Analysis Of Stiffness And Elastic Deformation For A Four-degree-of-freedom 4sps + Sp Parallel Manipulator With A Sp Passive Constrained Leg

摘要

The total stiffness matrix and elastic deformation of a four-degree-of-freedom (4-dof) four-spherical joint-active prismatic joint-spherical joint plus spherical joint-prismatic joint (4SPS + SP) parallel kinematic machine (PKM) with a passive constrained leg are studied systematically. First, the workspace of this PKM is constructed, and the poses of the active/constrained forces are determined. Second, based on the poses of active/constrained forces, the formulae are derived for solving the kinematics/statics, and some singularities of this PKM are determined. Third, a stiffness matrix of four spherical joint-active prismatic joint-spherical joint (SPS) active legs and one spherical joint-prismatic joint (SP) passive constrained leg is established. Finally, a total stiffness matrix and the elastic deformation of this PKM are solved and analysed based on the kinematics/statics formulae, the stiffness matrix of legs, and the principle of virtual work.