A new computer-oriented approach with efficient variables for multibody dynamics with motion constraints

This paper presents a new formulation for automatic generation of the motion equations of arbitrary multibody systems. The method is applicable to systems with rigid and flexible bodies. The number of degrees of freedom (DOF) of the bodies' interconnection joints is allowed to vary from 0 to 6. It permits the system to have tree topology or closed structural loops. The formulation is based on Kane's method. Each rigid or flexible body's contribution to the system generalized inertia force is expressed in a similar manner; therefore, it makes the formulation quite amenable to computer solution. All the recursive kinematic relations are developed, and efficient motion variables describing the elastic motion and the hinge motion are adopted to improve modeling efficiency. Motion constraints are handled by the new form of Kane's equation. The final mathematical model has the same dimension with the generalized speeds of the system and involves no Lagrange multipliers, so it is useful for control system design. A sample example is given to interpret several concepts it involves, while the numerical simulations are shown to validate the algorithm's accuracy and efficiency.