A comparative study of inverse dynamics in a spatial redundantly actuated parallel mechanism constrained by two point-contact higher kinematic pairs

A life-sized spatial redundantly actuated parallel mechanism (RAPM) constrained by two point-contact higher kinematic pairs (HKPs) has been designed, inspired by the mastication of human beings. To facilitate its real-time control in practice, an accurate inverse dynamics model is built in this paper. Firstly, its constrained motions are described, thereafter three dynamics methods, i.e., Newton-Euler’s law, the Lagrangian equations and the principle of virtual work, respectively, are used to explore its rigid-body inverse dynamics. Symbolic results show that model structures based on these approaches are quite different. The model via Newton-Euler’s law well reflects the nature of the mechanism in terms of the constraint forces at HKPs, while those from the latter two methods do not contain them. Despite this, the actuating torques from these three models are identical. The comparisons between the dynamics models of the RAPM and its counterpart free of HKPs clarify that the constraints at HKPs greatly alter the model structures and numerical results, and the computational difficulties are considerably larger in the models of the RAPM.