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.
Highlights
Multibody system dynamics methods (MSDMs) that have been developed since 50 years ago[1,2,3,4,5,6,7] provide effective methods for dynamics analysis of modern mechanical systems
Computational precision of the new version of MSTMM is discussed in Rui et al.[17], see Table 1, which demonstrates that the new version of MSTMM has higher precision than discrete time transfer matrix method for multibody system dynamics (MSD)
The tree multibody system may be regarded as the assembling of branch subsystems and simple chain subsystems
Summary
Multibody system dynamics methods (MSDMs) that have been developed since 50 years ago[1,2,3,4,5,6,7] provide effective methods for dynamics analysis of modern mechanical systems. The MSTMM has been applied widely in engineering for following aspects: the study procedure of MSD is simplified because of no need to establish the system global dynamics equation; the computational speed is increased greatly because the system matrix order is always low, and it is highly programmable. Comparing to algorithms in Featherstone,[8] Brandl et al.[9], Rodriguez et al.[10] and Saha[11], the expression of new version of MSTMM is the most concise and evident since the kinematics and dynamics information are contained in the transfer matrix of each element, different from others that these information are processed separately makes the computational process tedious. The automatic deduction method of overall transfer equation for tree systems as well as closed-loop-and-branch-mixed systems is formed, which would provide theoretical support for the software development based on the new version of MSTMM.
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