Motion generation mechanisms such as pick-and-place robots often have exact
ing 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 methodologie
s. In this paper we present a method in which intermediate 'precision' posi
tions arc described as distributions. This expands the resulting set of acc
eptable 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 ac
ceptability 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 t
his methodology. (C) 2001 Published by Elsevier Science Ltd.