The transfer matrix method for multibody systems, known as the “Rui method”, is a new method for dealing with multibody system dynamics, which does not need the global dynamics equations of the system, keeps high computational speed, and is highly formalized programming. This method has been widely applied to scientific research and key engineering of many complex mechanical systems in more than 50 research fields. The following aspects regarding the transfer matrix method for multibody systems are reviewed in this paper: history, basic principles, formulas, algorithm, and applications in engineering. Some hot topics in this field are also reviewed and prospected, mainly regarding to the improvement of the computational stability and efficiency.

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