Recursive Formulations And Numerical Methods For Dynamics Of Multibody Systems With Closed-Loops

Dynamics of multibody system is the theory about mechanics of complex mechanical systems and is extensively applied in machineries, vehicles, aerospaces, and robotics. It is a hot topic in applied mechanics due to its theoretical significance and application value.Significant achievements have been achieved in modeling and solving methods of multibody system by scholars from the entire world. However, there are still some new problems arising continuously from practical engineering. Among them, the modeling and solving methods of multibody system with closed-loops and redundant constraints which is common in the mechanical engineering are not satisfactory in many respects, expecially in the case of the system having singular configurations. Based on the existing methods, some improvements about the analysis of such systems are obtained by this paper, which are summarized as follows:(1) According to the kenimatic recursive relations between the outboard and inboard body and the interaction forces between the tree-end body and its inboard body, the mechanical insight of the traditional recursive formulation for multibody systems with open-loops is revealed:the effect of the tree-end-body on the dynamics of the system can be quantitatively described by the transmission of inertias and forces from the tree-end-body to its inboard body. The original system can be reduced to the system without the tree-end-body of the original system. Repeating the reduction process, any open-loop system can be reduced to the system with only one body. Therefore, the system acceleration can be obtained recursively without the requirement of forming the system mass matrix. In the process of the reduction, the mass matrix and generalized forces of a body changes accordingly. However, when they are stable, they are just the mass matrix and generalized forces of the same body but being one of the tree-end-body of a reduced system, which considerably facilitates the computation of joint constraint forces.(2) Treated the reaction forces of cut-joints as applied forces, a multibody system with closed-loops is reduced to the system with only one body by the obtained law of the transmission of inertias and forces. Meanwhile, the system accelerations in constraint equations of cut-joints are replaced sysmatically by the corresponding reaction forces of cut-joints. In this way, the programable recursive formulation of systems with closed-loops is presented, and a software based on the proposed method is developed. Numerical examples validate the proposed method.(3) In this paper, it is rigorously proved that:kinematics of systems with redundant constraints corresponding to the different sets of independent constraint equations are definitely coincident; the reason of incoincidence among the numerical results is explained; a viable methodology of numerical analysis of the system with singular configuration is presented by the synthesis of constraint stablization and the control of constraints violation.(4) The criterion of the uniqness of reaction forces of joints in the system with redundant constraints is presented. A methodology of combining two joints linking one pair of bodies is proposed, and the details in the combination of two revolute joints or cylinderical joints are given.