AN EXPLICIT MATRIX FORMULATION OF THE DYNAMIC EQUATIONS FOR FLEXIBLE MULTIBODY SYSTEMS - A RECURSIVE APPROACH

The dynamic simulation of complex rigid/flexible multibody systems relies greatly on the presentation and development of the equations of motion. To achieve computational speed in the execution and to further develop the control algorithms, the expressions involved in the kinematics and the subsequent coefficients associated with the equations of motion must be clearly defined. The intention of this paper is to develop a recursive formulation based on finite element method where all terms are presented in a matrix form. The methodology permits one to identify the coupling between rigid and flexible body motion, and build the necessary arrays for the application at hand. The equations of motion are based on Kane's equation and the general matrix representation for n bodies of its partial velocities and partial angular velocities. The algorithm developed is applied to a single two-link robot manipulator and the subsequent explicit equations of motion are presented.