MODELING OF ELASTIC RACKET PROPERTIES IN THE DYNAMIC COMPUTER SIMULATION OF TENNIS

Abstract

INTRODUCTION: Experimental difficulties in tennis research caused by the complexity of the stroke and the short contact phase demand the development of complex computer simulations models which can lead to a better understanding of the tennis stroke. Two different methods are currently in use: (1) The direct dynamics approach, which simulates the dynamic interaction between arm, hand, racket and ball, considering all inertial properties. (2) The finite element method, which analyses the elastic behavior of rackets under static conditions. The aim of this study was to evaluate a complex dynamic simulation model of the tennis stroke, including the elastic racket properties. Therefore a combination of both approaches was tested, by using the results of a finite element analysis as input for a flexible racket model in direct dynamics. METHODS: The racket model was an elastic beam (78 nodes) with parameters determined experimentally. For the dynamic analysis, the model was combined with a multiple rigid body pendulum simulating the players’ arm. By comparing the results of various stroke simulations with different boundary conditions and experimental data, the requirements of a flexible simulation model were worked out. The interesting parameters are acceleration and the vibration frequencies of the racket. RESULTS: First it must be stated that a complex dynamic tennis simulation including all important mechanical properties (inertial and elastic) of the racket is possible (Fig. 1). Second, the analysis of the vibrational parameters indicates that the tennis racket behaves as a freely vibrating body. Only the combination of this racket model with a suitable hand-racket-connection can simulate a real tennis stroke (Fig. 2). Thus, with the described model different previous results could be validated by computer simulation: (1) It is not necessary to fix the handle with large grip forces. (2) Racket tests with a clamped handle lead to incorrect results. CONCLUSIONS: The findings of this evaluation study confirm the possibilities of dynamic tennis simulation. Further investigations concerning the influences of racket properties (e.g., stiffness, node locations) on stroke characteristics are conceivable. [Figures]