Multi-objective genetic algorithm and Castigliano's theorem for stiffness optimisation of parallel robots: case study of conventional Stewart platforms

Study of stiffness characteristics plays a key role in application of parallel robots in precision manufacturing. In this study, stiffness index improvement is utilised as the objective function to obtain optimal configurations and dimensions for parallel robots. The optimisation goal is to maximise the stiffness index throughout workspace of the robots. First, stiffness of the robots is obtained by the strain energy of main components of the robots and Castigliano's theorem. For a more realistic simulation, compliance of moving platform of the robots is considered. Then a non-dominated sorting genetic algorithm (NSGA-II) is utilised to solve the optimisation problem. A comprehensive case study of stiffness analysis of three conventional SPS (spherical- prismatic-spherical) Stewart platforms to examine such a platform's optimised design is performed. The relationship between the objective and decision spaces is investigated. A similar approach can be utilised to study optimised design for other parallel robots. Findings of this study provide a general stepwise and conceptual approach to the stiffness analysis of parallel robots that depends on design parameters and configuration of the robots. In case of Stewart platforms, 3SPS configuration was found to be optimised in terms of stiffness performance in their workspace.