Abstract
The implementation and development of a spatially translating and rotating beam finite element for the purpose of modelling flexible manipulators is presented. Flexible manipulators are subject to dynamic loads from link and actuator masses undergoing acceleration, and structural or applied damping. To model these effects, a spatial beam element is developed which accounts for the effects of axial loads on lateral vibration, Rayleigh damping, and actuator and payload masses modelled as lumped masses. Hamilton’s principle is employed to derive the governing differential equations for the spatial beam element, and compatibility matrices are developed for their assembly. The method is generalised to facilitate application to manipulators of different geometry and applied joint motion, and proves to be very stable. Joint motions are utilised which produce smooth acceleration profiles as opposed to sharp profiles used in typical industrial manipulators. Comparisons with published data illustrate good agreement. The beam element presented shows promise as a useful design tool and a basis for further study in the implementation of flexible manipulators.
