A three-step methodology for dimensional tolerance synthesis of parallel manipulators

Computing the maximal pose error given an upper bound on model parameters uncertainties, called perturbations in this paper, is challenging for parallel robots, mainly because the direct kinematic problem has several solutions, which become unstable in the vicinity of parallel singularities. In this paper, a local uniqueness hypothesis that allows safely computing pose error upper bounds using nonlinear optimization is proposed. This hypothesis, together with a corresponding maximal allowed perturbation domain and a certified crude pose error upper bound valid over the complete workspace, will be proved numerically using a parametric version of Kantorovich theorem and certified nonlinear global optimization. Then, approximate linearizations are used in order to determine approximated tolerances reaching a prescribed maximal pose error over a given workspace. Those tolerances are finally verified using optimal pose error upper bounds, which are computed using global optimization techniques. Two illustrative examples are studied in order to highlight the contributions of the paper.