2.7 Steady-state walking and ground reaction forces

Walking speed is defined as the center-of-mass velocity in the fore–aft direction. Steady-state walking is thought of as a state in which walking speed is constant. In reality, walking speed fluctuates slightly throughout the gait cycle, but during steady-state walking, the net change in walking speed from the beginning to the end of the gait cycle is zero.

(a) For steady-state walking, sketch the vertical and fore–aft ground reaction force components as functions of percent gait cycle. Which of these plots can be used to directly compute the fluctuations in fore–aft velocity over the gait cycle?

(b) On the relevant ground reaction force plot from part (a), label the following: (i) range when walking speed is increasing, (ii) range when walking speed is decreasing, (iii) instant when walking speed reaches a maximum, and (iv) instant when walking speed reaches a minimum. Please explain your answers. To simplify the problem, you may focus your analysis on the ground reaction forces acting on a single limb (i.e., ignore the ground reaction forces from the contralateral limb during double-support).

(c) How do the timings of increasing and decreasing walking speed you identified in part (b) compare to what you would expect from a simple, inverted-pendulum model of walking?

(d) Re-sketch the steady-state walking horizontal ground reaction force as a function of percent gait cycle. On this plot, sketch how you would expect the horizontal ground reaction force to change in the following conditions: (i) the person was speeding up, and (ii) the person was slowing down.