Kinematics/statics of a 4-DOF over-constrained parallel manipulator with 3 legs

A 4-DOF over-constrained RRPU + 2UPU parallel manipulator (PM) with 3 legs is proposed, and its kinematics, statics, workspace, and singularity are studied systematically. First, the structure constraints and DOF (degree of freedom) of this PM are analyzed; and the geometric constrained equations are derived. Second, some analytic formulae are derived for solving the inverse/forward displacements, velocities, accelerations, active forces and torque of this PM. Third, a reachable workspace of this PM is constructed and analyzed. Finally, some analytic solutions are given and verified by its simulation mechanism.