Probabilistic Models in Computer Automated Slider-Crank Function Generator Design

Using deterministic algebraic techniques, it is possible to synthesize function generator mechanisms which can produce extremely small structural error. However, due to normal variations in dimensions inherent in the manufacture of the components of the mechanism, there may be an extremely low probability of assembling a mechanism which approaches the accuracy predicted by a deterministic representation of the mechanism. This paper presents a probabilistic model of the slider-crank function generator, and a method of optimization of this model. Mechanisms are optimized on the basis of both deterministic and probabilistic models, and the resulting optima are compared by computer simulated production. If the statistical properties of the production techniques are known, it is possible to significantly increase the production yield of acceptable mechanisms by using the probabilistic model for design optimization.