A highly efficient computational strategy to model the inverse dynamics of a novel 4-DOF parallel mechanism with direct constraints from the base at two point-contact higher kinematic pairs

A spatial parallel mechanism (PM) that mimics the human masticatory system and then reproduces chewing behaviours has been proposed in a bio-inspired manner. Its end effector is directly constrained by the base at two point-contact higher kinematic pairs (HKPs), which imitate the temporomandibular joints (TMJs) in the masticatory system. The six chains play the role of the primary chewing muscles. The two direct constraints from the base simultaneously produce parasitic motions and actuation redundancy, rendering the inverse dynamics considerably complicated and time-consuming, which does not facilitate the model-based real-time motion and/or force control. As such, finding an efficient computational strategy is the aim of this study. Inspired by the procedure wherein the target PM is formed, the dynamic model of its counterpart free of these constraints can be utilised to build an efficient model. To validate the effectiveness of the proposed strategy, three dynamic methods, namely, Khalil-Ibrahim method, natural orthogonal complement, and Kane's equations, are employed. Under each of them two models are built for comparison. In the first model, the method is applied directly to the target PM as a regular strategy. In the second model, a highly efficient strategy is proposed. The dynamic model of its counterpart is built first, and then the direct constraints from the base at HKPs are formulated, reaching the inverse dynamic model of the target PM. The results show that the second model is far superior to the first in alleviating the computational complexity without any accuracy loss. It is concluded that the target PM is designed based on its counterpart free of HKPs; then its dynamic model can also be built based on that of its counterpart as a highly efficient strategy.