Kinematics and singularity analysis of a 3-RPS parallel mechanism

The 3-RPS parallel mechanism with arc prismatic pairs is presented, this mechanism possesses a moving platform, a fixed platform, and three limb kinematic chains. Each limb kinematic chain consists of revolute pair R, a arc prismatic pair P, and a spherical joint S. The axis of revolute pairs are intersect each other and coplanar, the angle between two axes is 60°. Mobility, inverse solution and workspace of mechanism are analyzed via screw theory. This mechanism with three degrees of freedom, and the rotational center of moving platform is an intersection point of three straight lines, which passing through each center of arc rod and the center of spherical joint, and this intersection point changes with the posture of the moving platform. Furthermore, the Jacobian constraint matrix, the Jacobian actuation matrix and the Jacobian overall matrix are obtained, the singularity configurations of pose of moving platform are analyzed by a fixed rotation point or a fixed pose. The result provides a theoretical basis for kinematics and dynamics of this parallel mechanism.