Biomechanics and energetics of bipedal and quadrupedal walking

Muscles set the metabolic demand of walking by lifting and accelerating the center of mass, supporting weight and swinging the limbs. Walking animals conserve energy with an inverted pendulum-like exchange of the gravitational potential and kinetic energies of the center of mass. I studied a variety of species including humans to better understand the factors that set the metabolic cost of walking and the function of the inverted pendulum mechanism. Penguins have a very high metabolic cost of walking (per unit weight). Previous speculation attributed this to excessive work of waddling and poor inverted-pendulum exchange. Rather, I found that emperor penguins conserve a large fraction of their mechanical energy with a novel three-dimensional inverted pendulum-like mechanism. Walking is likely expensive for penguins because their short legs require rapid generation of muscular force. Walking quadrupeds also use inverted pendulum-like mechanics. I found that the four legs of a dog behave like the two legs of a biped because the motions of the fore limbs lag the ipsi-lateral hindlimbs by less than a quarter of the stride and the fore limbs support more than half of body weight. I counteracted the force of gravity on walking humans and found that this only slightly disrupts the inverted pendulum mechanism. Thus, the relatively high (per unit weight) metabolic cost of walking in reduced gravity is not explained by the work performed on the center of mass. But, in normal gravity, performing work on the center of mass and generating force to support body weight equally explain about 60% of the increase in net metabolic rate over a four-fold speed range. Furthermore, when humans carry loads of 30% body weight at moderate speeds, net metabolic rate increases in direct proportion to both performing work on the center of mass and generating force to support weight, suggesting that the metabolic cost of swinging the limbs is relatively small at these speeds. A more complete understanding of the biomechanical determinants of the metabolic cost of walking must consider both the muscular costs of performing work and generating force.