Dynamics of Rigid Multibody Systems with Clearances in the Joints*

Abstract

ABSTRACT An approach for calculation of reaction and friction forces between pairs of bodies in spatial mechanical systems, as well as contact points in joints with clearances is presented. Coulomb friction is taken into consideration. Problems are solved iteratively, to satisfy both kinematic and dynamic equations. Matrix methods are used to derive the nonlinear kinematic constraint equations. Newton-Euler dynamic equations are applied for solution of direct and inverse problems of dynamics. External and inertia forces for each configuration of the kinematic chain the contact points and corresponding normal forces are calculated. Relative positions of the coordinate systems of the links are computed and, their new positions relative to the inertia reference frame are estimated. An iterative algorithm is suggested for calculation of forces and computing generalized coordinate increments for achieving the prescribed accuracy of system end-effectors. Kinematic and dynamic equivalents of rotational, translational, and prismatic pairs with clearances are suggested. A model of joints with clearances is applied for solution of the direct and inverse problems of dynamics, taking into account presence of unilateral reactions, viscous friction, contact friction, and impact in bearings. An example of a triple pendulum with rotational pairs, a driving force on the end-effector, and large clearances is presented.