Multipoint Constraints with Lagrange Multiplier for System Dynamics and Its Reduced-Order Modeling

Abstract

A general formulation is presented to linear multipoint constraints, underlying that the linkages of mechanical system dynamics are governed by kinematic constraint conditions. Both rigid and interpolated multipoint constraints are then described in a formulation based on the Lagrange multiplier adjunction. The proposed formulation can directly offer reaction forces, which are essential information to modeling linkages of mechanical components. In particular, in the interpolated multipoint constraints, the proposed formulation is more numerically stable than the conventional master-slave formulation that has invertible issues with respect to choice of the constraint nodes. The other aim of the work is to condense the original equations of motion into degrees of freedom at certain nodes only, named as condensation nodes, for better computational and modeling efficiencies. In the proposed Lagrange multiplier based formulation, accuracy of the reduced model can be improved by dynamic correction. The performance of the proposed method is theoretically evaluated by comparing the master-slave elimination, which is the most widely used approach of the multipoint constraints, and it is demonstrated through numerical examples.