Optimal path programming of the Stewart platform manipulator using the Boltzmann-Hamel-d'Alembert dynamics formulation model

In this paper, the dynamics formulation of a general Stewart platform manipulator (SPM) with arbitrary geometry and inertia distribution is addressed. Based on a structured Boltzmann-Hamel-d'Alembert approach, in which the true coordinates are for translations and quasi-coordinates are for rotations, a systematic methodology using the parallelism inherent in the parallel mechanisms is developed to derive the explicit closed-form dynamic equations which are feasible for both forward and inverse dynamics analyses in the task space. Thus, a singularity-free path programming of the SPM for the minimum actuating forces is presented to demonstrate the applications of the developed dynamics model. Using a parametric path representation, the singularity-free path programming problem can be cast to the determination of undetermined control points, and then a particle swarm optimization algorithm is employed to determine the optimal control points and the associated trajectories. Numerical examples are implemented for the moving platform with constant orientations and varied orientations. (C) Koninklijke Brill NV, Leiden and The Robotics Society of Japan, 2008.