Kinetics and kinematics data are measured using force platforms and three-dimensional cameras in the gait analysis laboratory. Reducing errors related to the force platform when collecting data was necessary. This study describes a new calibration method for centre of pressure of laboratory force platforms using a sandal with extended bar. Firstly, a subject was asked to put his weight vertically on various places of the force platforms using the sandal to create a correction table. Secondly, nine validation trials were conducted to examine the accuracy of the force platforms after correction. The data taken from the centre of pressure and the motion capture were analyzed. Then the erroneous position of the centre of pressure data was translated to the correct position by using weighted average of the vector mostly close to the validation point. The method used in this study allowed to reduce the maximum error from 24.6 mm to 2.7 mm

Aduayom-Ahego, Akouetevi

Ehara, Yoshihiro

Inoue, Shota

Niigata Regional Repository

60
Abstract
　Kinetics and kinematics data are measured using 
force platforms and three-dimensional cameras in 
the gait analysis laboratory. Reducing errors related 
to the force platform when collecting data was 
necessary. This study describes a new calibration 
method for centre of pressure of laboratory force 
platforms using a sandal with extended bar. Firstly, 
a subject was asked to put his weight vertically 
on various places of the force platforms using the 
sandal to create a correction table. Secondly, nine 
validation trials were conducted to examine the 
accuracy of the force platforms after correction. 
The data taken from the centre of pressure and 
the motion capture were analyzed. Then the 
erroneous position of the centre of pressure data 
was translated to the correct position by using 
weighted average of the vector mostly close to the 
validation point. The method used in this study 
allowed to reduce the maximum error from 24.6 
mm to 2.7 mm.
Introduction
　Three-dimensional (3D) motion analysis is 
widely used in clinical decision making and sport 
biomechanics [1]. Modern gait analysis 
laboratories are equipped with 3D multi-cameras 
and force platforms (FP) that enable the researcher 
to take the kinetics and kinematics data. FP are 
used to measure the vertical, anterior-posterior 
and medio-lateral components of the ground 
reaction force (GRF) vector. It can also be used to 
calculate the centre of pressure (COP) of a subject 
exerting force on it. The joint moment can be 
calculated by combination of the kinematic data 
and the kinetic data [2]. A previous study reported 
that errors up to ± 30 mm when measuring the 
COP with piezoelectric force platforms were 
generated. These errors could be due to the 
deformation of the top plate and transducers; a 
correction algorithm was then proposed by 
Bobbert et al to correct the deformation when 
calculating a point of force application [3]. Joint 
moments will be affected if there is an error in the 
system. Valid results of the joint moments can 
only be obtained if the determination of the COP is 
accurate. 
　To calibrate the force platforms, heavy devices 
have been used [4]. However these devices were 
difficult to move during the data collection. A 
Report article
Development of new methods to calibrate centre of pressure obtained 
from force platform
Akouetevi Aduayom-Ahego1, 3, Yoshihiro Ehara1, 2, Shota Inoue1
1Graduate School of Health and Welfare, Niigata University of Health and Welfare, Niigata Japan
2Department of Prosthetics & Orthotics and Assistive Technology, Niigata University of Health and Welfare, Niigata, Japan
3Ahelite Brace, Accra Ghana
Key words:  centre of pressure, calibration, force platform
Received: 28 August 2017/Accepted: 2 November 2017
Corresponding author: Akouetevi Aduayom-Ahego
Graduate School of Health and Welfare, Niigata University of Health and Welfare, 1398 Shimami-cho, Kita-ku, Niigata 950-3198, 
Japan
TEL/FAX: +81-25-257-4441,  E-mail: hwd15001@nuhw.ac.jp
61
Niigata Journal of Health and Welfare Vol.17, No.1
previous study also used a rigid rod with a pointed 
tip at each end to calibrate the force platform [5]. 
The former method requires a subject to exert 
force by using a hand held loading-bar. Hence 
the force applied might not be efficient to get 
adequate magnitude of GRF equivalent to the 
adult’s weight. Andrea et. al also developed a 
re-calibration device of approximately 5 kg and 
composed of a triaxial load cell, a triangular stage 
and a template. However this device required an 
amplifier before calibrating the force platform 
[6]. To avoid this difficulty, an alternative method 
should be used. The new method will use a sandal 
with extended bar in this study. A subject will apply 
force on the various points of the force platforms 
using the sandal. At the same time a new method 
to correct the COP was developed. The purpose of 
the present study is to develop a new method to 
correctly calibrate the location of the COP using 
a simple tool. 
Materials and Methods
　The new calibration device is consisted of a bar 
of approximately 1m long and 35 mm diameter 
fixed on the top of the wooden sandal. A metallic 
ball point of 20 mm diameter was attached to the 
sole of the wooden sandal. Three markers set on 
the device; one on the top of the bar and the other 
two in front and behind the sandal respectively 
(Figure 1). The three markers represent the local 
coordinate system (LCS). These markers were used 
to determine the location of the centre of the ball 
point described below: a metallic tube of 16 mm 
inner diameter and 22 mm long was embedded in 
a wooden base-plate and was placed on the floor. 
The ball point of the calibration device was placed 
in the inner diameter of the tube then the extended 
bar was rotated (Figure 2). The marker positions 
were taken with infrared cameras (VICON, 
Oxford Metrics, UK). The Matlab (Math Works, 
USA) script was used to determine the centre of 
the rotation of the ball point as the stationary point 
during the motion. The location of the centre of 
the ball point in the LCS of the calibration device 
was stored in the computational program. 
　A male tester (30 years old with 64 kg weight) 
was asked to put one leg on the sandal and he was 
ordered to put his weight on many places of the 
Figure 1.  Device used for the calibration.
Figure 2.  The ball point of the device was put in the 
inner diameter of a metallic tube embedded 
in the wooden base-plate.
62
Running head: New methods to calibrate centre of pressure
committee of the Niigata University of Health and 
Welfare was obtained (No. 17810).
Data processing 
　A computational program was developed using 
Matlab to calculate the position of the COP before 
and after the calibration. With a motion capture 
system, a computational program was used to 
calculate the contact point of the ball point with 
the force platform. This contact point is the COP 
taken from the motion capture system (COPv). 
The COPv data were assumed to be at the correct 
position. However the data of the COP from the 
force platform (COPf) contain error. The 90 trials 
were used to create the correction table. 
　The correction table contains a list of the COPf 
and the correction vectors. The correction vectors 
are the vectors from COPf  to COPv (eq.1). 
Correction vector at each COPf  in the correction 
table = vector from COPf  to COPv  (1)
To validate the correction method, the nine 
validation trials were used with the correction 
table. The following equations were used to 
correct the COP position.
From the correction table, correction vectors of 
four points most closely to the COPf were used 
for the weighted average to create the correction 
vector for the COPf (eq.2). Then the correction 
vectors for the COPf are added to the COPf to 
make the corrected COP. (eq.3)
Correction vector for the COPf of the validation 
trials = (C1/r1+C2/r2+C3/r3+C4/r4)/k. (2)
Here, C1, C2, C3, C4; Correction vector at each 
closer point in the correction table
r1, r2, r3, r4; distance from the validation point to 
each closer point in the correction table.
k = 1/r1+1/r2+1/r3+1/r4
two AMTI (Advanced Mechanical Technology 
Incorporation, USA) force platforms (Figure 3). 
While taking the data, the subject grabbed a 
handrail at his lateral side to stabilize his balance. 
The weight was applied as vertically as possible 
on the force platforms.
　The location of the three marker set on the 
calibration device were collected with 11 VICON 
system cameras (Oxford Metrics, UK) at a 
sampling rate of 100 Hz to calculate the location 
of the center of the ball point and at the same time 
the force platforms data were collected at 1 kHz to 
calculate the COP. For each position the COP and 
the marker position data were taken at about three 
seconds. Ten points on the progression direction 
and 9 points on the lateral direction calibration 
trials were taken on each force platform (a total of 
10 times 9 trials were taken to cover the surface of 
each force platform) to make the correction table 
(Figure 4). Then the other nine trials were used to 
check the accuracy of the force platform.     
　The subject approved his consent in participating 
in this study and approval from the ethical 
Figure 3.  Subject applying weight vertically 
on the force platform.
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Niigata Journal of Health and Welfare Vol.17, No.1
Motion capture system
COP
Force plate 2 correction table
Figure 4.  Graphical representation of the correction table made from the trials taken 
on the force platform 2.
○ : The position of COP data taken by the motion capture system
*  : The COP taken by force platform before calibration
Motion capture system
Before
After
Force plate 1 after calibration
Figure 5.  Position of COPv and COPf  data of the force plate 1 after calibration.
○ : The position of COP data taken by the motion capture system
*  : The COP taken by force platform before calibration
•  : The new position of COP after calibration
64
Running head: New methods to calibrate centre of pressure
Discussion
　The present paper reported the development 
of new method to calibrate the COP of FP using 
simple tools. The effectiveness of this methods 
was tested on two commercial FP in a gait analysis 
laboratory. The results in figure  4 show the 
difference between the COP data from the motion 
capture system (COPv) and the erroneous COP 
data from the FP (COPf). Before the calibration 
of the FP, the error recorded at the COP was very 
significant about 22.2 mm for the first FP and 24.6 
mm for the second FP. Motion capture systems 
and FP are used in clinical decision making and 
research in biomechanics to estimate the net joint 
moments for analysis. The influence generated 
from the FP could be critical in analyzing the data. 
Reducing the errors that influence the accuracy 
of data measurement is very necessary. Andrea 
et al. developed a portable system to re-calibrate 
the FP and the system was effective in reducing 
Corrected COPf = COPf + Correction vector for 
the validation trials (3)
Results
　Figure 4 shows graphic representation of the 
correction table of the COPv and COPf data for 
the 90 trials on one of the force plate. The same 
graphic representation was also obtained for the 
other force platform. This correction table contains 
the correct data of the motion capture system 
and the erroneous data of COP. Figure 5 and 6 
show the position of COPv and COPf  data before 
and after calibration of the two force platforms. 
Before the calibration, the maximum difference 
between COPv and COPf was 22.2 mm and 24.6 
mm respectively for the FP 1 and FP 2. And after 
calibration the maximum was reduced to 2.5 mm 
and 2.7 mm respectively.
 
Motion capture system
Before
After
Force plate 2 after calibration
Figure 6.  Position of COPv and COPf data of the force platform 2 after calibration.
○ : The position of COP data taken by the motion capture system
*  : The COP taken by force platform before calibration
•  : The new position of COP after calibration
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Niigata Journal of Health and Welfare Vol.17, No.1
test to support the clinical movement analysis 
laboratory accreditation process. Gait and 
Posture. 2003; 17:205-213.
6.　 Andrea C, Angelo C, Lorenzo C. A portable 
system for in-situ re-calibration of force 
platforms: Experimental validation. Gait and 
Posture. 2009; 29: 449-453.
7.　 James M, Peter S, Ray P. Accuracy of centre 
of pressure measurement using a piezoelectric 
force platform. Clinical Biomechanics. 1999; 
14: 357-360.
the error up to 11mm maximum. More over their 
system needs an amplifier when collecting the 
data and the device is about 5 kg weight [6]. James 
et al also developed a FP calibration system by 
applying symmetrically single point force on two 
force platforms and could reduce the COP error at 
about 1 mm, however errors generating from the 
two feet could cancel out [7]. 
　The validation data were used to check the 
translation of the position of these erroneous COPf 
position to the correct position. The method used in 
this study allows to correct the position of the COP 
data. This calibration method reduced systematic 
error related to COP up to 22 mm maximum 
when collecting kinetics and kinematics data. 
The calibration device described in this paper is 
composed of a common wooden sandal especially 
used when wearing Japanese traditional wear 
kimono. It is a light weighted device less than 
1.35 kg. It is therefore portable and can be used 
to calibrate the force platform of the gait analysis 
laboratory.
Conflicts of interest
　None declared.
References
1.　 Kim K, Jeon K. Comparisons of knee and 
ankle joint angles and ground reaction force 
according to functional differences during 
single-leg drop landing. Journal of Physical 
Therapy Science. 2016; 28:1150-1154.
2.　 Winter DA. Moments of force and 
mechanical power in jogging. Journal of 
Biomechanics.1983; 16(1):91-97.
3.　 Bobbert MF, Schamhardt HC. Accuracy of 
determining the point of force application 
with piezoelectric force plates. Journal of 
Biomechanics. 1990; 23:705-710.
4.　 Gill HS, O’Connor JJ. A new testing rig for 
force platform calibration and accuracy tests. 
Gait and Posture. 1997; 5 (3):228-232.
5.　 John PH, Scott SW, Steven JS. A proposed 


Development of new methods to calibrate centre of pressure obtained from force platform

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Development of new methods to calibrate centre of pressure obtained from force platform

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