Figure 2. From force platform records to velocity and vertical displacement of the centre of mass.

The two top panels show, expanded, the vertical and fore-aft force during the step indicated in Fig. 1. The subject mass (M) times the simulated gravity (a_v) was subtracted from the vertical force (F_v) measured by the force platform, so that the signal above and below zero is proportional to the net vertical acceleration of the centre of mass of the subject. The fore-aft force in this passage is positive when the push against the platform is directed forward causing a deceleration of the centre of mass. The third panel shows the forward velocity obtained from the integration of the fore-aft force (hatched areas under the F_f curve) and evaluating the integration constant from the photocells signal. The fourth panel shows the vertical velocity, obtained from the integration of the vertical force minus the body weight (hatched areas under the F_v − Ma_v curve) assuming the integration constant is equal to zero. The bottom panel shows the vertical displacement of the centre of mass obtained from the integration of the vertical velocity (hatched areas under the V_v curve). The mechanical energy traces, such as those shown in Fig. 3, are calculated from the velocity and vertical displacement of the centre of mass as explained in the text.