Dynamics of a rigid multibody system with loop constraints using only independent motion variables

This paper presents a reduced order dynamical formulation for a hinge-connected rigid multibody system with loop constrains in which only independent motion variables appear. A tree configuration system with a base body and branch chains is firstly acquired by cutting one of the loop bodies in half, and general equations of motion are formulated using a matrix version of Kane's equations where explicit expressions of the system mass matrix and nonlinear forces are presented. Then, with the constraint equations in terms of time derivatives of motion variables, reduced-order equations for the loop constrained system are formulated using a new form of Kane's equations for constrained system without introducing any multipliers such that the number of dimensions of the equations is equal to the number of degrees of freedom. Finally, a numerical simulation based on a space robot is carried out using both the formulation presented and the dynamic software ADAMS, and the results demonstrate the approach of this paper.