This paper presents the Dynamics modeling for a 3-dof special 3-PSP (Prismatic-Spherical-Prismatic) parallel manipulator using Natural Orthogonal Complement method. The 3-PSP mechanism consists of a movable platform (formed like a star) and a fixed base that are connected to each other by means of three PSP legs. The manipulator consists of 15 joints which three of them are driven by three independent actuators. The remaining twelve joints (nine revolute for three spherical and three upper prismatic) are functioning as passive joints. In this design, we have chosen to actuate the first prismatic joint in each leg by connecting the motor to a ball screw. By differentiating the constraint equations (resulting from the manipulator structure) with respect to both active and passive joints the Joint Orthogonal Complement matrix is driven. This matrix derives all the passive joints velocities in the terms of active joint velocities. Utilizing the twist of each rigid body and the Joint Orthogonal Complement matrix, the Natural Orthogonal Complement (NOC) matrix is derived. The use of this matrix will enable us to derive the equations of motion for the 3-PSP manipulator. The derived equations could be either used in inverse dynamics applications or direct dynamics simulations for this manipulator.

Keywords