Leg compliance is required to explain the ground reaction force patterns and speed ranges in different gaits

Two simple models, vaulting over stiff legs and rebounding over compliant legs, are employed to describe the mechanics of legged locomotion. It is agreed that compliant legs are necessary for describing running and that legs are compliant while walking. Despite this agreement, stiff legs continue to be employed to model walking. Here, we show that leg compliance is necessary to model walking and, in the process, identify the principles that underpin two important features of legged locomotion: First, at the same speed, step length, and stance duration, multiple gaits that differ in the number of leg contraction cycles are possible. Among them, humans and other animals choose a gait with M-shaped vertical ground reaction forces because it is energetically favored. Second, the transition from walking to running occurs because of the inability to redirect the vertical component of the velocity during the double stance phase. Additionally, we also examine the limits of double spring-loaded pendulum (DSLIP) as a quantitative model for locomotion, and conclude that DSLIP is limited as a model for walking. However, insights gleaned from the analytical treatment of DSLIP are general and will inform the construction of more accurate models of walking.