Mobility analysis of the 3-UPU parallel mechanism based on screw theory

A method based on screw theory is proposed to perform mobility analysis of a 3-UPU manipulator with three translational degrees. The method includes four steps: (1) representation of motions of joints in each serial kinematic chain in a 3-UPU manipulator with screws (twist system); (2) generation of wrenches reciprocal to all twists in each serial chain; (3) put wrenches of all three! serial kinematic chains together in a reference frame; (4) analyse all wrenches of all serial chains independently and get the independent constraint motions of end effector. If the number of the allowed independent motions is more than the number of anticipant degrees of freedom, the parallel manipulator has uncontrollable degrees of freedom and is in singular configuration. Three types of singularity are given and posture calculating method for each type of singularity is proposed.