Time-Differentiable Null Space Method for Constrained Mechanical Systems (Application to a Rheonomic System)

Abstract

The governing equations of multibody systems are, in general, formulated in the form of differential algebraic equations (DAEs) involving the Lagrange multipliers. For efficient and accurate analysis, it is desirable to eliminate the Lagrange multipliers and dependent variables. Methods called null space method and Maggi’s method eliminate the Lagrange multipliers by using the null space matrix for the coefficient matrix which appears in the constraint equation in velocity level. In a previous report, the author presented a method to obtain a time differentiable null space matrix for scleronomic systems, whose constraint does not depend on time explicitly. In this report, the method is generalized to rheonomic systems, whose constraint depends on time explicitly. Finally, the presented method is applied to four-bar linkages.