Inverse dynamics and inertia coupling analysis of a parallel mechanism with parasitic motions and redundant actuations

In this paper, a bio-inspired masticatory mechanism has been developed to reproduce the chewing behaviors of human beings. It is a natural spatial parallel mechanism constrained directly by the base at its end effector. These constraints form two point-contact higher kinematic pairs, producing parasitic motions and redundant actuations simultaneously. To facilitate the model-based control, a rigid-body inverse dynamic model is built and the inertia coupling is analyzed. Firstly, by virtue of a dynamic method, the Hessian matrices of the constraint equations and the kinetic energy are derived. The modeling process is straightforward, and the correctness is validated by virtue of the classical Lagrange equations. However, from the comparison between the technique in this method and a classical method in computing the first time derivative of the Jacobian matrices and the Coriolis-centrifugal force matrix, the former is more time-consuming. Secondly, the inertia coupling is analyzed via the inertia matrix in the joint space, showing that the first, third, and fourth active joints are the most strongly coupled. Finally, by comparing both the inverse dynamics and inertia coupling of the target mechanism and its counterpart, the foregoing constraints raise the computational cost of the inverse dynamics extraordinarily but greatly alleviate the inertia coupling.