Abstract
Bipedal walking following inverted pendulum mechanics is constrained by two requirements: sufficient kinetic energy for the vault over midstance and sufficient gravity to provide the centripetal acceleration required for the arc of the body about the stance foot. While the acceleration condition identifies a maximum walking speed at a Froude number of 1, empirical observation indicates favoured walk-run transition speeds at a Froude number around 0.5 for birds, humans and humans under manipulated gravity conditions. In this study, I demonstrate that the risk of 'take-off' is greatest at the extremes of stance. This is because before and after kinetic energy is converted to potential, velocities (and so required centripetal accelerations) are highest, while concurrently the component of gravity acting in line with the leg is least. Limitations to the range of walking velocity and stride angle are explored. At walking speeds approaching a Froude number of 1, take-off is only avoidable with very small steps. With realistic limitations on swing-leg frequency, a novel explanation for the walk-run transition at a Froude number of 0.5 is shown.
Highlights
Bipedal walking fits a mechanical description as an ‘inverted pendulum’, in which the body’s kinetic energy turns to potential energy at midstance and is returned as kinetic energy as the body falls during the second half of stance (Cavagna et al 1977); this is the mechanical definition of walking
The low speed limit for walking, due to the requirement of sufficient kinetic energy to power the vault over the leg, is indicated by (i): the slowest walking speeds are only achievable with small step lengths and low step frequencies
Walking at high Froude numbers and the associated high step frequencies is unappealing to humans
Summary
Bipedal walking following inverted pendulum mechanics is constrained by two requirements: sufficient kinetic energy for the vault over midstance and sufficient gravity to provide the centripetal acceleration required for the arc of the body about the stance foot. I demonstrate that the risk of ‘take-off ’ is greatest at the extremes of stance. This is because before and after kinetic energy is converted to potential, velocities (and so required centripetal accelerations) are highest, while concurrently the component of gravity acting in line with the leg is least. With realistic limitations on swing-leg frequency, a novel explanation for the walk–run transition at a Froude number of 0.5 is shown
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