Elimination of Redundant Cut Joint Constraints for Multibody System Models

Abstract

The problem of dependent cut joint constraints for kinematic loops in rigid multibody systems is addressed. The constraints are reduced taking into account the subalgebra generated by the screw system of the kinematic loop. The elimination of dependent constraint equations is based on constructing a basis matrix of the screw algebra generated by loop’s screw system. This matrix is configuration independent and thus always valid. The determination of the sufficient constraints is achieved with a SVD or QR decomposition of this matrix. Unlike all other proposed approaches the presented method is singularity consistent because it is not the Jacobian which is decomposed, but instead a basis matrix for the loop algebra. Since this basis is obtained after a finite number of cross products the computational effort is negligible. Furthermore, because the elimination process is only necessary once in advance of the integration/simulation process, it proved valuable even if it does not remove all dependent constraints, as for paradoxical mechanisms.