Plate Padding
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When one adds a pad to the surface of the plate, the CP coordinates need to be corrected. Figure 1 shows the relationship between the force plate reference frame (X'Y'Z' system) and the pad reference frame (XYZ system). F is the ground reaction force vector. Note that the coordinate system used in the figure is reaction-oriented rather than action-oriented. The +Y axis is the direction of motion.

Figure 1

Point P' shown in the figure is where the GRF is applied to the plate. In other words, the CP coordinates reported by the force plate software is the coordinates of point P' in the X'Y'Z' system. But if the investigator wants to use the pad reference frame (XYZ system), the coordinates of point P in the XYZ system must be obtained as the CP coordinates. (Since the pad plane is where the interaction between the body and the environment occurs, it is likely that one wants to use the pad reference frame instead of the plate reference frame.) Point P is the intersect of vector F and the pad surface. Since points P' and P are on the line of action of vector F, using P instead of P' as the CP does not affect the moment produced by F.

Let the thickness of the pad be t and vetor [nx, ny, nz] be the unit vector of F. Then:

k = t / nz        [1a]

x = x' + knx        [1b]

y = y' + kny        [1c]

where k = a scale constant, [x, y] = the coordinates of point P in the XY-system, and [x', y'] = the coordinates of point P' in the X'Y'-system. [x, y] above are the new CP coordinates to be used in the data analysis.

A problem arises when the pad is soft. Deformation of the pad causes change in man-environment interface plane. There is no solution for this in terms of CP coordinates.
When one wants to use the ground reaction force data in the inverse dynamics, one can use either of the two different coordinate sets as the position of the CP: [x, y, 0] or [x', y', -t]. This is because both points P and P' are on the line of action of vector F. This also means that even if your pad is soft, you can still use [x', y', -t] as CP. Don't forget to include in your inverse dynamics model the free torque (Tz shown in Figure 1d of Ground Reaction Force).

One may want to compute the corrected CP coordinates directly from the force and moment components obtained from the plate. For example, the corrected CP of an AMTI force-plate can be easily obtained from [3a & b] of Center of Pressure:

        [2a]

        [2b]

where [x, y] = the position of the CP, t = the thickness of the pad, [a, b, c] = the true origin of the plate reported in the calibration sheet, [Fx, Fy, Fz] = the ground reaction force measured from the plate, and [Mx, My, Mz] = the moment measured from the plate. KwonGRF uses [2a & b] in computing the CP for the AMTI plates and for the Bertec plates. Note again that AMTI uses the action-oriented coordinate system while KwonGRF uses the reaction-oriented coordinate system.

[7a & b] of Center of Pressure can be corrected for the Kistler plates as well:

        [3a]

        [3b]

 

Young-Hoo Kwon, 1998-