A finite element approach to the inverse dynamics and vibrations of variable geometry trusses

This paper presents a novel numerical approach to solving the inverse dynamics of variable geometry trusses (VGTs) with elastic elements, allowing designers to accurately and efficiently determine motor action requirements, the time-dependent behavior of the structure, and the contribution of vibration modes to the motion. The dynamic equations have been simplified by assuming that movements of the structure are relatively slow, since VGTs are generally used in situations requiring high accuracy. Unlike existing techniques, the formulation is based on simple finite element models. The analysis is based on modal coordinates, and takes place in two stages: first, motor actions are calculated in a model with no actuator stiffness; then, small-amplitude, undamped vibrations are obtained in a model that includes actuator stiffness. The method is validated by simulating a pinned planar flexbeam and a three-dimensional VGT.