The Kinematic Model with Three Degrees of Freedom Associated to the Direct Throwing in Basketball Game

Abstract

The paper presents a reverse kinematic analysis for the free through to basket in order to determine the possible angular movement speed of the arm segments during throw flexion. The body segments offering three freedom degrees to the kinematic model are: the arm, the forearm and the hand. From geometric conditions regarding to the possibility of the ball to get through the basket and the analysis of the parabolic trajectory of the ball, one could determine the mathematical relations for the limitative values of the horizontal and vertical components of the initial velocity and consequently, for the calculation of the initial angle of throwing the ball. On the other hand, from the expression of the flexion movement of the considered body segments, it could be possible to obtain the calculation of the initial throw velocity as functions of the anthropometric data of the analyzed subject, of flexion angles and angular velocity of movement of the body segments. Using some models of functional mathematic analysis, from the two equations with three unknowns, one could determine the variation field of the system solutions. By setting the conditions related to the numeric limits of variation for the angular speed, the numeric field of the possible solutions for the equation system is straitened.