Transfer matrix method for multibody System (MSTMM) is a new multibody dynamics method developed in recent 20 years. It has been widely used in both science research and engineering for its special features as follows: without global dynamics equations of the system, high programming, low order of system matrix, and high computational speed. Based on MSTMM and its above features, a theorem to deduce automatically the overall transfer equations of multibody systems by handwriting or by computer is proposed in this paper. The theorem is effective for multibody systems with various topological structures, including chain systems, closed-loop systems, tree systems, general systems composed of one tree subsystem, and some closed-loop subsystems. This theorem makes it possible to program large scale software of multibody system dynamics with much higher programming, and much higher computational speed because of the above features of MSTMM. Formulations of the proposed method as well as two examples are given to verify this method.

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Compared to classical mechanics, the transfer matrix method for multibody systems is a rather novel approach for analyzing multibody system dynamics. For its features that it avoids the global dynamics equation of the system, keeps a high computational speed and allows highly formalized programming, this method has been widely used in science research as well as design of dynamics performance and experiments for various complicated mechanical systems. Up to now, there have been more than 50 research directions in science research and key engineering applications based on this method. In this paper, the following aspects are systematically reviewed: history, basic principles, formulas, algorithm, automatic deduction theorem of overall transfer equation, visualized simulation and design software, comparison with other dynamics methods, tendency, and future research directions.

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