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 ($TE$), deviation of transmission angle from 90° ($TA$) 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 ($f_{TE}$), quality of motion ($f_{TA}$) and reliability ($f_G$); 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.

在这项研究中，提出了一种基于协作博弈论、基于可靠性的设计优化 (RBDO) 和蒙特卡罗模拟 (MCS) 协同作用的新方法，以解决路径生成四杆机构的基于可靠性的多目标优化综合问题。 ，考虑到尺寸不确定性对机构可靠性的影响。跟踪误差（$吨乙$), 传输角偏离 90° ($吨\mathrm{一种}$) 和 Grashof 约束的失效概率被定义为三个性能标准，它们的最小化分别提高了机构的精度、运动质量和可靠性。为此，考虑了三个目标函数，即精度（$F_{吨乙}$), 运动质量 ($F_{吨\mathrm{一种}}$) 和可靠性 ($F_G$); 每个目标函数都分配给一个玩家。为了进行优化过程，提出了一种博弈模型，其中通过定义纳什讨价还价函数来使用合作博弈场景来模拟玩家之间的交互。这样，将机构的三目标优化设计转化为单目标优化问题。使用本研究方法获得的结果与文献报道的结果的比较表明，机构的可靠性显着提高，同时保持了确定性设计中的运动精度和质量。特别地，合成机构的跟踪误差和传输角与 90°的偏差分别为 0.0006 和 666.36，