Humans tend to swing their arms when they walk, a curious behaviour since the arms play no obvious role in bipedal gait. It might be costly to use muscles to swing the arms, and it is unclear whether potential benefits elsewhere in the body would justify such costs. To examine these costs and benefits, we developed a passive dynamic walking model with free-swinging arms. Even with no torques driving the arms or legs, the model produced walking gaits with arm swinging similar to humans. Passive gaits with arm phasing opposite to normal were also found, but these induced a much greater reaction moment from the ground, which could require muscular effort in humans. We therefore hypothesized that the reduction of this moment may explain the physiological benefit of arm swinging. Experimental measurements of humans (n= 10) showed that normal arm swinging required minimal shoulder torque, while volitionally holding the arms still required 12 per cent more metabolic energy. Among measures of gait mechanics, vertical ground reaction moment was most affected by arm swinging and increased by 63 per cent without it. Walking with opposite-to-normal arm phasing required minimal shoulder effort but magnified the ground reaction moment, causing metabolic rate to increase by 26 per cent. Passive dynamics appear to make arm swinging easy, while indirect benefits from reduced vertical moments make it worthwhile overall.

The plantigrade human foot rolls over the ground during each walking step, roughly analogous to a wheel. The center of pressure progresses on the ground like a wheel of radius 0.3 L (leg length). We examined the effect of varying foot curvature on the mechanics and energetics of walking. We controlled curvature by attaching rigid arc shapes of various radii to the bottoms of rigid boots restricting ankle motion. We measured mechanical work performed on the center of mass (COM), and net metabolic rate, in human subjects (N=10) walking with seven arc radii from 0.02–0.40 m. Simple models of dynamic walking predict that redirection of COM velocity requires step-to-step transition work, decreasing quadratically with arc radius. Metabolic cost would be expected to change in proportion to mechanical work. We measured the average rate of negative work performed on the COM, and found that it followed the trend well (r²=0.95), with 2.37 times as much work for small radii as for large. Net metabolic rate (subtracting quiet standing) also decreased with increasing arc radius to a minimum at 0.3 L, with a slight increase thereafter. Maximum net metabolic rate was 6.25 W kg^–1 (for small-radius arc feet), about 59% greater than the minimum rate of 3.93 W kg^–1, which in turn was about 45% greater than the rate in normal walking. Metabolic rate was fit reasonably well (r²=0.86) by a quadratic curve, but exceeded that expected from COM work for extreme arc sizes. Other factors appear to increase metabolic cost for walking on very small and very large arc feet. These factors may include effort expended to stabilize the joints (especially the knee) or to maintain balance. Rolling feet with curvature 0.3 L appear energetically advantageous for plantigrade walking, partially due to decreased work for step-to-step transitions.

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.

Muscle–tendon units about the ankle joint generate a burst of positive power during the step-to-step transition in human walking, termed ankle push-off, but there is no scientific consensus on its functional role. A central question embodied in the biomechanics literature is: does ankle push-off primarily contribute to leg swing, or to center of mass (COM) acceleration? This question has been debated in various forms for decades. However, it actually presents a false dichotomy, as these two possibilities are not mutually exclusive. If we ask either question independently, the answer is the same: yes! (1) Does ankle push-off primarily contribute to leg swing acceleration? Yes. (2) Does ankle push-off primarily contribute to COM acceleration? Yes. Here, we summarize the historical debate, then synthesize the seemingly polarized perspectives and demonstrate that both descriptions are valid. The principal means by which ankle push-off affects COM mechanics is by a localized action that increases the speed and kinetic energy of the trailing push-off limb. Because the limb is included in body COM computations, this localized segmental acceleration also accelerates the COM, and most of the segmental energy change also appears as COM energy change. Interpretation of ankle mechanics should abandon an either/or contrast of leg swing versus COM acceleration. Instead, ankle push-off should be interpreted in light of both mutually consistent effects. This unified perspective informs our fundamental understanding of the role of ankle push-off, and has important implications for the design of clinical interventions (e.g. prostheses, orthoses) intended to restore locomotor function to individuals with disabilities.