Kinematics of Parallel Manipulators with Two End-Effectors

Abstract

In this paper methods of position analysis and determination of analogues of velocities and accelerations of the third class and the fifth class parallel manipulators (PM) with two end-effectors are developed. Position analysis of the considered PM is made by the method of conventional generalized coordinates. According to this method the system of loop-closure equations of mechanisms irrespective of their complexity are transformed to one equation with one variable parameter-the conventional generalized coordinate. Analogues of the angular velocities and the angular accelerations of the considered PM are determined by differentiating the loop-closure equations with respect to the generalized coordinates. In this case we obtain the system of linear equations for the analogues of angular velocities and angular accelerations. Determinants of these system of linear equations are Jacobians of the PM.