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Center of Pressure (GRF Application Point) Computation of the CP Application

Center of Pressure (GRF Application Point)

As shown in Figure 1, all the forces acting between the foot and the ground can be summed to yield a single ground reaction force vector (F) and a free torque vector (T_z). The point of application of the ground reaction force on the plate is the center of pressure (CP). All the small reaction forces collectively exert on the surface of the plate at the CP.

    Figure 1

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Computation of the CP

Generally, the true origin of the strain gauge force-plate is not at the geometric center of the plate surface. This is due to problems in the manufacturing process. The manufacturers usually go through a series of calibrations and estimate the position of the true origin. Here, we assume that the true origin (O' shown in Figure 2) is at (a, b, c). The Z component of the CP position is always 0. The moment measured from the plate is equal to the moment caused by F about the true origin plus T_z:

   Figure 2

   [1]

or:

   [2]

Eventually:

    [3]

Therefore, the position of the CP can be computed from the moment caused by the ground reaction force about the true origin, M_x, M_y & M_z, the ground reaction force, F_x, F_y & F_z, and the location of the true origin, a, b & c. M_x, M_y, M_z, F_x, F_y & F_z can be directly measured from the 6 channels of the AMTI plates while the position of the true origin can be found in the calibration data sheet.

The Kistler plates provide a different channel configurations: F_1z, F_2z, F_3z, F_4z, F_1x + F_2x, F_3x + F_4x, F_1y + F_4y, & F_2y + F_3y. In Figure 3a, the location of the sensors are described by three distance factors: a, b & g. Among these g is the depth of the sensor center from the surface. The sum of the moments caused by the four forces is equal to the moment caused by the ground reaction force (F) plus the free vertical torque (T_z) as shown in Figure 3b.

    Figure 3

   [4]

   [5]

   [6]

Therefore,

   [7]

One must know a, b & g to compute of x & y and subsequently T_z. Note in [7] that only 8 groups of ground reaction force data are required to compute x, y & T_z:

F_1x+F_2x, F_3x+F_4x
F_1y+F_4y, F_2y+F_3y
F_1z, F_2z, F_3z, F_4z

This is why a Kistler force plate has 8 channels of output. Further simplifying [7]:

,    [8]

where

.    [9]

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Application

Here are important issues one has to pay attention to.

	As shown in [3] & [7], the CP position, (x, y), can be very sensitive to errors in the moment & force components for a small Fz. This is why we get erroneous CP positions at the beginning and end of the foot contact phase where Fz is fairly small. A small error can be easily introduced during the zero-setting procedure if the system is not well set up.
	For this reason, one needs to set the threshold for Fz. If Fz is smaller than the threshold, the program does not generate the CP coordinates.
	The CP position needs to be corrected if one adds a pad on the surface of the plate and use the center of the pad surface as the origin of the reference frame. See Plate Padding for the details.

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© Young-Hoo Kwon, 1998-