Dynamic Analysis of Planar Mechanisms With Fuzzy Joint Clearance and Random Geometry

Abstract

The dynamic characteristics of planar mechanisms with fuzzy joint clearance and random geometry are studied in this paper. The dynamics model for the mechanism is constructed by utilizing Baumgarte approach in which the clearance size is a fuzzy number, while the geometry parameters are assumed as random variables. A hybrid contact force model, which consists of the Lankarani–Nikravesh model, improved Winkler elastic foundation model and modified Coulomb friction force model, is applied to construct revolute clearance joint. In order to solve the dynamics model, two methodologies are developed: confidence region method for quantification of random and fuzzy uncertainties (CRMQRFU) and confidence region method with transformation method (CRMTM). In the CRMQRFU, fuzzy numbers are first decomposed into intervals under the given membership level. Then, a general framework is proposed for quantification of random and interval uncertainties in the mechanism. In the CRMTM, a transformation method is applied to transform intervals into deterministic arrays, while probability theory is used to obtain the confidence regions under the given fuzzy values. The confidence region, considering random and fuzzy uncertainties, is obtained by fuzzy set theory. Finally, two examples are used to demonstrate the validity and feasibility of these methods.