Analysis of constraint forces in multibody systems based on the null space matrix method of differential equation type

Abstract

In previous papers, the author presented motion analysis methods of multibody systems. In the presented methods, the null space matrix for the constraint Jacobian is obtained by solving a differential equation, then the Lagrange multipliers are eliminated from the equation of motion with the obtained null space matrix.This enables us to perform efficient computation. The elimination of the Lagrange multipliers, however, may become drawback for analysis of constraint forces/moments since the Lagrange multipliers correspond to the constraint forces/moments for the considered constraints. In this report, a new method which can analyze constraint forces/moments efficiently with keeping advantage of the methods presented in the previous papers is developed. First, governing equations which involve the constraint forces/moments explicitly are derived by introducing relative displacements that violate the constraints, called anti-constraint relative displacements. Then a procedure to determine the constraint forces/moments with eliminating the Lagrange multipliers is presented. In addition, extension of the presented method to systems with redundant constraints is given. Finally, validity of the presented method is verified by some numerical examples.

Keywords

• multibody dynamics
• constraint force/moment
• null space matrix
• elimination of lagrange multiplier
• redundant constraint