Analysis of stiffness and elastic deformation for a four-degree-of-freedom 4SPS + SP parallel manipulator with a SP passive constrained leg

Abstract

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.