
Calibration Matrix Provided by the Manufacturer Forceplate (straingaugetype) manufacturers normally provide a unique calibration matrix for each plate. This matrix is the result of a series of computerized calibrations at the factory. For example, AMTI provides with a calibration matrix in the following form:
where a_{ij} = element of the calibration matrix given in either N/(mV/V of excitation) or N·m/(mV/V of excitation). Bertec provides with calibration matrices in a similar form:
where b_{ij} is given in either N/V (first 3 rows) or N·m/V (last 3 rows). In either case, the diagonal terms of the calibration matrix are the actual calibration coefficients while the offdiagonal terms are the crosstalk terms. In an ideal situation in which there is no crosstalk among the channels, all the offdiagonal terms become 0. Some crosstalks always exist in the straingaugetype plates. The corrected calibration matrix to be used in converting the outputs from the channels to force & moment components has the following form:
where c_{ij} is in either N/ADU (force channels, first 3 rows) or N·cm/ADU (moment channels, last 3 rows). Here, ADU stands for the A/D converter unit. Matrix C can be applied to the channel output matrix for the computation of the actual force & moment components:
where [F_{x}, F_{y}, F_{z}] = the ground reaction force, [M_{x}, M_{y}, M_{z}] = the moment about the true origin of the plate, [F_{x}', F_{y}', F_{z}', M_{x}', M_{y}', M_{z}'] = the outputs from the 6 channels of a straingauge plate in ADU. See the Center of Pressure page for the details of the true origin of the plate. Figure 1 shows the typical system layout of the ground reaction force measurement system. The signals from the plate are first amplified by an amplifier and fed to the A/D converter residing in the computer. The analog signals are converted to digital info (numbers) by the A/D converter. Thus the final output of the such a system is the digitalized voltage levels of the channels with the unit being ADU. Although the calibration matrices provided by the manufacturers ([1] & [2]) basically present the response characteristics of the plates, they are not readily applicable and need some corrections. This is because the matrices provided by the manufacturers do not directly relate the output from the A/D converter to the actual physical quantities such as force and moment.
Matrix Correction for the AMTI Plates Assuming that the excitation voltage of the plate is E V, the relationship between the channel outputs and the actual GRF components at stage 1 shown in Figure 1 can be expressed as
where [F_{x}, F_{y}, F_{z}] = the ground reaction force in N, [M_{x}, M_{y}, M_{z}] = the moment about the true origin in N·m, a_{ij} = element of the calibration matrix provided by AMTI, and [F_{x}', F_{y}', F_{z}', M_{x}', M_{y}', M_{z}'] = channel outputs at stage 1 in mV. At stage 2 shown in Figure 1, the relationship between the amplified channel outputs and the actual force and moment components becomes
where G = the gain of the amplifier, and [F_{x}', F_{y}', F_{z}', M_{x}', M_{y}', M_{z}'] = channel outputs at stage 2 in V. Note in [6] that 10^{6} was multiplied to the element to change the unit of the channel outputs from mV to V. Now, let's assume that the maximum input voltage range of the A/D converter be R V and the resolution of the converter be L bits. In other words, R V is equivalent to 2^{L} ADU:
Changing the unit of the channel outputs from V to ADU in [6], at stage 3 shown in Figure 1:
where [F_{x}', F_{y}', F_{z}', M_{x}', M_{y}', M_{z}'] = channel outputs at stage 3 in ADU, and k = the correction coefficient. For example, the typical setup for an AMTI plate is E = 10, G = 4000, R = 20 (10 to 10 V), and L = 12 (12 bits). Therefore, correction coefficient k shown in [8] is
From [3], [8], and [1] of ReactionOriented Coordinate System:
where a_{ij} = element of the calibration matrix provided by AMTI, and c_{ij} = element of the corrected calibration matrix. Note here that 10^{2} was multiplied to the elements for the moment components to convert the resulting unit of the moment from N·m to N·cm because cm rather than m is commonly used as the unit of position in the ground reaction force analysis. The resulting force & moment components computed by applying matrix C in [10] are described in the reactionoriented coordinate system and readily applicable in the inverse dynamics. See the ReactionOriented Coordinate System page for the details. The correction coefficient for a Bertec plate becomes

© YoungHoo Kwon, 1998 