Study on automatic deduction method of overall transfer equation for tree systems as well as closed-loop-and-branch-mixed systems

Abstract

The transfer matrix method for multibody systems has been developed for 20 years and improved constantly. The new version of transfer matrix method for multibody system and the automatic deduction method of overall transfer equation presented in recent years make it more convenient of the method for engineering application. In this article, by first defining branch subsystem, any complex multibody system may be regarded as the assembling of branch subsystems and simple chain subsystems. If there are closed loops in the system, the loops should be ''cut off,'' thus a pair of ''new boundaries'' are generated at each ''cutting-off'' point. The relationship between the state vectors of the pair of ''new boundaries'' may be described by a supplement equation. Based on above work, the automatic deduction method of overall transfer equation for tree systems as well as closed-loop-and-branch-mixed systems is formed. The results of numerical examples obtained by the automatic deduction method and ADAMS software for tree system dynamics as well as mixed system dynamics have good agreements, which validate the features of proposed method such as high computational speed, more effective for complex systems, no need of the system global dynamics equation, highly programmable, as well as convenient popularization and application in engineering. KeywordsNew version of transfer matrix method for multibody systems, branch subsystem, closed-loop subsystem, tree system, mixed system, automatic deduction method of overall transfer equation Date

Multibody system transfer matrix method: The past, the present, and the future

“…Faced with the requirement of automatically generating symbolic or closed-form overall transfer equations of multibody systems for theoretical study or for computer implementation in general-purpose software, Rui et al 23 presented the automatic assembly theorem of the overall transfer equations for systems with various topologies by using linear MSTMM and DT-MSTMM, and for chain and closed-loop topologies by using NV-MSTMM. Rui et al 27 and Sun et al 39 generalized NV-MSTMM to branch as well as mixed closed-loop-andbranch topologies. Recently, Rui 32,40 greatly improved and simplified the NV-MSTMM automatic assembly method for various topologies including chain, closed-loop, tree, and general systems together with his PhD supervisor Dieter Bestle.…”