Research on the Symbolic Deduction Method for the Overall Transfer Matrix of Multibody System by Computer

The computational efficiency of dynamic method and its degree of computer automation are crucial to speedily solve the dynamic problems of complicated mechanical systems in practical engineering. Transfer matrix method for multibody systems (MSTMM) has been successfully applied in the dynamic analyses of many mechanical systems as a result of its high stylization and efficiency. The overall transfer equation of multibody system plays a vital role in MSTMM, and its automatic deduction is one of the salient features of high stylization. The key to deducing the system’s overall transfer equation is the deduction for its overall transfer matrix which is mainly composed of elements’ transfer and geometrical matrices. In this study, the symbolic expression consisting of the sequence numbers of elements and their input points is put forward to represent elements’ transfer and geometrical matrices, and it is described by the class TransferMatrix in computer. The class MainTM is designed to represent the system’s main transfer and geometrical matrices, which together compose the system’s overall transfer matrix. The symbolic deduction for the overall transfer matrix by computer is achieved through the operator overloading in object-oriented technology. A numerical example is performed to validate the proposed method. The present study lays a foundation for developing the dynamic analysis software for mechanical systems based on the theory of MSTMM.