Modelling uncertainty in the combined kinematic and dynamic synthesis of a four bar linkage

The early stages of design are often characterized by uncertainty. However, important design decisions are made in these stages in the presence of uncertainty. Fuzzy and Bayesian compromise Decision Support Problems (DSPs) are found to be effective in modelling this uncertainty and making decisions in such situations. In this paper, the combined kinematic and dynamic synthesis of a four bar linkage, a classic example in mechanical engineering that involves both imprecise and stochastic uncertainty, is presented. A fuzzy compromise DSP involving fuzzy membership functions is used to model imprecise information. Stochastic uncertainty is modelled by a Bayesian compromise DSP using Gaussian distributions. The crisp formulation (ignoring uncertainty) is presented first, followed by the fuzzy and Bayesian formulations. The results of the various models and their validation are also presented. A comparison is made between the information obtained from the crisp, fuzzy and Bayesian formulations by performing certain parametric studies. The emphasis in this paper is on the method rather than the results per se.