Redirection of center-of-mass velocity during the step-to-step transition of human walking

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Abstract
SUMMARY Simple dynamic walking models based on the inverted pendulum predict that the human body9s center of mass (COM) moves along an arc during each step, with substantial work performed to redirect the COM velocity in the step-to-step transition between arcs. But humans do not keep the stance leg perfectly straight and need not redirect their COM velocity precisely as predicted. We therefore tested a pendulum-based model against a wide range of human walking data. We examined COM velocity and work data from normal human subjects (N=10) walking at 24 combinations of speed (0.75 to 2.0 m s–1) and step length. These were compared against model predictions for the angular redirection of COM velocity and the work performed on the COM during redirection. We found that the COM is redirected through angular changes increasing approximately linearly with step length (R2=0.68), with COM work increasing with the squared product of walking speed and step length (R2=0.82), roughly in accordance with a simple dynamic walking model. This model cannot, however, predict the duration of COM redirection, which we quantified with two empirical measures, one based on angular COM redirection and the other on work. Both indicate that the step-to-step transition begins before and ends after double support and lasts about twice as long – approximately 20–27% of a stride. Although a rigid leg model can predict trends in COM velocity and work, the non-rigid human leg performs the step-to-step transition over a duration considerably exceeding that of double support.