between instrumented and normal shoeswere found in maximum GRF for the instrumented shoes[8]. Although there are insufficient statistical results to statethat there are no significant differences for gait when usingour wearable system, as shown in table 2, in this study wenever found large differences for the parameters between ourwearable system and a normal shoe, because we adopted thesmall triaxial force sensors in the development of the wearableforce plate (size: 80 × 80 × 15 mm3), which allows naturalor near-natural gait.

The force measurements on the x- and y-axes by usingthe wearable system demonstrated both amplitude and phaseshifts from the reference measurements (see figure 8), and thediscrepancy in CoP trajectory is slightly larger than the resultsreported by Veltink et al [7]. The output signals of the forceplate and motion capture data in the reference sensor systemwere filtered by a low-pass filter with a cut-off frequency of10 Hz, which may lead to phase shifts in the measurementsbetween the reference system and the wearable system. Themost likely source of amplitude error in the triaxial GRFmeasurement was in the orientation estimate of the movingforce plate system using triaxial inertial sensors, which couldonly implement the x- and y-axial angular displacements’ re-calibration. In the future we will integrate a triaxial magneticsensor [15] for estimating the heading angle (z-axial angulardisplacement) during gait, because the z-axial (vertical axis)cumulative error induced by the drift effect of the gyroscopesensor could be re-calibrated using the accelerometer in thewearable system. A Kalman filter will be used to decrease theeffect of white noise of magnetometers and accelerometersby integrating measurements of the gyroscope, accelerometerand magnetometer. On the other hand, only six triaxial force

sensors were used to design the prototype of the wearablesystem to measure CoP and triaxial GRF, and if we fixmore triaxial force sensors beneath the shoe, the precision ofthe wearable system will be improved.

References

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