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In this study, an analytical approach based on bi-level multi-objective game theory is proposed and implemented for dimensional synthesis of the planar crank-rocker four-bar mechanisms. Two players, namely, Stroke (S) and Time Ratio (TR) are considered in the level playing the role of a leader. The third player, Transmission Angle (TA), is placed in a lower level operating with the role of the follower' role. Players' behavior at upper level is also modeled as a cooperative game. In addition to this, the interaction between upper and lower levels is modeled as a Stackelberg game wherein an analytical approach is given to provide an explicit function of the follower's Rational Reaction Set (RRS). Such analytical approach of Stackelberg game theory leads to an interesting relationship of length of the coupler and rocker links. It is, therefore, advised that by adopting equal lengths for coupler link and rocker link, one can guaranty the optimality of the transmission angle deviation, ensuring the Grashof condition. Consequently, the stroke, time ratio, and transmission angle criteria are derived explicitly as mathematical functions explaining the links of mechanism's normalized dimensions. The aforementioned approach coupled with the proposed formulas and charts, greatly simplifies the synthesis of the mechanisms with optimal transmission angle while adopting any desired values of both stroke and time ratio. The theoretical approach proposed are explained with illustrated examples. [ABSTRACT FROM AUTHOR]

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 (T E), deviation of transmission angle from 90° (T A) 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 T E ), quality of motion ( f T A ) 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. [ABSTRACT FROM AUTHOR]

In this paper, a fuzzy rule-based system (FRS) has been used for optimal reliability-based robust controller design for a two-mass-spring system with probabilistic uncertainties in its parameters. In this way, a multiobjective uniform-diversity genetic algorithm (MUGA) is first used to find a Pareto front of two-mass-spring system in a deterministic approach. This paper considers a two-mass-spring system under an impulse input. Two conflicting objective functions in this model include settling time of the second mass and control effort exerted on the first mass. Consequently, such Pareto front is then obtained for a two-mass-spring system with probabilistic uncertainties in its parameters using the probabilities of failure of those objective functions through a Monte Carlo simulation approach. It is shown that the FRS system removes the difficulty of selecting suitable crisp values and obligation due to a defining limit state function. Besides, the multiobjective Pareto optimization of such robust controllers using MUGA unveils some very important and informative trade-offs among those objective functions. Consequently, some optimum robust controllers can be compromisingly chosen from the Pareto frontiers. [ABSTRACT FROM PUBLISHER]