Kinematics of the 4-RUU parallel manipulator generator of the Schönflies motion by means of screw theory

This work deals with the inverse–forward kinematic analysis of a symmetric parallel manipulator equipped with a rotary actuator generator of three independent translations and one rotation motion. The closure equations of the displacement analysis are easily formulated based on the unknown coordinates of two points embedded in the moving platform. The input–output equations of velocity and acceleration of the robot are systematically obtained through the reciprocal-screw theory. The pseudo-kinematic pairs that connect the limbs to the fixed platform and a passive kinematic chain connected to the robot manipulator eliminate the handling of rank-deficient Jacobian matrices, which is an undisputable advantage from the computational point of view. Furthermore, this strategy allows the use of the Lie algebra se(3) without the inherent restrictions associated with the limited mobility of the robot.