Efficiency, speed, and scaling of two-dimensional passive-dynamic walking

We address performance limits and dynamic behaviours of the two dimensional passive-dynamic bipedal walking mechanisms of Tad McGeer. The results highlight the role of heelstrike in determining the mechanical efficiency of gait, and point to ways of improving efficiency. We analyse several kneed and straight-legged walker designs, with round feet and and point-feet. We present some necessary conditions on the walker mass distribution to achieve perfectly efficient (zero-slope-capable) walking for both kneed and straight-legged models. Our numerical investigations indicate, consistent with a previous study of a simpler model, that such walkers have two distinct gaits at arbitrarily small ground-slopes, of which the longer-step gait is stable at small slopes. Energy dissipation can be dominated by a term proportional to (speed) 2 from tangential foot velocity at heelstrike and from kneestrike, or a term proportional to (speed) 4 from normal foot collisions at heelstrike, depending on the gait, ground-slope, and walker design. For all zeroslope capable straight-legged walkers, the long-step gaits have negligible tangential foot velocity at heelstrike and are hence especially fast at low power. Some apparently chaotic walking motions are numerically demonstrated for a kneed walker.