On the first-order decoupling of dynamical equations of motion for elasticmultibody systems as applied to a two-link flexible manipulator

An improved method for deriving elastic generalized coordinates is consider ed. Then Kane's equations of motion for multibody systems consisting of an arbitrary number of rigid and elastic bodies is presented. The equations ar e in general form and are applicable for any desired holonomic system. Flex ibility in choosing generalized speeds in terms of generalized coordinate d erivatives in Kane's method is used. It is shown that proper choice of a co ngruency transformation between generalized coordinate derivatives and gene ralized speeds leads to equations of motion for holonomic multibody systems consisting of an arbitrary number of rigid and elastic bodies. These equat ions are decoupled in first-order terms. In order to show the use of this m ethod, a simple system consisting of a lumped mass, a spring and a clamped- free elastic beam is modeled. Finally, the numerical implementation of deco upling using congruency transformation is discussed and shown via simulatio n of a two-degrees-of-freedom flexible robot.