Transfer Matrix Method for Multibody Systems

11Theorem to Deduce the Overall Transfer Equation Automatically

11.1 Introduction

The transfer matrix method for multibody systems (MSTMM) provides a new idea, a simple and efficient method of studying complex multibody system dynamics (MSD) that differs from all previous ways. The MSTMM can be applied widely to the dynamics of complex multibody systems with various topologies, such as chain multibody systems, tree multibody systems, closed‐loop multibody systems, general multibody systems etc. In principle, as long as the transfer matrix of the element is obtained, various MSD problems could be solved with ease. Applying the MSTMM, according to the topology figure of the system dynamics model and the automatic deduction theorem of the overall transfer equation, with the transfer matrix of each element in a system the overall transfer equation and overall transfer matrix of the system would be deduced manually or by computer. Then with the substitution of the system boundary condition into the overall transfer equation of the system, the overall transfer equation of the system and the transfer equation of the element can be solved.

For general MSD methods, the global dynamics equation of the system should be established again if there is any change in the elements. However, the same kinds of elements (elements with the same input end number and motion mode) share the same transfer matrix in various multibody systems. Therefore, the same transfer matrix expression can be used ...