Nonlinear dynamic modeling and performance analysis of a redundantly actuated parallel manipulator with multiple actuation modes based on FMD theory

A novel redundantly actuated parallel manipulator (PM) with multiple actuation modes was developed recently by the author. In this paper, the further research is implemented and a systematic methodology is proposed to develop the rigid–flexible coupling dynamic model (RFDM) of the novel PM based on the flexible multi-body dynamics theory. Firstly, under the floating frame of reference, an arbitrary flexible link of the novel PM is regarded as an Euler–Bernoulli beam and the finite element approach is employed to discretize the flexible beam. Then, one kind of planar beam element with lumped masses and moments of inertia at both ends is presented and a corresponding dynamic model is deduced based on the Lagrangian formulation. On this basis, the RFDM of system is formulated by virtue of the augmented Lagrangian multipliers approach. Given the stiff characteristic of system dynamic model, the hybrid TR-BDF2 numerical algorithm combined with Baumgarte stabilization approach is employed to address the nonlinear RFDM so as to balance the solution efficiency and precision. Based on the RFDM and its degradation model, i.e., the rigid dynamic model, one dynamic simulation experiment is designed to investigate the dynamic performance of the PM. Numerical results indicate that the practical motion of the PM manifests rigid–flexible coupling characteristic, and the redundant actuation modes can attenuate the effect of link flexibility and improve the trajectory tracking precision of end-effector in comparison with the non-redundant actuation modes. Finally, to validate the presented methodology, the obtained numerical results are compared with a virtual prototype model developed based on SimMechanics. The results will be helpful for structure optimization and efficient controller design of the PM with multiple actuation modes.