Rigid-flexible coupling dynamic modeling and investigation of a redundantly actuated parallel manipulator with multiple actuation modes

A systematic dynamic modeling methodology is presented to develop the rigid-flexible coupling dynamic model (RFDM) of an emerging flexible parallel manipulator with multiple actuation modes. By virtue of assumed mode method, the general dynamic model of an arbitrary flexible body with any number of lumped parameters is derived in an explicit closed form, which possesses the modular characteristic. Then the completely dynamic model of system is formulated based on the flexible multi-body dynamics (FMD) theory and the augmented Lagrangian multipliers method. An approach of combining the Udwadia-Kalaba formulation with the hybrid TR-BDF2 numerical algorithm is proposed to address the nonlinear RFDM. Two simulation cases are performed to investigate the dynamic performance of the manipulator with different actuation modes. The results indicate that the redundant actuation modes can effectively attenuate vibration and guarantee higher dynamic performance compared to the traditional non-redundant actuation modes. Finally, a virtual prototype model is developed to demonstrate the validity of the presented RFDM. The systematic methodology proposed in this study can be conveniently extended for the dynamic modeling and controller design of other planar flexible parallel manipulators, especially the emerging ones with multiple actuation modes.