A Parallel Manipulator with Planar Configurable Platform and Three End-Effectors

This work reports on the kinematic analysis of a planar parallel manipulator endowed with a configurable platform assembled with six terminal links serially connected by means of revolute joints. This topology allows the robot manipulator to dispose of three relative degrees of freedom owing to the mobility of an internal closed-loop chain. Therefore, the proposed robot manipulator can admit three end-effectors. The forward displacement analysis of the configurable planar parallel manipulator is easily achieved based on unknown coordinates denoting the pose of each terminal link. Thereafter, the analysis leads to twelve quadratic equations which are numerically solved by means of the Newton homotopy method. Furthermore, a closed-form solution is available for the inverse position analysis. On the contrary, the instantaneous kinematics of the robot manipulator is investigated by means of the theory of screws. Numerical examples are included with the purpose to illustrate the method of kinematic analysis.