Abstract: For lower mobility parallel manipulators (PMs), the constrained forces/torques appear because the structure constraint exists. The constrained forces/torques must be considered in analyzing the stiffness for PMs because the constrained forces/torques can produce elastic deformation and affect the precision of PM. The stiffness of a traditional parallel manipulator 3-RPS is analyzed to illustrate this method. First, the constrained forces are analyzed on the basis of the observation method. Second, the 6×6 Jacobian matrix is established, and the statics model is established by applying the principle of virtual work. Finally, the deformation of the PM is analyzed with the active forces and the constrained forces considered. The stiffness of 3-RPS PM is analyzed by converting the 3-DOF PM into a 6-DOF PM free from constrained forces/torques by setting virtual P joints along the direction of constrained forces. This method provides some new points of view for lower mobility PMs.

Key words: Jacobian matrix, Statics, Stiffness