Abstract
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.
Highlights
Metamorphic mechanisms are members of the class of mechanisms that are able to change their configurations sequentially to meet different requirements [1]
Since the proposal of metamorphic mechanism in 1998 [2], it has been widely applied to various fields of engineering, such as bionic joint mechanism [3, 4], extendable/foldable flexible spacecraft mechanism [5], automated laying mechanism [6, 7], robot mechanism [8], and space metamorphic parallel mechanism [9]. e applications of the current metamorphic mechanisms are mainly based on task-orientated constrained metamorphic mechanisms [10], which have become the focus of analysis and research in the field of mechanism
Constrained metamorphic mechanism is a kind of mechanism, which realizes configuration transformation by using geometric constraints and/or force constraints to reduce the number of degrees of freedom (DOFs) of a multi-DOF metamorphic mechanism to the number of driving links [12]
Summary
Metamorphic mechanisms are members of the class of mechanisms that are able to change their configurations sequentially to meet different requirements [1]. To solve the impulse acting on the moving component B1, the rotating joint O1 connecting the moving component B1 and the frame B0 can be released based on multibody systems dynamics [35, 36], and the stable impact motion system can be transformed into the multibody system f which is only subject to ideal constraints. According to the Newton–Euler equation, the constraint force at the cutoff joint O1 can be expressed as the form of generalized acceleration vector pq€ in the stable impact motion system: pFcutf pDcutpq€ + pHcutf,. It is emphasized that with respect to PCMM with closed-loop constraints, it can be transformed into multibody systems in the tree system by cutting off the metamorphic joints in the loop when PCMM is changed from one configuration to the so that its impact dynamic analysis can be carried out by the tree system theory mentioned above
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