Abstract. The paper deals with the inverse dynamics of a kinematic chain of the human upper limb when throwing the ball at the basketball, aiming to calculate the torques required to put in action the technical system. The kinematic chain respects the anthropometric features regarding the length and mass of body segments. The kinematic parameters of the motion were determined by measuring the angles of body segments during a succession of filmed pictures of a throw, and the interpolation of these values and determination of the interpolating polynomials for each independent geometric coordinate. Using the Lagrange equations, there were determined the variations with time of the required torques to put in motion the kinematic chain of the type of triple physical pendulum. The obtained values show, naturally, the fact that the biggest torque is that for mimetic articulation of the shoulder, being comparable with those obtained by the brachial biceps muscle of the analyzed human subject. Using the obtained data, there can be conceived the mimetic technical system, of robotic type, with application in sports, so that to perform the motion of ball throwing, from steady position, at the basket.
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.
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