[A theoretical model of the transition phase in human locomotion]

In this study we examine the bifurcation of the transition between walking and running. Beuter and Lalonde (1986) have conjectured that the pertinent parameters separating walking and running can be described by a cusp singularity (Thom, 1972). In this model, the unidimensional state space is characterized by support duration and the bidimensional parameter space is characterized by the subject's weight and speed. To test this model eight males walked and ran on a motor driven treadmill at an increasing or decreasing speed with or without additional loads corresponding to 0%, 7% and 14% of their body weight. Velocities corresponding to transitions between the two modes of locomotion indicate that on the average the walk-run transition occurs at higher speed than the run-walk transition illustrating an hysteresis effect. In addition, the average difference between the transitions decreases as the load increases [mean 0 = 0.235 m/s, +/- 0.09 m/s, mean 7 = 0.104 m/s, +/- 0.07 m/s and mean 14 = 0.041 m/s, +/- 0.06 m/s] corresponding to an F ratio of F = 2.72, 0.05 less than p less than 0.1. A comparison of the differences in transition velocity at 0% and 14% is statistically different (t = 2.8, p less than 0.025). These results tend to support the existence of an elementary cusp singularity separating the two locomotion modes and suggest that the mechanisms controlling these transitions can be described by a hysterisis cycle and a small number of parameters.