Motion Analysis of Multibody Systems Subject to Friction Based on the Null Space Matrix Method of Dierential Equation Type

Abstract

This paper treats analysis of rigid multibody systems subject to friction force. The authors has presented analysis methods of motion and constraint forces. In the presented motion analysis method, a nullspace matrix for the constraint Jacobian is obtained by solving a dierential equation. In the constraint force analysis method, relative displacements which violate the constraints are introduced. In this paper, motion analysis method of rigid multibody systems subject to friction force is presented. The friction force is assumed to be of Coulomb friction type. In the Coulomb friction model, kinetic friction depends on the normal reaction force and is given as a unique valued function, while static friction depends on the state of the system and is not a unique valued function. Thus in the presented method, treatment of the analysis is separated according to the relative velocity between bodies subjected to friction. A numerical example is given to show validity of the presented method.