Deduction method of the overall transfer equation of linear controlled multibody systems
The transfer matrix method for multibody systems (MSTMM) which is a highly efficient and novel approach for multibody system dynamics, was proposed and perfected in the past 20 years. The deduction of the overall transfer equation of the system is one of the key techniques in MSTMM. The topology figure of the dynamics model of multibody systems is a novel pictorial expression to describe the relationship among the state vectors of connection points of different elements in MSTMM. In this paper, the block diagram in control theory is introduced and incorporated into the topology figure of the dynamics model to represent the connection relationship between different mechanical elements in the system as well as the control relations. Meanwhile, the transfer equations of the controlled element, control subsystem and the overall transfer equation of the linear controlled multibody systems are deduced. The proposed method greatly reduces the efforts to study the linear controlled multibody systems since the procedures are stylized. Two numerical examples are given to validate the proposed method.