Energy-conserving impact algorithm for the heel-strike phase of gait

Significant ground reaction forces exceeding body weight occur during the heel-strike phase of gait. The standard methods of analytical dynamics used to solve the impact problem do not accommodate well the heel-strike collision due to the persistent contact at the front foot and presence of contact at the back foot. These methods can cause a non-physical energy gain on the order of the total kinetic energy of the system at impact. Additionally, these standard techniques do not quantify the contact force, but the impulse over the impact. We present an energy-conserving impact algorithm based on the penalty method to solve for the ground reaction forces during gait. The rigid body assumptions are relaxed and the bodies are allowed to penetrate one another to a small degree. Associated with the deformation is a potential, from which the contact forces are derived. The empirical coefficient-of-restitution used in the standard approaches is replaced by two parameters to characterize the stiffness and the damping of the materials. We solve two simple heel-strike models to illustrate the shortcomings of a standard approach and the suitability of the proposed method for use with gait.