Kinematics and Inverse Dynamic Model of a 3-PRS Paralel Robot

This paper develops the inverse kinematics and dynamics model of a general 3-PRS mechanism, which is a lower mobility parallel manipulator with each leg having a prismatics-revolution-spherical joints configuration. The analysis of each leg?s motion provides the constraint equations for the task space allowing to develop a dimensionally-homogeneous Jacobian matrix relating the linear and angular velocity of the task space. The inverse dynamics model is obtained by separating the platform and legs at the spherical joints. Then, the joint coordinates are used for the dynamic modelling of each leg while the task space coordinates are used for the platform's dynamics. The inverse dynamics model is given by the projection of the legs' and platform's dynamics onto the active joint space. Moreover, the method can be applied to analyse the mechanism when the actuators are installed on: the prismatic or revolute joints. The model presented here holds fewer mathematical operations compared to those reported in other works.