Effects of Mass Distribution and Configuration on the Energetic Losses at Impacts of Bipedal Walking Systems

Understanding the dynamics of human walking is a complex task due to the interaction of the musculoskeletal and the central nervous systems. Nevertheless, the use of simple models can provide useful insight into the mechanical aspects of bipedal locomotion. Such models exploit the observations that human walking significantly relies on passive dynamics and inverted pendulum-like behaviour. The mechanical analysis of walking involves the study of the finite motion single support phase and the impulsive motion of the impacts that occur at heel strike. Such impacts are dominant events because they represent a sudden topology transition and moreover, they are the main cause of energy consumption during the gait cycle. The aim of this work is to gain insight into the dynamics and energetics of heel strike. We use a concept that decouples the dynamics of the biped to the spaces of admissible and constrained motions at the topology transition. This approach is then applied to a straight-legged biped with upper body. Detailed analysis and discussions are presented to quantify the effects of the mass distribution and the impact configuration on the energetics of walking. NOMENCLATURE AI Jacobian matrix of the impulsive inert constraints. AS Jacobian matrix of the finite motion constraints. M Mass matrix of the system. Pa Projector associated with the space of admissible motion. ∗Address all correspondence to this author. Pc Projector associated with the space of constrained motion. q Generalized coordinates of the system. q̇ Generalized velocities of the system. va Generalized velocities of the space of admissible motion. vc Generalized velocities of the space of constrained motion. L Step length. T Kinetic energy of the system. Ta Kinetic energy of the space of admissible motion. Tc Kinetic energy of the space of constrained motion. U Potential energy of the system. ξI Ratio of the pre-impact kinetic energy that is lost. ξL Energy loss due to impacts per unit distance. λ̄I Contact impulses on the colliding foot at heel strike. λS Contact forces on the stance foot during finite motion.