Stiffness analysis of a 3CPS parallel manipulator for mirror active adjusting platform in segmented telescope

In order to adjust the pose of mirror in segmented telescope initiatively, an active adjusting platform with a novel 3CPS PM as core module is proposed. It consists of a fixed base and a moving platform that is connected by three cylindrical-prismatic-spherical active legs. In this paper, the stiffness characteristics of the 3CPS PM with six DOF are studied systematically. First, the kinematics and statics are derived by the Rodrigues parameters method. Second, the stiffness matrix is proposed which is derived intuitively based on the principle of virtual work considering the compliances subject to both actuators and legs. Next, the elastic deformations of the moving platform corresponding to a given variation of pose parameters and external workload are analyzed. Moreover, applying a procedure iteratively over the workspace, the stiffness maps at initial height position are obtained. Finally, a FE model of the manipulator is constructed and the elastic deformations of FE model are basically coincident with that of analytic results. Both the analytical and FE results show that the stiffness characteristics of active adjusting platform satisfy the functional requirements of segmented telescope.

► A mirror active adjusting platform in segmented telescope with a novel 3CPS PM as core module is proposed.
► The formulae for solving kinematics and statics are derived based on the Rodrigues parameters.
► The stiffness matrix of 3CPS PM is derived intuitively.
► The variation tendency of stiffness within the workspace is presented.