Multi-objective reliability-based optimal synthesis of path generating four-bar mechanisms: A cooperative game theoretic approach

Abstract

In this study, a novel approach based on synergy of cooperative game theory, reliability-based design optimization (RBDO) and Monte Carlo simulation (MCS) is proposed to address the reliability-based multi-objective optimal synthesis of path generating four-bar mechanisms, taking into account the influence of dimensional uncertainty on the reliability of mechanism. Tracking error ([Formula: see text]), deviation of transmission angle from 90° ([Formula: see text]) and probability of failure of Grashof constraint are defined as three performance criteria whose minimization enhance the precision, quality of motion and reliability of mechanism, respectively. To do so, three objective functions are considered, namely, precision ([Formula: see text]), quality of motion ([Formula: see text]) and reliability ([Formula: see text]); each objective function is assigned to a player. To conduct the optimization procedure, a game model is proposed, in which the cooperative game scenario is employed by defining a Nash bargaining function to model the interaction between players. In this way, the three-objective optimum design of mechanism is cast into a single-objective optimization problem. The comparisons of the obtained results using the method of this research with those reported in the literature shows a significant improvement in reliability of mechanism, whilst both precision and quality of motion in deterministic design is maintained. Particularly, the tracking error and the deviation of transmission angle from 90° of the synthesized mechanism is 0.0006 and 666.36 respectively, whilst the reliability is guaranteed since no violation of Grashof constraint occurs in the presence of 10% parameter uncertainty.