Dynamic analysis and control of multibody systems using nonlinear combination methods

Abstract

In this paper, the computer computation of nonlinear combination methods in deformable multibody dynamics is described. The organization of the computer program, which is used to automatically construct and numerically solve the system of loosely coupled equations of motion expressed in terms of the Cartesian, Euler Angles and joint coordinates, is discussed. The main processor computer program consists of three main modules: constraint module, mass module and force module. The constraint module is used for the computation of the relationship among translational, rotational and joint accelerations. The mass module is used for the computation of the system mass matrix as well as the nonlinear Coriolis and centrifugal forces associated with the Cartesian, Euler Angles and modal coordinates. The force module is used to evaluate the generalized external and modal forces associated with the translational, rotational, joint and modal coordinates. Computational efficiency is achieved by taking advantage of the structure of the resulting sparse system of loosely coupled equations. Elimination of the modal coordinates leads to small number of equations that can be solved for joint accelerations. The joint and the modal accelerations are integrated forward in time using explicit numerical integration methods. The translational/rotational displacements and velocities can then be determined using the kinematic relationships. The multibody manipulator and the slider-crank mechanical systems are used as two examples to demonstrate the use of the computational procedure discussed in this paper. Copyright © 2010 John Wiley & Sons, Ltd.