On the First-Order Decoupling of Dynamical Equations of Motion for Elastic Multibody Systems as Applied to a Two-Link Flexible Manipulator

Abstract

An improved method for deriving elastic generalized coordinatesis considered. Then Kane's equations of motion for multibody systemsconsisting of an arbitrary number of rigid and elastic bodies ispresented. The equations are in general form and are applicable for anydesired holonomic system. Flexibility in choosing generalized speeds interms of generalized coordinate derivatives in Kane's method is used. Itis shown that proper choice of a congruency transformation betweengeneralized coordinate derivatives and generalized speeds leads toequations of motion for holonomic multibody systems consisting of anarbitrary number of rigid and elastic bodies. These equations aredecoupled in first-order terms. In order to show the use of this method,a simple system consisting of a lumped mass, a spring and a clamped-freeelastic beam is modeled. Finally, the numerical implementation ofdecoupling using congruency transformation is discussed and shown viasimulation of a two-degrees-of-freedom flexible robot.