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Static in situ calibration of force plates
Pergamon
Copyright
0021-9290(95)00109-3
TECHNICAL
STATIC
IN SITU
J. Biomechanics, Vol. 29, No. 5, pp. 659-665, 1996 0 1996 Elsevier Science Ltd. Ail ri&s -ed Printed in Great Britain 0021-9290/96 S15.00 + .OO
NOTE
CALIBRATION
OF FORCE
PLATES
M. G. Hall, H. E. Fleming, M. J. Dolan, S. F. D. Millbank and J. P. Paul* Bioengineering Unit, University of Strathclyde, Glasgow, U.K. Abstract-An in situ calibration protocol for ground-to-foot force measuring platforms is described. The methodology allows verification of the function of the force plate and allows accurate calibration for three force and moment channels. The effect of cross-sensitivity on recorded data is discussed along with the need for improvements in methodology to quantify this property. Keywords: Force plates; Kinetics; Calibration; Cross-sensitivity.
INTRODUCTION
MATERIALS
With the introduction of electrical resistance strain gauging in the University of California’s gait programme (Cunningham and Brown, 1952) ground-to-foot force measuring plates have become the standard kinetic measurement tool in human locomotion studies. They are generally used to measure, in three dimensions, the magnitude, position and direction of the ground reaction load actions applied to the foot in the stance phase of gait. Commonly this information is used as the input, along with kinematic data, to the ‘inverse dynamics’ approach for joint moment estimation using rigid body mechanics (Bresler and Frankel, 1950; Inman et al., 1981; Cappozzo, 1984; Winter, 1991). For these calculations to be valid, the force plate data must give a true representation of the ground reaction, and the errors associated with the measurement quantified. To date there have been no reports in the literature concerning the actual calibration of force plates located in situ Besser er al. (1993) considered the effect of attaching stairs to force plates and indicated the need for preloading to overcome tensile stresses imposed by the attachment process. Bobbert and Schamhardt (1990) and Mita et al. (1993) considered the accuracy of mcasurement of the location of the point of application of the applied force and found inconsistencies over the top plate, and differences in the individual characteristics among the load cells and amplifiers were reported as possible causes. Another possible. cause of some of the reported errors is a poor calibration. If the initial calibration is poor, then derived data, such as the point of application of the force will be poor, with errors propagating along the calculation. It is surprising that so little consideration has been given to the calibration of such equipment that is technically advanced and expensive. For the science of gait analysis to advance, accurate calibration procedures need to be developed and adopted by both clinical and research laboratories. The problems of cross-sensitivity also need to be addressed by both the manufacturers and the users of force plates. This paper presents a ‘static’ in situ calibration method designed to provide calibration factors for each output signal. Furthermore, it allows quantification of the crosstalk on the output channels to ensure that correct data are recorded from complex loading situations.
Received in find form 2 August 1995. * Author to whom correspondence should be addressed.
AND hfETHODS
In this exercise two piezo-electric force plates were calibrated. Other laboratories using resistive strain gauge devices could use the same procedures. Two Kistler p&o-electric type 92616 force plates with associated type 5001 charge and type 5217 summing amplifiers were evaluated (Kistler Instrumente AG, CH-8408 Winterthur, Switzerland). These force plates use four three-component force transducers positioned near the comers of the force plate. Bach transducer yields a voltage for the normal force component and one for each of the two shear components (Martini, 1983). The force plate and amplifier system has six voltage outputs, proportional to the three components of the applied force and to the three moments about the origin of the plate. The force plates were recessed into the basement floor of the biomechanics laboratory of the Biocngineering Unit, University of Strathclyde, in a purpose built pit, in accordance with the manufacturer’s instructions. The voltage outputs of the amplifiers were sampled at 50 Hz using the A/D card of a VICON gait analysis system (Oxford Metrics Ltd, Oxford, U.K.). For such calibration however any PC with suitable A/D handling facilities could be used. This laboratory uses a right-handed orthogonal axis system defined as having positive directions of: X (horizontal, longitudinal in the laboratory, generally the direction of progression during testing), Y (up) and Z (horizontal, to the right). The local axes of each force plate are as defined by the manufacturers, but the nomenclature and positive directions of the axes were interchanged to conform to the laboratory standard (Fig 1). All calibration procedures were performed with the plates in situ. This allowed evaluation of the system as it would be used, eliminating possible inaccuracies due to preloading the plates during mounting Furthermore, it minim&d disturbance to the working of the laboratory. Three calibration procedures were performed in total for each force plate. In two procedures vertical forces were applied, using calibrated weights. Where required, horizontal forces were applied using a purpose. built rig. The masses used to load the plates were calibrated to a maximal fractional error of 50 x 10m6 by a local testing house, using masses tracable to National Standards, The voltage outputs from the piezo-electric plates are subject to slow drift due to capacitance leakage.. To avoid errors incurred by this inherent property, each voltage measurement was taken as the average value over a period of 0.5 s starting after load application as soon as the signal was seen to be constant. At each load level all voltage channels were sampled so that crosstalk between the channel for the load applied and the
659
660
Technical Note
600 mm 4
,.
., A-
100 mm \I
\ 100 mm
\/ I\
l
+x
100 mm \ _100 mm we
*Z Fig. 1. Force plate showing positions and directions of its local axes systemand the scribed grid pattern on the top surface other channels could be quantified. The force plates have grid positions semi-permanently marked out on their top surface which is parallel to the X-Z plane. The lines scored on the top surface are normally invisible to all but the closest of inspections, but are readily seen when chalk dust is rubbed onto the surface. They comprise: lines parallel to the X-axis one being in the vertical plane including the Y-axis and two 0.1 m to each side of this. Similarly three lines were drawn parallel to the Z-axis but with 0.15 m in spacing, as shown in Fig. 1. This produced a surface grid pattern of six lines with nine nodes.
VERTICAL
CALIBRATION
The output corresponding to the vertical force, Fy, was calibrated by applying dead weights of up to 1250 N to the centre of the plate. The outputs corresponding to the two vertical plane moments, MC and Mz, were calibrated using a point loader which allowed accurate application of a vertical load to the plate’s surface at the node positions on the calibration grid. The point loader is seen in Fig. 2. The design was based on a linear caged ball bearing and minimised the horizontal shear force by ensuring that the load was applied vertically. Load was applied by placing weights on the platen. Stability was provided by three adjustable legs located on the ground away from the force plate being calibrated. To aid stability the height of the platen-adapter was made to be 0.17 m which is small relative to the leg span of 0.68 m. A set square was used to ensure that the central shaft was perpendicular to the surface of the plate. A ball bearing of 15 mm diameter was used to transmit the load at the point to the plate’s surface. The load transmitting ball bearing could easily be located by using the reflective nature of its smooth, polished finish. By sighting along the scribe lines of the plate, the point loader was positioned so that the reflections of the lines on the ball bearing were collinear and straight. The curved surface of the ball magnified any misalignment. Loading was applied up to a maximum of 500 N, limited bv the stabilitv of the weight stack. Mx and Mz were calibrated to-& 50 and k-75 Nm, res-ptively, using the nine nodes.
HORIZONTAL
CALIRRATION
Horizontal forces were applied to the force plates in the horizontal plane using the pulley rig system shown in Fig 3 to calibrate the shear forces, Fx and Fz, and the moment about the vertical axis, My. Access to the sides of the plates in situ was limited, making it impossible to apply forces acting in the horizontal plane containing the origin of the force plate. A ‘latch plate’ was adopted to apply the force to the plate, but as a consequence a moment was produced about the horizontal axis perpendicular to that of the applied force. Calibrated masses hung on the steel wire produced a vertical force which was then converted to a horizontal one by using two pulleys. The pulleys had an outside diameter of 250 mm and ran on a central shaft of 21 mm diameter on 3 mm diameter ball races. The large pulley to bearing diameter ratio reduced the moment due to bearing friction, ensuring a virtually friction free system. The framework which supported the pulleys was manufactured from commercially available perforated angle iron. The lowest part of the bottom pulley was just above the surface of the plate, and the tensioned wire did not come into contact with the surrounding floor surface. The latch plate was located over the scribed grid lines using the apices of two ‘tear drop’ location holes in its top surface, to indicate the centre of the plate. The structure had a tendency to be pulled forward due to the otherwise unbalanced horizontal force acting between the structure and the force plate. This was balanced by the use of the mechanical stop shown in Fig 3. The adjustable nature of the structure allowed the mechanical stop and frame to be positioned around the pit in any orientation parallel to the sides of the force plates. By application of force perpendicular to the Z axis, Fx and My calibration was performed to f 500 N and + 50 Nm, respectively. Application perpendicular to the X-axis allowed Fz and My calibration up to + 300 N and +45 Nm, respectively. CALIBRATION
AND
CROSSSENSlTIVlTY
ANALYSIS
A 6 x 6 cross-sensitivity matrix [CS] was calculated to describe the effect of each applied action (Fx., Fy,, I+., MC,, My. and Mz,) on each output signal channel (Fx., Fy,, Fz,, Mx,, My. and Mz,), measured in computer units (cu), for both force
Technical Note
661
Internal shaft and /platen assembly
Caged ball bearings Stabilizing
leg
External cage and housing
‘4
(a)
(b)
Ace
plate origin
Mz = F.d
Fig. 2. (a) Schematic diagram of point loader. By using massescalibrated by a suitable testing house and assuming a friction-free bearing, the load F is known. (b) Loading system on force plate equivalent to that of Fig. 2(a). plates. Cross-sensitivities additive.
[CS]
=
was assumed to be linear and
fill the working range of the Fy channel. A compromise situation was reached, whereby the Fy channel (FycsFy) was calibrated using data from the point loader, and checked against the data
FxcsFx
FxcsFy
FxcsFz
FxcsMx
FxcsMy
FxcsMz
FycsFx
FycsFy
FycsFz
FycsMx
FycsMy
FycsMz
FzcsFx
FzcsFy
FzcsFz
FzcsMx
FzcsMy
FzcsMz
1
MxcsFx
MxcsFy
MxcsFz
MxcsMx
MxcsMy
MxcsMz
’
1
MycsFx
MycsFy
MycsFz
MycsMx
MycsMy
MycsMz
MzcsFx
MzcsFy
MzcsFz
MzcsMx
MzcsMy
MzcsMz
Each component refers the sensitivity of one channel to another. For example, FxcsMz refers to the cross-sensitivity effect of applied Mz on the signal channel of Fx. The cross-sensitivity coefficients of the matrix were calculated by consideration of the applied forces and moments accurately applied in the calibration procedure in a step wise manner using least-squares regression analysis in the Minitab software package (Minitab Inc., PA, U.S.A.). In the methodology described above, the only pure force or moment that can be applied is Fy vertically through the centre of the plate. This is most accurately done via the point loader, as with the dead weight stack it was hard to ensure that the weights were directly above the origin due to their bulkiness and the weights had to be. applied as quickly as possible. However, the maximum applied vertical force with the point loader does not
(1)
I
from the dead weight stacks. The cross-sensitivity effects of abplied Fy on all other channels (FxcsFy, FzcsFy, MxcsFy, MycsFy and MzcsFy) were also calculated from this load application.
where CS,,
= (FxcsFy,
FycsFy,
S = (FL
FzcsFy,
MxcsFy,
FY., Fz., Mx,,
MycsFy,
MzcsFy),
MY., Mz.).
The effect of applied Mx on all channels was considered using the point loader on locations lying offset from the origin and vertically above the Z-axis. Here the only applied actions are
Technical Note
Additional
spacers
Origin of force plate’in pit
(a)
Vertic‘al offset d
*
IFN L-1c (b)
My = F.d
(cl
tvlx = F.d
Fig. 3. (a) Schematic diagram of pulley system for horizontal load application. (b) Moment induced by applying horizontal load at floor level a vertical distance d above the origin. (c) Loading system on the force plate corresponding to F being offset a horizontal distance d from the origin as shown in Fig. 3(a). Mx and Fy. The effects of Fy calculated above, were first subtracted, leaving the effect due to the applied Mx only. cs where CSM, = (FxcsMx,
_ f.3- PF,‘FY.) hfx Mx. FycsMx,
FzcsMx,
(3)
’ MxcsMx,
directly above the X-axis, where only applied Fx and its associated moment Mz occurred. The effect of applied Mz was first subtracted, leaving only the effect of applied Fx for each output channel
MycsMx,
cs
MzcsMx).
=
S
-
(CL.
Fx
By a similar method, using locations vertically above the X-axis, the effect of Mz on all channels (FxcsMz, FycsMz, FzcsMz, MxcsMz, MycsMz and MzcsMz) was determined by cs
where CSMZ = (FxcsMz,
= s - WSFY . FY.) MI Mz. ’ FycsMz,
FzcsMz,
MxcsMz,
(4)
Mz.)
Fx,
where CSr, = (FxcsFx,
FycsFx,
(5)
’
FzcsFx,
MxcsFx,
MycsFx,
MzcsFx).
The effect of applied Fz was considered for the pulley locations acting directly above the Z-axis of the force plate. The effect of the associated moment, Mx, was first subtracted to give the effect of Fz.
MycsMz,
MzcsMz).
The remaining node locations were used to evaluate the calibration. With the pulley system, the horizontally applied forces each have a moment associated with them due to the load application by the latch system.The moment applied will be due to the force acting at a constant moment arm identified by the position of the wire. This was measured to be 45 mm above the origin, and using this assumption the applied moment can be determined. Calibration of applied Fx considered locations parallel and
cs
=
S
-
(CL.
FZ
where CS,, = (FxcsFz,
Mx.1
Fz. FycsFz,
FzcsFz,
’
(6)
MxcsFz, MycsFz,
MzcsFz).
Using the calibration method described above, My moments can only be applied with either assooiated Fx, and Mz,, or Fz, and Mx,. The effect of My, on all channels was evaluated for pulley locations other than those acting directly vertically above
Technical Note
663
the X- and Z-axes. The previously calculated effects of the applied Fx, Fz, Mx and Mz were first subtracted.
cs
_ s - (CS,, . Fx,) - (CS,, . Fz.) - (C&f,. Mx,) - (CS,, . Mz.) , MYMY.
where CSvv = (FxcsMy,
FycsMy,
FzcsMy,
MxcsMy,
(7)
MycsMy,
DISCUSSION
MzcsMy).
In theory it is possible to apply a pure My moment to the force plate. This however involves the use of two pulley rig systems, each applying equal but opposite forces acting as a force couple. A problem with such a set up would be balancing the weight stacks on the two pulley systems accurately. The cross-sensitivity coefficients were used to produce a series of calibration equations which allowed an accurate prediction of the applied loading conditions from the signals recorded on all channels (Fx,.,, FY,,,Fz,,,, Mx,.,, MY,.,, Mz,,,). These were Fx,,,
=
Fx. - Fy;y;;;Fy Fx..
Fyest = [ Fys Fz,,,
=
Mx.=,
-
Mz,,,
=
[
MY. Mz.
-
FycsFy
-
-
Fx,. MzcsFx
FzcsMx
My.. -
-
FycsFy
-
My..
FzcsFz
FzcsFz
-
This method of calculation has small errors associated with it. These are due to coefficients using the signal value rather than the true applied value to predict the magnitude of the crosssensitivity. Given that cross-sensitivities are of the order of l%, the cross-sensitivity predicted will be in error by about 0.01% per term, resulting in a maximum worst-case error of 0.05% per equation.
RESULTS The cross-sensitivity matrices for the two plates are shown in Table 1. The relative cross-sensitivity effects are shown in Table 2. These values refer to the effect of 1 unit (N or Nm) of applied action on the recorded signal, expressed in terms of units of the signal (N or Nm). For example, for force plate 1, 1 N of applied Fy results in 6.04 x 10e3 N recorded on the Fx channel, a cross-sensitivity of 0.604%. The manufacturers supply crosssensitivity data for the force channels only, as they consider the force plate alone rather than as part of the whole system including the amplifiers. The manufacturer’s figures are seen in Table 4. The cross-sensitivities reported here for the system as a whole, confirm the force channels to be working at about the levels expected by the manufacturers, given that the calibration method described above is not ideal, but is rather a practical method of calculating the cross-sensitivity. To evaluate the calibration, the mean difference sensitivities (MDS) for each of the 6 channels of both force plate was calculated by comparing the estimated action using the calibration equations to the actual action applied for the N locations and load levels. } MDS =
. (9) N These are seen in Table 3. The results indicate that the calibration equations allowed the prediction of the applied action to well within the one peramt ievel.
. MzcsMx MxcsMx
FxcsFx’
1.-
1
FycsFy
’
1
I . FzcsFz ’ Mz, . MxcsMz 1 .MzcsMz MxcsMx’ MzcsMz
1
Mz, MycsMz
. MycsMx MxcsMx
Mx, -
MxcsMy
MzcsMz Mz, . FzcsMz
-
MycsMy Mx,
Fz,’ MzcsFz -
FzcsMy
-
Fz.. MycsFz
Mz, . FycsMz -
MycsMy
FzcsFz
MzcsMz
1.-
1
Mz, . FxcsMz -
FycsMy
MycsMy
Fz.. MxcsFz
FycsFy
FycsFy
My.. -
MxcsMx
FxcsMy
MycsMy
. FycsMx
Mx.. -
Fy,. MzcsFy -
-
MxcsMx
Fy.. MycsFy
FxcsFx
My,.
MxcsMy
Fy. ’ MxcsFy -
MycsFx
FxcsFx
Mx, . FxcsMx
Mx,
Fy.. FzcsFy -
FxcsFx Fx..
=
FzcsFz
Fx, . MxcsFx
[ MY.,
-
FxcsFx
Mx,
-
Fz, . FycsFz
Fx. ’ FzcsFx
Fz. =
FycsFx
FxcsFx
[
Fz, . FxcsFz FzcsFz
-
The techniques described allowed the output channels of a force plate to be accurately calibrated, and thereby verity if the crosstalk is within the manufacturer’s specifications. This verification however, was an estimate, due to the practical inability to apply pure forces and moments to the plates in situ. For example, to apply pure horizontal forces, the line of action of the load must be directly through the origin, which is situated below the &face of the plate. On Kistler piezo-electric plates, no
-
MzcsMz
_ My,. MzcsMyl MycsMy
.I
1
MycsMy’
1 .1 MzcsMz’
I!21 ‘“’
fittings exist to allow such a force application. Consequently, any horizontal force has an applied moment associated with it. Therefore, any cross-sensitivity measured on non-loaded channels will have components due to both. The exact point of application of the force cannot be accurately determined nor easily changed using this latch plate system. Using this system, the moment arm was well known and was defined by the line of action of the cable. However this results in the components being indeterminate as the moment applied is inherently linked to the applied force due to the constant moment arm. Thus a ‘true’ cross-sensitivity matrix was not produced Piezo-electric plate manufacturers, using in house multi-component force calibrators (Martini, 1983) are able to apply pure forces and verify crosstalk to +0.2% accuracy. Even using such specialist machinery, they acknowledge that the transducers’ crosstalk specifications are very difficult to determine. The manufacturer’s approach is clearly impractical in the clinical department (the principal market for the force plate). One possible approach is for the manufacturers to supply fixtures and fittings with the plates, along with a calibration protocol, to allow accurate calibration of the force plates in situ. Manufacturers of strain gauged based force plates supply a calibration matrix which is applied to the outputs to account for cross-sensitivity, This will represent the situation within the plate at the time of delivery. It is uncertain however what the values will be when the instrument is installed and how it will vary with time, thus a calibration is still required. The need to produce calibration equations becomes apparent if one considers the effect of cross-sensitivity on an example of recorded data of a 67 kg subject in the stance phase of walking (Fig 4). The manufacturer’s specifications for crosstalk for our force plates are used. Table 4 illustrates the effect at two points, one in early, and the other in late stance. The maximum permissible crosstalk, expressed as a percentage of the measured load, shows the vertical force having a large effect on the measured horizontal forces, making up to 20% of the measured value.
664
Technical Note Table 1. Cross-sensitivity matrices for the two force plates
FPl
Fx, (NJ
FY. (N)
Fza (NJ
Mx, (Nm)
MY. (Nm)
Fxs (4 FY. (d Fz. (4 MA (4 MY, (4 Mzs (4
- 2.99198 - 0.00804 0.025232 - 0.00679 0.038728 0.006488
0.01806 - 0.81226 - 0.01499 - 0.00851 0.01686 - 0.00689
- 0.03550 - 0.01019 6.40726 - 0.01595 - 0.02711 0.00454
- 0.00402 - 0.01632 0.10626 - 3.81591 - 0.16378 - 0.06694
- 0.08299 0.05679 0.24226 0.04399 - 24.6245 - 0.02768
0.02361 - 0.00355 0.11904 0.00596 0.11742 3.93524
FP2
Fxa (W 3.20624 - 0.00809 0.06151 0.00046 0.00038 0.01688
FY. N 0.03332 - 0.79779 0.04171 0.00632 0.03933 0.02932
Fz. (N)
Mx. W-4
MY. (NW 0.05172 - 0.00103 0.04635 - 0.00347 - 24.2445 0.01473
Mz, Pm) 0.06987 0.02552 0.03217 0.01387 - 0.15197 - 3.76976
Fxs (4 FY. (4 Fzs C-4 M-s (4 MY. W Mz, (4
0.01821 - 0.00964 - 6.33152 0.00911 0.05490 0.00774
- 0.01231 - 0.04283 - 0.04826 3.62642 0.11456 - 0.05189
Mz, (Nm)
Table 2. Relative cross-sensitivity for the two force plates, expressed as the ratio of the individual load sensitivities to the principal cross-sensitivity coefficients FPl Fx, PJ) FY~(N) Fzs (N Mx, Wm) MY. (W W Oud FP2 Fx. WI FY. (NJ J% N Mx, Pm) MY. (Nm) Mz. (Nm)
Fxa (NJ 1 9.90 x 3.98 x 1.78 x 1.57 x 1.65 x
10-a 1O-3 1O-3 10-a 1O-3
F-G PO i.0101 9.71 x 1.27 x 1.57 x 4.48 x
10-s 1O-4 10-s lo-”
FY. (NJ
Fz. (NJ
Mx. Wm)
MY, (Nm)
Mz, (Nm)
lo-’ 1O-3 1O-4 10-a
0.0119 2.33 x 1O-3 1 4.18 x lo-” 1.10 x 10-s 1.15 x 10-a
1.34 x 1oy3 0.0200 0.0167 1 6.65 x lo-’ 0.0170
0.0277 0.0649 0.0378 0.0115 1 7.03 x lo- 3
7.89 x 1O-3 4.37 x 1o-3 0.0186 1.56 x lo-” 4.77 x lo-’ 1
FY. (NJ 0.0104 1 6.59 x lo-” 1.74 x 10-j 1.62 x 1O-3 7.78 x 1O-3
Fza (NJ 5.68 x lo-” 0.0121 1 2.51 x 10-j 2.27 x 1O-3 2.05 x 1O-3
Mx, (Nm) 3.84 x 1O-3 0.0537 7.62 x 1O-3 1 5.96 x 1O-3 0.0138
MY, (Nm) 0.0161 1.29 x 1O-3 7.32 x lo-” 9.57 x 1o-4 1 3.91 x 1o-3
Mz. (Nm) 0.0218 0.0320 5.08 x 1O-3 3.83 x lo-” 6.27 x 1O-3 1
6.04x 1 2.34 x 2.23 x 6.85 x 1.75 x
1O-3
Table 3. Mean difference sensitivities calculated using the calibration equations
FPl-Fx FPl-Fy FPl-Fz FPl-Mx FPl-My FPl-Mz FP2-Fx FP2-Fy FP2-Fz FP2-Mx FPZ-My FP2-Mz
MDS (%)
SE
N
0.04662 0.20302 0.05079 0.08965 0.11078 0.31291 0.11117 0.01877 0.28622 0.04296 0.13330 0.10259
0.072 0.156 0.110 0.409 0.174 0.281 0.112 0.209 0.074 0.487 1.740 0.408
20 45 36 30 39 iFI 45 36 30 39 30
Clearly if inferences about gait are to be made from the ground reaction forces care must be taken to ensure that apparent changes in the smaller horizontal forces are real, not just an effect of the change in the vertical load. The use of crosssensitivity calibration equations will reduce these errors. Results from our calibration procedure indicated that the actual force and. moment ~ values can be predicted to within 0.3% of the true value or better.
Fig. 4. Typical curves of variation with time of ground reaction force components for a 67 kg test subject.
CONCLUSION The procedures reported here relate to the calibration of Kistler piezo-electric force plates. The same procedures may be applied to other types such as those based on electrical resistive strain gauges. The calibration procedures described in this paper allow the output channels of a force plate to be accu tely calibrated with the minimum amount of specialist equi f ment
Technical Note
665
Table 4. Typical peaks during early and late stances (a) EarIy stance Measurand Value Effect on Spec. crosstalk Maximal crosstalk Measured load Max. crosstalk as Percentage of load (b) Late stance Measurand Value Effect on Spec. crosstalk Maximal crosstalk Measured load Max. crosstalk as Percentage of load
A-P (Fx)
Vertical (Fy)
- 138N
M-L (Fz)
726 N
-42N
FY
Fz
Fx
Fz
Fx
FY
Q +2% 2.76 N
d kl% 1.38 N
d *la? 7.26 N
Q *l% 7.26 N
Q *l% 0.42 N
c f2% 0.84 N
726 N f 0.4%
42N f 3.3%
138 N f 5.3%
42N + 17.3%
138N + 0.3%
726 N f 0.1%
A-P (Fx) 141 N Fz FY
Vertical (Fy) 801 N Fx
Fz
M-L (Fz) -36N Fx
FY
d *2% 2.82 N
S&l% 1.41 N
< kl% 8.01 N
< f 1% 0.36 N
< *2% 0.72 N
801 N * 0.4%
36N * 3.9%
141 N & 5.7%
36N f 22.3%
141 N * 0.3%
801 N f 0.1%
and disturbance. The procedures also enable the crosstalk to be estimated and compensated for. It is hoped that these procedures, or similar procedures, will be adopted by clinical and research laboratories to ensure accurate performance of their force plates. To further assist the accurate calibration of force plates, it is recommended that manufacturers should supply fixtures and fittings, along with clearly defined protocols, to allow the users of their force plates to perform practical in situ calibration and evaluation of crosstalk. Acknowledgements-MGH, MJD and SFDM were supported by SERC studentships. HEF and JPP were supported by the European Community AIM project CAMARC II. REFERENCES
Besser, M. P., Kowalk, D. L. and Vaughan, C. L. (1993) Mounting and calibration of stairs on piezoelectric force platforms. Gait Posture 1, 231-235.
Bobbert, M. F. and Schamhardt, H. C. (1990) Accuracy of determining the point of force application with piezoelectric force plates. J. Biomechanics 23, 705-710. Bresler, B. and Frankel, J. P. (1950) The forcesand moments in the leg during level walking. Trans. Am Sot. Me& Engng ?2,27-36. Cappozzo, A. (1984) Gait analysis methodology, Hum. Momt. Sci. 2, 27-50. Cunningham, D. M. and Brown, G. W. (1952) Two devices for measuring the forces acting on the human body during walking. Proc. Sot. Expt. Stress Analyt. 9, 75-90. Inman, V. T., Ralston, H. J. and Todd, F. (1981) Human Walking. Williams & Wilkins, Baltimore. Martini, K. H. (1983) Multicomponent dynamometers using quartz crystals as sensing elements. Inst. Sot. Am. Trans. 22, 35-46. Mita, K., Akataki, K., Itoh, K., Nogami, H., Katoh, R., Ninomi, S., Watakabe, M. and Suzuki, N. (1993) An investigation of the accuracy in measuring the body centre of pressure in a standing posture with a force plate. Frontiers Med. Biol. Engng $201-213.
Winter, D. A. (1991) Biomechanics and Motor Control of Human Gait, 2nd Edition. University of Waterloo Press, Waterloo.
Copyright
0021-9290(95)00109-3
TECHNICAL
STATIC
IN SITU
J. Biomechanics, Vol. 29, No. 5, pp. 659-665, 1996 0 1996 Elsevier Science Ltd. Ail ri&s -ed Printed in Great Britain 0021-9290/96 S15.00 + .OO
NOTE
CALIBRATION
OF FORCE
PLATES
M. G. Hall, H. E. Fleming, M. J. Dolan, S. F. D. Millbank and J. P. Paul* Bioengineering Unit, University of Strathclyde, Glasgow, U.K. Abstract-An in situ calibration protocol for ground-to-foot force measuring platforms is described. The methodology allows verification of the function of the force plate and allows accurate calibration for three force and moment channels. The effect of cross-sensitivity on recorded data is discussed along with the need for improvements in methodology to quantify this property. Keywords: Force plates; Kinetics; Calibration; Cross-sensitivity.
INTRODUCTION
MATERIALS
With the introduction of electrical resistance strain gauging in the University of California’s gait programme (Cunningham and Brown, 1952) ground-to-foot force measuring plates have become the standard kinetic measurement tool in human locomotion studies. They are generally used to measure, in three dimensions, the magnitude, position and direction of the ground reaction load actions applied to the foot in the stance phase of gait. Commonly this information is used as the input, along with kinematic data, to the ‘inverse dynamics’ approach for joint moment estimation using rigid body mechanics (Bresler and Frankel, 1950; Inman et al., 1981; Cappozzo, 1984; Winter, 1991). For these calculations to be valid, the force plate data must give a true representation of the ground reaction, and the errors associated with the measurement quantified. To date there have been no reports in the literature concerning the actual calibration of force plates located in situ Besser er al. (1993) considered the effect of attaching stairs to force plates and indicated the need for preloading to overcome tensile stresses imposed by the attachment process. Bobbert and Schamhardt (1990) and Mita et al. (1993) considered the accuracy of mcasurement of the location of the point of application of the applied force and found inconsistencies over the top plate, and differences in the individual characteristics among the load cells and amplifiers were reported as possible causes. Another possible. cause of some of the reported errors is a poor calibration. If the initial calibration is poor, then derived data, such as the point of application of the force will be poor, with errors propagating along the calculation. It is surprising that so little consideration has been given to the calibration of such equipment that is technically advanced and expensive. For the science of gait analysis to advance, accurate calibration procedures need to be developed and adopted by both clinical and research laboratories. The problems of cross-sensitivity also need to be addressed by both the manufacturers and the users of force plates. This paper presents a ‘static’ in situ calibration method designed to provide calibration factors for each output signal. Furthermore, it allows quantification of the crosstalk on the output channels to ensure that correct data are recorded from complex loading situations.
Received in find form 2 August 1995. * Author to whom correspondence should be addressed.
AND hfETHODS
In this exercise two piezo-electric force plates were calibrated. Other laboratories using resistive strain gauge devices could use the same procedures. Two Kistler p&o-electric type 92616 force plates with associated type 5001 charge and type 5217 summing amplifiers were evaluated (Kistler Instrumente AG, CH-8408 Winterthur, Switzerland). These force plates use four three-component force transducers positioned near the comers of the force plate. Bach transducer yields a voltage for the normal force component and one for each of the two shear components (Martini, 1983). The force plate and amplifier system has six voltage outputs, proportional to the three components of the applied force and to the three moments about the origin of the plate. The force plates were recessed into the basement floor of the biomechanics laboratory of the Biocngineering Unit, University of Strathclyde, in a purpose built pit, in accordance with the manufacturer’s instructions. The voltage outputs of the amplifiers were sampled at 50 Hz using the A/D card of a VICON gait analysis system (Oxford Metrics Ltd, Oxford, U.K.). For such calibration however any PC with suitable A/D handling facilities could be used. This laboratory uses a right-handed orthogonal axis system defined as having positive directions of: X (horizontal, longitudinal in the laboratory, generally the direction of progression during testing), Y (up) and Z (horizontal, to the right). The local axes of each force plate are as defined by the manufacturers, but the nomenclature and positive directions of the axes were interchanged to conform to the laboratory standard (Fig 1). All calibration procedures were performed with the plates in situ. This allowed evaluation of the system as it would be used, eliminating possible inaccuracies due to preloading the plates during mounting Furthermore, it minim&d disturbance to the working of the laboratory. Three calibration procedures were performed in total for each force plate. In two procedures vertical forces were applied, using calibrated weights. Where required, horizontal forces were applied using a purpose. built rig. The masses used to load the plates were calibrated to a maximal fractional error of 50 x 10m6 by a local testing house, using masses tracable to National Standards, The voltage outputs from the piezo-electric plates are subject to slow drift due to capacitance leakage.. To avoid errors incurred by this inherent property, each voltage measurement was taken as the average value over a period of 0.5 s starting after load application as soon as the signal was seen to be constant. At each load level all voltage channels were sampled so that crosstalk between the channel for the load applied and the
659
660
Technical Note
600 mm 4
,.
., A-
100 mm \I
\ 100 mm
\/ I\
l
+x
100 mm \ _100 mm we
*Z Fig. 1. Force plate showing positions and directions of its local axes systemand the scribed grid pattern on the top surface other channels could be quantified. The force plates have grid positions semi-permanently marked out on their top surface which is parallel to the X-Z plane. The lines scored on the top surface are normally invisible to all but the closest of inspections, but are readily seen when chalk dust is rubbed onto the surface. They comprise: lines parallel to the X-axis one being in the vertical plane including the Y-axis and two 0.1 m to each side of this. Similarly three lines were drawn parallel to the Z-axis but with 0.15 m in spacing, as shown in Fig. 1. This produced a surface grid pattern of six lines with nine nodes.
VERTICAL
CALIBRATION
The output corresponding to the vertical force, Fy, was calibrated by applying dead weights of up to 1250 N to the centre of the plate. The outputs corresponding to the two vertical plane moments, MC and Mz, were calibrated using a point loader which allowed accurate application of a vertical load to the plate’s surface at the node positions on the calibration grid. The point loader is seen in Fig. 2. The design was based on a linear caged ball bearing and minimised the horizontal shear force by ensuring that the load was applied vertically. Load was applied by placing weights on the platen. Stability was provided by three adjustable legs located on the ground away from the force plate being calibrated. To aid stability the height of the platen-adapter was made to be 0.17 m which is small relative to the leg span of 0.68 m. A set square was used to ensure that the central shaft was perpendicular to the surface of the plate. A ball bearing of 15 mm diameter was used to transmit the load at the point to the plate’s surface. The load transmitting ball bearing could easily be located by using the reflective nature of its smooth, polished finish. By sighting along the scribe lines of the plate, the point loader was positioned so that the reflections of the lines on the ball bearing were collinear and straight. The curved surface of the ball magnified any misalignment. Loading was applied up to a maximum of 500 N, limited bv the stabilitv of the weight stack. Mx and Mz were calibrated to-& 50 and k-75 Nm, res-ptively, using the nine nodes.
HORIZONTAL
CALIRRATION
Horizontal forces were applied to the force plates in the horizontal plane using the pulley rig system shown in Fig 3 to calibrate the shear forces, Fx and Fz, and the moment about the vertical axis, My. Access to the sides of the plates in situ was limited, making it impossible to apply forces acting in the horizontal plane containing the origin of the force plate. A ‘latch plate’ was adopted to apply the force to the plate, but as a consequence a moment was produced about the horizontal axis perpendicular to that of the applied force. Calibrated masses hung on the steel wire produced a vertical force which was then converted to a horizontal one by using two pulleys. The pulleys had an outside diameter of 250 mm and ran on a central shaft of 21 mm diameter on 3 mm diameter ball races. The large pulley to bearing diameter ratio reduced the moment due to bearing friction, ensuring a virtually friction free system. The framework which supported the pulleys was manufactured from commercially available perforated angle iron. The lowest part of the bottom pulley was just above the surface of the plate, and the tensioned wire did not come into contact with the surrounding floor surface. The latch plate was located over the scribed grid lines using the apices of two ‘tear drop’ location holes in its top surface, to indicate the centre of the plate. The structure had a tendency to be pulled forward due to the otherwise unbalanced horizontal force acting between the structure and the force plate. This was balanced by the use of the mechanical stop shown in Fig 3. The adjustable nature of the structure allowed the mechanical stop and frame to be positioned around the pit in any orientation parallel to the sides of the force plates. By application of force perpendicular to the Z axis, Fx and My calibration was performed to f 500 N and + 50 Nm, respectively. Application perpendicular to the X-axis allowed Fz and My calibration up to + 300 N and +45 Nm, respectively. CALIBRATION
AND
CROSSSENSlTIVlTY
ANALYSIS
A 6 x 6 cross-sensitivity matrix [CS] was calculated to describe the effect of each applied action (Fx., Fy,, I+., MC,, My. and Mz,) on each output signal channel (Fx., Fy,, Fz,, Mx,, My. and Mz,), measured in computer units (cu), for both force
Technical Note
661
Internal shaft and /platen assembly
Caged ball bearings Stabilizing
leg
External cage and housing
‘4
(a)
(b)
Ace
plate origin
Mz = F.d
Fig. 2. (a) Schematic diagram of point loader. By using massescalibrated by a suitable testing house and assuming a friction-free bearing, the load F is known. (b) Loading system on force plate equivalent to that of Fig. 2(a). plates. Cross-sensitivities additive.
[CS]
=
was assumed to be linear and
fill the working range of the Fy channel. A compromise situation was reached, whereby the Fy channel (FycsFy) was calibrated using data from the point loader, and checked against the data
FxcsFx
FxcsFy
FxcsFz
FxcsMx
FxcsMy
FxcsMz
FycsFx
FycsFy
FycsFz
FycsMx
FycsMy
FycsMz
FzcsFx
FzcsFy
FzcsFz
FzcsMx
FzcsMy
FzcsMz
1
MxcsFx
MxcsFy
MxcsFz
MxcsMx
MxcsMy
MxcsMz
’
1
MycsFx
MycsFy
MycsFz
MycsMx
MycsMy
MycsMz
MzcsFx
MzcsFy
MzcsFz
MzcsMx
MzcsMy
MzcsMz
Each component refers the sensitivity of one channel to another. For example, FxcsMz refers to the cross-sensitivity effect of applied Mz on the signal channel of Fx. The cross-sensitivity coefficients of the matrix were calculated by consideration of the applied forces and moments accurately applied in the calibration procedure in a step wise manner using least-squares regression analysis in the Minitab software package (Minitab Inc., PA, U.S.A.). In the methodology described above, the only pure force or moment that can be applied is Fy vertically through the centre of the plate. This is most accurately done via the point loader, as with the dead weight stack it was hard to ensure that the weights were directly above the origin due to their bulkiness and the weights had to be. applied as quickly as possible. However, the maximum applied vertical force with the point loader does not
(1)
I
from the dead weight stacks. The cross-sensitivity effects of abplied Fy on all other channels (FxcsFy, FzcsFy, MxcsFy, MycsFy and MzcsFy) were also calculated from this load application.
where CS,,
= (FxcsFy,
FycsFy,
S = (FL
FzcsFy,
MxcsFy,
FY., Fz., Mx,,
MycsFy,
MzcsFy),
MY., Mz.).
The effect of applied Mx on all channels was considered using the point loader on locations lying offset from the origin and vertically above the Z-axis. Here the only applied actions are
Technical Note
Additional
spacers
Origin of force plate’in pit
(a)
Vertic‘al offset d
*
IFN L-1c (b)
My = F.d
(cl
tvlx = F.d
Fig. 3. (a) Schematic diagram of pulley system for horizontal load application. (b) Moment induced by applying horizontal load at floor level a vertical distance d above the origin. (c) Loading system on the force plate corresponding to F being offset a horizontal distance d from the origin as shown in Fig. 3(a). Mx and Fy. The effects of Fy calculated above, were first subtracted, leaving the effect due to the applied Mx only. cs where CSM, = (FxcsMx,
_ f.3- PF,‘FY.) hfx Mx. FycsMx,
FzcsMx,
(3)
’ MxcsMx,
directly above the X-axis, where only applied Fx and its associated moment Mz occurred. The effect of applied Mz was first subtracted, leaving only the effect of applied Fx for each output channel
MycsMx,
cs
MzcsMx).
=
S
-
(CL.
Fx
By a similar method, using locations vertically above the X-axis, the effect of Mz on all channels (FxcsMz, FycsMz, FzcsMz, MxcsMz, MycsMz and MzcsMz) was determined by cs
where CSMZ = (FxcsMz,
= s - WSFY . FY.) MI Mz. ’ FycsMz,
FzcsMz,
MxcsMz,
(4)
Mz.)
Fx,
where CSr, = (FxcsFx,
FycsFx,
(5)
’
FzcsFx,
MxcsFx,
MycsFx,
MzcsFx).
The effect of applied Fz was considered for the pulley locations acting directly above the Z-axis of the force plate. The effect of the associated moment, Mx, was first subtracted to give the effect of Fz.
MycsMz,
MzcsMz).
The remaining node locations were used to evaluate the calibration. With the pulley system, the horizontally applied forces each have a moment associated with them due to the load application by the latch system.The moment applied will be due to the force acting at a constant moment arm identified by the position of the wire. This was measured to be 45 mm above the origin, and using this assumption the applied moment can be determined. Calibration of applied Fx considered locations parallel and
cs
=
S
-
(CL.
FZ
where CS,, = (FxcsFz,
Mx.1
Fz. FycsFz,
FzcsFz,
’
(6)
MxcsFz, MycsFz,
MzcsFz).
Using the calibration method described above, My moments can only be applied with either assooiated Fx, and Mz,, or Fz, and Mx,. The effect of My, on all channels was evaluated for pulley locations other than those acting directly vertically above
Technical Note
663
the X- and Z-axes. The previously calculated effects of the applied Fx, Fz, Mx and Mz were first subtracted.
cs
_ s - (CS,, . Fx,) - (CS,, . Fz.) - (C&f,. Mx,) - (CS,, . Mz.) , MYMY.
where CSvv = (FxcsMy,
FycsMy,
FzcsMy,
MxcsMy,
(7)
MycsMy,
DISCUSSION
MzcsMy).
In theory it is possible to apply a pure My moment to the force plate. This however involves the use of two pulley rig systems, each applying equal but opposite forces acting as a force couple. A problem with such a set up would be balancing the weight stacks on the two pulley systems accurately. The cross-sensitivity coefficients were used to produce a series of calibration equations which allowed an accurate prediction of the applied loading conditions from the signals recorded on all channels (Fx,.,, FY,,,Fz,,,, Mx,.,, MY,.,, Mz,,,). These were Fx,,,
=
Fx. - Fy;y;;;Fy Fx..
Fyest = [ Fys Fz,,,
=
Mx.=,
-
Mz,,,
=
[
MY. Mz.
-
FycsFy
-
-
Fx,. MzcsFx
FzcsMx
My.. -
-
FycsFy
-
My..
FzcsFz
FzcsFz
-
This method of calculation has small errors associated with it. These are due to coefficients using the signal value rather than the true applied value to predict the magnitude of the crosssensitivity. Given that cross-sensitivities are of the order of l%, the cross-sensitivity predicted will be in error by about 0.01% per term, resulting in a maximum worst-case error of 0.05% per equation.
RESULTS The cross-sensitivity matrices for the two plates are shown in Table 1. The relative cross-sensitivity effects are shown in Table 2. These values refer to the effect of 1 unit (N or Nm) of applied action on the recorded signal, expressed in terms of units of the signal (N or Nm). For example, for force plate 1, 1 N of applied Fy results in 6.04 x 10e3 N recorded on the Fx channel, a cross-sensitivity of 0.604%. The manufacturers supply crosssensitivity data for the force channels only, as they consider the force plate alone rather than as part of the whole system including the amplifiers. The manufacturer’s figures are seen in Table 4. The cross-sensitivities reported here for the system as a whole, confirm the force channels to be working at about the levels expected by the manufacturers, given that the calibration method described above is not ideal, but is rather a practical method of calculating the cross-sensitivity. To evaluate the calibration, the mean difference sensitivities (MDS) for each of the 6 channels of both force plate was calculated by comparing the estimated action using the calibration equations to the actual action applied for the N locations and load levels. } MDS =
. (9) N These are seen in Table 3. The results indicate that the calibration equations allowed the prediction of the applied action to well within the one peramt ievel.
. MzcsMx MxcsMx
FxcsFx’
1.-
1
FycsFy
’
1
I . FzcsFz ’ Mz, . MxcsMz 1 .MzcsMz MxcsMx’ MzcsMz
1
Mz, MycsMz
. MycsMx MxcsMx
Mx, -
MxcsMy
MzcsMz Mz, . FzcsMz
-
MycsMy Mx,
Fz,’ MzcsFz -
FzcsMy
-
Fz.. MycsFz
Mz, . FycsMz -
MycsMy
FzcsFz
MzcsMz
1.-
1
Mz, . FxcsMz -
FycsMy
MycsMy
Fz.. MxcsFz
FycsFy
FycsFy
My.. -
MxcsMx
FxcsMy
MycsMy
. FycsMx
Mx.. -
Fy,. MzcsFy -
-
MxcsMx
Fy.. MycsFy
FxcsFx
My,.
MxcsMy
Fy. ’ MxcsFy -
MycsFx
FxcsFx
Mx, . FxcsMx
Mx,
Fy.. FzcsFy -
FxcsFx Fx..
=
FzcsFz
Fx, . MxcsFx
[ MY.,
-
FxcsFx
Mx,
-
Fz, . FycsFz
Fx. ’ FzcsFx
Fz. =
FycsFx
FxcsFx
[
Fz, . FxcsFz FzcsFz
-
The techniques described allowed the output channels of a force plate to be accurately calibrated, and thereby verity if the crosstalk is within the manufacturer’s specifications. This verification however, was an estimate, due to the practical inability to apply pure forces and moments to the plates in situ. For example, to apply pure horizontal forces, the line of action of the load must be directly through the origin, which is situated below the &face of the plate. On Kistler piezo-electric plates, no
-
MzcsMz
_ My,. MzcsMyl MycsMy
.I
1
MycsMy’
1 .1 MzcsMz’
I!21 ‘“’
fittings exist to allow such a force application. Consequently, any horizontal force has an applied moment associated with it. Therefore, any cross-sensitivity measured on non-loaded channels will have components due to both. The exact point of application of the force cannot be accurately determined nor easily changed using this latch plate system. Using this system, the moment arm was well known and was defined by the line of action of the cable. However this results in the components being indeterminate as the moment applied is inherently linked to the applied force due to the constant moment arm. Thus a ‘true’ cross-sensitivity matrix was not produced Piezo-electric plate manufacturers, using in house multi-component force calibrators (Martini, 1983) are able to apply pure forces and verify crosstalk to +0.2% accuracy. Even using such specialist machinery, they acknowledge that the transducers’ crosstalk specifications are very difficult to determine. The manufacturer’s approach is clearly impractical in the clinical department (the principal market for the force plate). One possible approach is for the manufacturers to supply fixtures and fittings with the plates, along with a calibration protocol, to allow accurate calibration of the force plates in situ. Manufacturers of strain gauged based force plates supply a calibration matrix which is applied to the outputs to account for cross-sensitivity, This will represent the situation within the plate at the time of delivery. It is uncertain however what the values will be when the instrument is installed and how it will vary with time, thus a calibration is still required. The need to produce calibration equations becomes apparent if one considers the effect of cross-sensitivity on an example of recorded data of a 67 kg subject in the stance phase of walking (Fig 4). The manufacturer’s specifications for crosstalk for our force plates are used. Table 4 illustrates the effect at two points, one in early, and the other in late stance. The maximum permissible crosstalk, expressed as a percentage of the measured load, shows the vertical force having a large effect on the measured horizontal forces, making up to 20% of the measured value.
664
Technical Note Table 1. Cross-sensitivity matrices for the two force plates
FPl
Fx, (NJ
FY. (N)
Fza (NJ
Mx, (Nm)
MY. (Nm)
Fxs (4 FY. (d Fz. (4 MA (4 MY, (4 Mzs (4
- 2.99198 - 0.00804 0.025232 - 0.00679 0.038728 0.006488
0.01806 - 0.81226 - 0.01499 - 0.00851 0.01686 - 0.00689
- 0.03550 - 0.01019 6.40726 - 0.01595 - 0.02711 0.00454
- 0.00402 - 0.01632 0.10626 - 3.81591 - 0.16378 - 0.06694
- 0.08299 0.05679 0.24226 0.04399 - 24.6245 - 0.02768
0.02361 - 0.00355 0.11904 0.00596 0.11742 3.93524
FP2
Fxa (W 3.20624 - 0.00809 0.06151 0.00046 0.00038 0.01688
FY. N 0.03332 - 0.79779 0.04171 0.00632 0.03933 0.02932
Fz. (N)
Mx. W-4
MY. (NW 0.05172 - 0.00103 0.04635 - 0.00347 - 24.2445 0.01473
Mz, Pm) 0.06987 0.02552 0.03217 0.01387 - 0.15197 - 3.76976
Fxs (4 FY. (4 Fzs C-4 M-s (4 MY. W Mz, (4
0.01821 - 0.00964 - 6.33152 0.00911 0.05490 0.00774
- 0.01231 - 0.04283 - 0.04826 3.62642 0.11456 - 0.05189
Mz, (Nm)
Table 2. Relative cross-sensitivity for the two force plates, expressed as the ratio of the individual load sensitivities to the principal cross-sensitivity coefficients FPl Fx, PJ) FY~(N) Fzs (N Mx, Wm) MY. (W W Oud FP2 Fx. WI FY. (NJ J% N Mx, Pm) MY. (Nm) Mz. (Nm)
Fxa (NJ 1 9.90 x 3.98 x 1.78 x 1.57 x 1.65 x
10-a 1O-3 1O-3 10-a 1O-3
F-G PO i.0101 9.71 x 1.27 x 1.57 x 4.48 x
10-s 1O-4 10-s lo-”
FY. (NJ
Fz. (NJ
Mx. Wm)
MY, (Nm)
Mz, (Nm)
lo-’ 1O-3 1O-4 10-a
0.0119 2.33 x 1O-3 1 4.18 x lo-” 1.10 x 10-s 1.15 x 10-a
1.34 x 1oy3 0.0200 0.0167 1 6.65 x lo-’ 0.0170
0.0277 0.0649 0.0378 0.0115 1 7.03 x lo- 3
7.89 x 1O-3 4.37 x 1o-3 0.0186 1.56 x lo-” 4.77 x lo-’ 1
FY. (NJ 0.0104 1 6.59 x lo-” 1.74 x 10-j 1.62 x 1O-3 7.78 x 1O-3
Fza (NJ 5.68 x lo-” 0.0121 1 2.51 x 10-j 2.27 x 1O-3 2.05 x 1O-3
Mx, (Nm) 3.84 x 1O-3 0.0537 7.62 x 1O-3 1 5.96 x 1O-3 0.0138
MY, (Nm) 0.0161 1.29 x 1O-3 7.32 x lo-” 9.57 x 1o-4 1 3.91 x 1o-3
Mz. (Nm) 0.0218 0.0320 5.08 x 1O-3 3.83 x lo-” 6.27 x 1O-3 1
6.04x 1 2.34 x 2.23 x 6.85 x 1.75 x
1O-3
Table 3. Mean difference sensitivities calculated using the calibration equations
FPl-Fx FPl-Fy FPl-Fz FPl-Mx FPl-My FPl-Mz FP2-Fx FP2-Fy FP2-Fz FP2-Mx FPZ-My FP2-Mz
MDS (%)
SE
N
0.04662 0.20302 0.05079 0.08965 0.11078 0.31291 0.11117 0.01877 0.28622 0.04296 0.13330 0.10259
0.072 0.156 0.110 0.409 0.174 0.281 0.112 0.209 0.074 0.487 1.740 0.408
20 45 36 30 39 iFI 45 36 30 39 30
Clearly if inferences about gait are to be made from the ground reaction forces care must be taken to ensure that apparent changes in the smaller horizontal forces are real, not just an effect of the change in the vertical load. The use of crosssensitivity calibration equations will reduce these errors. Results from our calibration procedure indicated that the actual force and. moment ~ values can be predicted to within 0.3% of the true value or better.
Fig. 4. Typical curves of variation with time of ground reaction force components for a 67 kg test subject.
CONCLUSION The procedures reported here relate to the calibration of Kistler piezo-electric force plates. The same procedures may be applied to other types such as those based on electrical resistive strain gauges. The calibration procedures described in this paper allow the output channels of a force plate to be accu tely calibrated with the minimum amount of specialist equi f ment
Technical Note
665
Table 4. Typical peaks during early and late stances (a) EarIy stance Measurand Value Effect on Spec. crosstalk Maximal crosstalk Measured load Max. crosstalk as Percentage of load (b) Late stance Measurand Value Effect on Spec. crosstalk Maximal crosstalk Measured load Max. crosstalk as Percentage of load
A-P (Fx)
Vertical (Fy)
- 138N
M-L (Fz)
726 N
-42N
FY
Fz
Fx
Fz
Fx
FY
Q +2% 2.76 N
d kl% 1.38 N
d *la? 7.26 N
Q *l% 7.26 N
Q *l% 0.42 N
c f2% 0.84 N
726 N f 0.4%
42N f 3.3%
138 N f 5.3%
42N + 17.3%
138N + 0.3%
726 N f 0.1%
A-P (Fx) 141 N Fz FY
Vertical (Fy) 801 N Fx
Fz
M-L (Fz) -36N Fx
FY
d *2% 2.82 N
S&l% 1.41 N
< kl% 8.01 N
< f 1% 0.36 N
< *2% 0.72 N
801 N * 0.4%
36N * 3.9%
141 N & 5.7%
36N f 22.3%
141 N * 0.3%
801 N f 0.1%
and disturbance. The procedures also enable the crosstalk to be estimated and compensated for. It is hoped that these procedures, or similar procedures, will be adopted by clinical and research laboratories to ensure accurate performance of their force plates. To further assist the accurate calibration of force plates, it is recommended that manufacturers should supply fixtures and fittings, along with clearly defined protocols, to allow the users of their force plates to perform practical in situ calibration and evaluation of crosstalk. Acknowledgements-MGH, MJD and SFDM were supported by SERC studentships. HEF and JPP were supported by the European Community AIM project CAMARC II. REFERENCES
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