Dynamics of a class of parallel wrists

This paper presents a dynamic model of parallel wrists with all links constrained to have a spherical motion with the same center. The model can also be applied to serial wrists. The model, based on Lagrangian formulation of dynamics, exploits the feature that all the links have the same fixed point. Three parameters defining the platform orientation are used as generalized coordinates. This choice allows the use of the generalized inertia matrix (GIM) appearing in the model to calculate effective dynamic performance indices proposed in a previous paper. The model can solve both the direct and the inverse dynamic problems. It also contains the Jacobian matrix useful to characterize the kinematic behavior of parallel manipulators. By the model it is shown that the best performances are reached in the workspace regions where the manipulator has a good kinematic and dynamic isotropy, whereas the incidence of nonlinear forces on performances is relevant at high end-effector speed. A numerical example is provided.