Does an instrumented treadmill correctly measure the ground reaction forces?

Since the 1990s, treadmills have been equipped with multi-axis force transducers to measure the three components of the ground reaction forces during walking and running. These measurements are correctly performed if the whole treadmill (including the motor) is mounted on the transducers. In this case, the acceleration of the treadmill centre of mass relative to the reference frame of the laboratory is nil. The external forces exerted on one side of the treadmill are thus equal in magnitude and opposite in direction to the external forces exerted on the other side. However, uncertainty exists about the accuracy of these measures: due to friction between the belt and the tread-surface, due to the motor pulling the belt, some believe that it is not possible to correctly measure the horizontal components of the forces exerted by the feet on the belt. Here, we propose a simple model of an instrumented treadmill and we demonstrate (1) that the forces exerted by the subject moving on the upper part of the treadmill are accurately transmitted to the transducers placed under it and (2) that all internal forces - including friction - between the parts of the treadmill are cancelling each other.