Improvement of the nullspace matrix method of differential equation type for motion analysis of multibody systems

Abstract

In a previous report, the author presented a motion analysis method for rigid multibody systems, called nullspace matrix method of differential equation type. The method determines the nullspace matrix by solving a differential equation with respect to the nullspace matrix, while many other methods which use the nullspace matrix determine it algebraically. Due to this the presented method can obtain the nullspace matrix for systems with redundant constraints or continue the computation when the systems pass through the singular configurations by using relatively large value of stabilization parameters. The presented method uses the QR decomposition whose computational cost is moderately high. In addition, when the system passes through the singular configurations, the accuracy and stability of the presented method decreases since the differential equation for the nullspace matrix becomes incomplete. This paper improves the method in the previous report in the aspects of the computational efficiency and treatment of the singular configurations. The validity of the improved method is verified by numerical examples.