LINEAR DECOUPLED MODELS FOR A SLEWING BEAM UNDERGOING LARGE ROTATIONS

A mathematical model for flexible slewing beams subjected to overall large rotations is presented. This kind of model can be useful in analyzing flexible single-link manipulations for laboratory tests. Major assumptions are as follows: straight beam neutral axis; horizontal rotation; small displacements but large overall rotations; in-plane deformation in the direction normal to the beam neutral axis and rigidity of added masses. If displacements are measured from a rotating frame which is floating with respect to the beam, the so-called rigid-body mode frame, the following can be demonstrated: when the angular speed is small enough compared to the lowest eigenfrequency of the flexible link, then linear uncoupled equations of motion can be used for the system. Should angular speed be relevant, then effects due to geometric stiffness can be of the same order of magnitude as effects of inertia coupling, and both of these counteracting terms must be included in the model. Both a continuous model and a discrete model are presented, as well as an example of an application to a real test case. © 1993 Academic Press Limited.