225 Dynamics Analysis of Badminton- smash-motion in Consideration of Racket Shaft Deformation : Influence of inertial parameters of racket on the swing motion

Abstract

The previous studies indicate that the motion dependent term make significant roles for generating end-point speed of linked segment system, especially, in high-speed swing motions. Furthermore, badminton racket has elastic shaft due mainly to trim its weight. The purposes of this study were to quantify dynamical functional roles of upper joint torques and to evaluate influences of inertial parameters on the roles during badminton smash motion in considering deformation of racket shaft. The deformation of racket shaft was modeled as angular displacements of virtual joint settled between adjacent segments by dividing the shaft into rigid segments. The restoring torques about individual virtual joint axes of the shaft were calculated by assuming rotational spring about each axis of the joints. The upper limb segments and parts of racket were modeled as a system of seven-rigid linked segments, and constraint axes of the elbow, wrist and the virtual joints were modeled with constraint equation in order to consider the anatomical or mechanical degree of freedom at the individual joints. A recurrent equation with respect to the expanded generalized velocity vector, which consists of generalized velocity vector and the time integration of the velocity vector, is derived to calculate the contribution of the joint torque terms, external joint force term, and gravity term to the generation of the expanded generalized velocity vector.