Multiple Plates
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For athletes in archery and shooting, or for the elderly, stability is often an important issue. The center of pressure (CP) pattern is used in assessing subjects' stability and one force-plate is commonly used in measuring the CP pattern in most cases. But this task can be done with multiple plates if plates are too small to house both feet on one, and so on. The foot-ground interaction can be analyzed plate by plate, but it may be also necessary to assess the overall interaction between the body and the ground as a whole.

Figure 1 shows a multiple-plate system. Point Ci shown in the figure is the CP of the plate. Four force vectors measured by the sensors are identified in the figure: Fi1, Fi2, Fi3, and Fi4. Vectors Fi and Tzi are the ground reaction force and the free vertical torque of the plate, respectively. System OiXiYiZi is the local reference frame of the plate while OXYZ is the global reference frame.

    Figure 1

Let the global position of sensor j in plate i (sensor ij) be

,    [1]

where Ri = the global position of the CP of plate i, and r'ij = the relative position of the sensor to the plate's CP. The moment of force (torque) caused by the forces acting on plate i about the global origin is

,    [2]

where Mi = the moment of force of plate i about the global origin, M'i = the moment of force of the plate about its CP, and

.    [3]

M'i shown in [3], the moment of force caused by the four forces shown in Figure 1 about the plate's CP, is in fact equal to the free vertical torque, Tzi shown in the figure, or:

.    [4]

From [3] and [4], the total moment of force of the plates about the global origin is then

,    [5]

where M = the resultant moment of force about the global origin, R = the combined CP, F = the resultant ground reaction force, and Tz = the resultant free vertical torque:

.    [6]

As shown in [6], the combined CP is assumed to be on the XY-plane of the global reference frame. 

The resultant ground reaction force can be expressed as the sum of the ground reaction forces measured at the plates:

    [7]

From [5]:

,    [8]

or

.    [9]

From [9]:

    [10]

Finally, the global position of the CP of the plate can be obtained from the global position of the origin of the plate (Oi shown in Figure 1) and the position of the CP in the plate reference frame:

,    [11]

where ROi = the global position of the origin of the plate, and r'i = the position of the CP in the plate reference frame.

In summary, the resultant ground reaction force, the resultant moment of force about the global origin, the combined CP, and the resultant free vertical torque can be obtained from [7], [8], and [10].

 

Young-Hoo Kwon, 1998-