Computationally Efficient Inverse Dynamics of a Spatial Parallel Mechanism Constrained Directly by the Base at Two Point-Contact Higher Kinematic Pairs

This study presents the efficient rigid-body inverse dynamics of a spatial parallel mechanism (PM) constrained directly by the base at two point-contact higher kinematic pairs (HKPs). The mechanism is designed to mimic the human masticatory system and is characterised by these constraints, from which parasitic motions and actuation redundancies are derived simultaneously. At the beginning, its constrained motions are analysed comprehensively. Then to seek efficient approaches to inverse dynamics and the influence of constraints at HKPs, three models are built using the Udwadia-Kalaba analytical mechanics method. In the first model, a dynamic model free of constraints from both the base and the chains to the end-effector is built first, and then these constraints are formulated to reach the complete dynamic model of the PM. In the second model, a dynamic model free of constraints only from the chains to the end-effector is built first, and then these constraints are imposed, achieving the complete dynamic model of the PM. Whilst in the third one, a dynamic model free of only direct constraints from the base to the end-effector is built first, and then these constraint forces are developed to arrive at the model of the PM. The results show that the second model is the most time-consuming. However, the first and third models can significantly reduce the computational complexity without any accuracy loss, which is even comparable to that of the PM's counterpart free of direct constraints from the base to the end-effector.