Kinematic analysis of the hydraulic shoulder: a 3-DOF redundant parallel manipulator

In this paper, kinematic modeling of a three DOF redundant parallel manipulator has been elaborated in detail. It is known, that on the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, whose closed-form solution derivation is a real challenge. This issue is of great importance noting that the forward kinematics solution is a key element in closed loop position control of parallel manipulators. Using the novel idea of kinematic chains recently developed for parallel manipulators, both inverse and forward kinematics of our parallel manipulator are fully developed, and a closed-form solution for the forward kinematic map of the parallel manipulator is derived. The closed form solution is finally verified by simulated trajectories in the workspace of the manipulator.