Bertec FIT - Calculation of the Point of Application of Force and Couple; Load Computation Example

Bertec Corporation Instrumented Treadmill Manual 25
Data Acquisition and Load Calculations
Calculation of the Point of Application of Force and Couple
A load system acting on a treadmill belt can be completely described by the six load components (i.e. the three force and three
moment components) calculated from the Force and signal scale factors equation. Alternatively, the same information can be
given as the three force components, the point of application of the force vector (x
p
, y
p
), and a couple (sometimes also referred
as “torque” or “free moment”) acting on the force plate. The point of application of the force and the couple are calculated from
the force and moment components as:
Where x
p
and y
p
are the coordinates of the point of application for the force (i.e. center of pressure) on the treadmill belt; h is
the height difference of the belt surface from the x-y plane of the coordinate system (see gures 11 and 12) and T
z
is the couple
acting on the force plate. The height h can be taken as 2.5 mm (0.10”).
Load Computation Example
Consider a case where the external amplier gain is set to 10 (note that the gain value is always the same for all of the six
channels). If, at an instant in time, the amplier voltage outputs for the six channels are:
Then, by dividing each output by the corresponding gain, the output signal values to be used in the Force and signal scale factors
equation are obtained:
Channel Output, V
1 -1.450
2 2.235
3 4.765
4 3.095
5 -0.575
6 -1.016
S
1
= -1.450/10 = -0.145 V
S
2
= 2.235/10 = 0.2235 V
S
3
= 4.765/10 = 0.4765 V
S
4
= 3.095/10 = 0.3095 V
S
5
= -0.575/10 = -0.0575 V
S
6
= -1.016/10 = -0.1016 V
x
p
=
-h
• F
x
- M
y
F
z
y
p
=
h
• F
y
+ M
x
F
z
T
z
= M
z
- x
p
• F
y
+ y
p
• F
x
Force and couple equation