Rigid-body inverse dynamics of a spatial redundantly actuated parallel mechanism constrained by two point contact higher kinematic pairs

This paper presents a comparative study of the rigid-body inverse dynamics of a spatial redundantly actuated parallel mechanism constrained by two point contact higher kinematic pairs (HKPs). Firstly, its constrained motions are analysed comprehensively, then four different models are formulated by the generalized momentum approach and the Lagrange-D'Alembert formulation to explore its inverse dynamics. In each method, the first model is built by employing the method directly to the mechanism. In the second model, the dynamic model of its non-redundantly actuated counterpart free of HKPs is built by this approach first, then the constraints from HKPs are modelled, to finally reach the model of the redundantly actuated parallel mechanism (RAPM) where that of its counterpart is utilised as the core. The four models give rise to equivalent numerical results, and the second model in both methods of the RAPM can alleviate the strong coupling between the parasitic motion variables and degrees of freedom (DOFs), boosting the computational speed as fast as that of its non-redundantly actuated counterpart without simplification or loss of accuracy. The comparisons between the mechanism and its counterpart validate that the HKP constraints greatly increase the computational complexity, and the torques required by the parasitic motions of the end effector are significantly smaller than those by the corresponding DOFs.