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.