• CN: 11-2187/TH
  • ISSN: 0577-6686

Journal of Mechanical Engineering ›› 2022, Vol. 58 ›› Issue (9): 49-61.doi: 10.3901/JME.2022.09.049

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Mathematic Description Method of Variable Topology Configuration for Dynamic Modeling of Metamorphic Mechanism

ZHOU Yang1,2, CHANG Boyan1,2, JIN Guoguang1,2, LIANG Dong1,2   

  1. 1. School of Mechanical Engineering, Tiangong University, Tianjin 300387;
    2. Tianjin Key Laboratory of Advanced Mechatronics Equipment Technology, Tianjin 300387
  • Received:2021-06-29 Revised:2021-10-08 Online:2022-05-05 Published:2022-06-23

Abstract: According to the variable topology characteristics of metamorphic mechanism, a modeling method is proposed to generate automatically any sub-mechanism dynamic model from metamorphic source dynamic model based on topology and multi-body system dynamics theory. Firstly, from the view of the topological composition and constraints of the metamorphic mechanism, the connotation of metamorphic mechanism is redefined and the configuration transformation mode from the source metamorphic mechanism to the sub-mechanism is simplified into two kinds: Reducing the number of components and keeping the number of components unchanged. Secondly, incidence matrix is used to describe the configuration transformation process of metamorphic mechanism, the elimination Ei, j-elementary matrix, the relevance-eliminating matrix Ij and the relevance-change matrix G are proposed to realize the configuration transformation. The topological structure change of the metamorphic mechanism is transformed into a series of matrix operations and a unified mathematical model is given. Finally, the transformation relationship among incidence matrix, Huston lower numbered body array and path matrix is established and the automatic generation mechanism of sub-configuration dynamic model of metamorphic mechanism is analyzed by R-W method. Taking a closed-loop five bar metamorphic mechanism with three configurations as an example, the dynamic model of source metamorphic mechanism is established, and all sub-mechanism dynamic models are generated by programming automatically. The dynamic characteristics of the mechanism are analyzed to verify the effectiveness and practicability of the proposed method.

Key words: metamorphic mechanism, incidence matrix, configuration transformation, dynamics, variable topology

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