A SPATIALLY TRANSLATING AND ROTATING BEAM FINITE-ELEMENT FOR MODELING FLEXIBLE MANIPULATORS

The development and application of a spatially translating and rotating beam finite element for the purpose of modeling flexible manipulators is presented. This spatial beam element incorporates effects of longitudinal loads on lateral vibration, gravitational body force, internal and external damping, and actuator and payload masses. Hamilton's Principle is used to derive the governing differential equations for the spatial beam element, and compatibility matrices are developed for their assembly. The approach is generalized and can be easily applied to manipulators of diverse geometry and applied joint motion. It is found that beam elements having axial rigidity, torsional deformation, modeled with cubic polynomial interpolation functions, and lateral deformation in two orthogonal directions, modeled with quintic polynomial interpolation functions, produce good results. The method presented is very stable and can be applied with relative ease. Comparisons with published data show good correlation and illustrate the appropriateness of the included effects of axial forces on lateral vibration in modeling flexible manipulators.