# A SIMPLE MATHEMATICAL MODEL FOR ESTIMATING FORCE AND TORQUE TO THE WRIST ELBOW AND SHOULDER IN SERVING, SPIKING AND BLOCKING IN VOLLEYBALL

Keywords:
indirect, measurement, volleyball, force, torque

### Abstract

INTRODUCTION: Spiking, blocking and serving with high speed ball may cause shoulder dislocation and subluxation, elbow contusion, wrist sprain, fingers sprains, fractures and dislocations. These damages may come from the impulses caused by a simple spike with the velocity of, say 25 m/s. We considered a mechanical model for which we used a mathematical relationship with which we can easily estimate the velocity of the ball, force and torque to the upper extremity. METHOD: In order to estimate ball velocity in spiking or serving, for example, we designed a ballistic pendulum with the mass of 20 kg and the length of 7m. This pendulum is essentially used for determining the velocity of bullets. Having this in mind, we used the rule of the pendulum, in order to determine the velocity of the ball as: V M gh e m BO P B = + 2 1 / ( ) . We have also found out the force transferred to the pendulum by equalizing the potential energy gained ( M gh P ) with the work done on it (TDq ), and we obtained this force as : F m V e t P B BO = + ( ) / 1 D . The contact time of the ball with the pendulum was also found as: D D t m V e l M gh P B BO P = + ( ) / 1 q , in which VBO is the initial velocity of the ball, MP mass of the pendulum, mB mass of the ball, e is the coefficient of restitution and h is the hight which the pendulum has gained by impact. RESULTS: We used two national team volley ball players, two top university players and two beginners as subjects. The results are given in table 1: Table 1. [table] CONCLUSION: The method we propose is very simple and reliable in use; it can also be applied to football, and handball. With the anthropometric data, the torque resulting from the measured force can easily be obtained.
Section

Muscle-Skeleton-Mechanics

Authors can retain copyright, while granting the International Society of Biomechanics in Sports (ISBS) the right of first publication.