Inverse dynamics and internal forces of the redundantly actuated parallel manipulators

This article first presents a novel method that solves the inverse force problem of the redundantly actuated parallel manipulators. By taking into account the elastic deformation of the supporting limbs, compatibility equation of the elastic deformation of all the supporting limbs is derived based on the law of conservation of energy, and then the solution to the inverse dynamics of the redundantly actuated parallel manipulators is derived by incorporating the deformation compatibility equation. Next, discussion on whether internal forces exist within the pseudo-inverse solution to the inverse dynamics of the redundantly actuated parallel manipulators is carried out, and effects of the stiffness of the supporting limbs on the internal forces are also discussed. Finally, a redundantly actuated forging manipulator 2SPS + R is investigated as a case, the proper actuated forces are obtained so as to coordinate the elastic deformation of the forging manipulator 2SPS + R and avoid destruction of the whole mechanical system.