Stiffness analysis of parallel manipulators with linear limbs by considering inertial wrench of moving links and constrained wrench

A stiffness of the parallel manipulators with linear limbs is analyzed by considering the inertial wrench of the moving links and the constrained wrench. First, a formula is derived for solving the dynamic active and constrained wrenches, the inertial wrench of moving links based on the principle of virtual work. Second, the relationship between the elastic deformations of limbs and the dynamic active/constrained wrench and the inertial wrench of moving links are discovered and analyzed. Third, a unified stiffness model of parallel manipulators is established by considering the inertial wrench of moving links and the dynamic active/constrained wrench. Fourth, a unified formula is derived for solving the elastic deformations of the moving platform by considering the inertial wrench of the moving links and the dynamic active/constrained wrenches. Finally, an analytic numerical example of the 3SPR-type parallel manipulator is given for solving its stiffness and elastic deformation. The correctness of derived formulae of the stiffness and the elastic deformations are verified by the analytic numerical solutions.