Incorporating uncertainty into mechanism synthesis

Motion generation mechanisms such as pick-and-place robots often have exacting constraints on the initial and final locations and angles. However, the intermediate locations and angles are not nearly as constrained. Previous attempts to synthesize mechanisms under such uncertain conditions employed permutation, quasi-precise (worst-case), and genetic algorithm methodologies. In this paper we present a method in which intermediate `precisionʹ positions are described as distributions. This expands the resulting set of acceptable solutions by adding an extra dimension to Burmester solutions, i.e., Burmester surfaces instead of Burmester lines. Treating the input variables as statistical variables allows designers the freedom to dictate both preferred input regions and preferred amounts of acceptability within the regions. Incorporating uncertainty quickly provides not only the entire feasible design space, but also the nominal, worst-case, and most importantly, the most highly recommended solutions. A headlight cover mechanism solution is provided to demonstrate the attractiveness of this methodology.