Truth Models for Articulating Flexible Multibody Dynamic Systems

Closed-form solutions are developed for the small elastic motions of planar, e exible, multilink systems arranged in chain topologies, in which the links are represented as Euler ‐Bernoulli bars in transverse vibration. The links are connected by pin joints, thereferencearticulation anglebetween adjacent links can bearbitrarily selected, and the system end conditions are set as either pinned or free. The characteristics of the solutions are investigated and are shown to consist of combinations of the characteristic expressions associated with classical end conditions for single links. These solutions are generalized to represent n links. A large-articulation e exible multibody model of a two-link planar manipulator is then developed and linearized about an arbitrary reference angle cone guration. One of the closed-form solutions serves as a truth model in the numerical and analytical evaluation of the use of varioustypesofassumedmodesinconjunctionwiththelinearizedmultibodymodel.Theresultsfurthercone rmthe validity of previously proposed guidelines for selecting assumed modes in articulating e exible multibody systems.

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