An Approach for the Impact Dynamic Modeling and Simulation of Planar Constrained Metamorphic Mechanism

This paper studied the impact dynamic modeling of the planar constrained metamorphic mechanism (PCMM) during configuration transformation. Based on the dynamic theory of the multi-rigid-body system and the coefficient of restitution equation, a new method for dynamic modeling of PCMM considering impact motions generated by configuration transformation is presented, which can be treated as a theoretical foundation for performance design and dynamic control. Firstly, the topology theory based on the impact motion can be classified as the stable impact motion and the mobile impact motion, which is the prerequisite for dynamic modeling and simulation. Secondly, the stable and mobile impact dynamic models for PCMM are established according to the dynamic theory of the multi-rigid-body system. Then, using these models, the corresponding impulse solving models are deduced combining with the coefficient of restitution equation. Finally, the examples of the stable impact motion and the mobile impact motion are respectively given, and the configuration-complete dynamic simulations are carried out. By comparing with the dynamic models without considering the impact motion, the dynamic characteristics of PCMM are analyzed. The theory and method proposed in this paper can be also applied in general planar robotic systems to deal with the problem of internal collision dynamics.