Usherwood James Richard
Structure and Motion Laboratory, The Royal Veterinary College, University of London, North Mymms, Herts AL9 7TA, UK.
Biol Lett. 2005 Sep 22;1(3):338-41. doi: 10.1098/rsbl.2005.0312.
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.
有足够的动能用于跨越身体重心，以及有足够的重力来提供身体围绕支撑脚做弧线运动所需的向心加速度。虽然加速度条件确定了弗劳德数为1时的最大行走速度，但经验观察表明，鸟类、人类以及在模拟重力条件下的人类在弗劳德数约为0.5时更倾向于从行走过渡到奔跑。在本研究中，我证明“起飞”风险在站立阶段的极端时刻最大。这是因为在动能转化为势能之前和之后，速度（以及所需的向心加速度）最高，而与此同时，与腿部方向一致的重力分量最小。本文探讨了行走速度和步幅角度范围的限制。在行走速度接近弗劳德数为1时，只有通过非常小的步幅才能避免“起飞”。考虑到摆动腿频率的实际限制，本文给出了弗劳德数为0.5时从行走过渡到奔跑的新解释。
