Contact Modeling and Identification of Planar Somersaults on the Trampoline

Abstract

This paper presents an extensive study on the trampoline-performed planar somersaults. First, a multibody biomechanical model of the trampolinist and the recurrently interacting trampoline bed are developed, including both the motion equations and the determination of joint reactions. The mathematical model is then identified –the mass and inertia characteristics of the human body are estimated, and the stiffness and damping characteristics of the trampoline bed are measured. By recording the actual somersault performances the motion characteristics of the stunts, i.e. the time variations of positions, velocities and accelerations of the body parts are also obtained. Finally, an inverse dynamics formulation for the system designated as an under-controlled system, is developed. The followed inverse dynamics simulation results in the torques of muscle forces in the joints that assure the realization of the actual motion. The reaction forces in the joints during the analyzed evolutions are also determined. Using the kinematic and dynamics characteristics, the nature of the stunts, the way the human body is maneuvered and controlled, can be studied.