Solving Stiffness and Elastic Deformation of Two Limited-Degree-of-Freedom Parallel Manipulators with a Constrained Leg Based on Active/Constrained Wrench

Some total stiffness matrices of two different limited-degree-of-freedom parallel manipulators (PMs) with an active/passive constrained leg are derived and their elastic deformations are solved based on active/constrained wrench. The force situations of these PMs are analyzed and the poses of the active/constrained wrench are first determined. Then, the elastic deformations of the active/constrained legs in these PMs are analyzed and the compliance matrices of the active/constrained legs are derived. Based on the 6 × 6 Jacobian matrices and the compliance matrices of active/constrained legs, some total stiffness matrices and the elastic deformations of these PMs are derived and analyzed.