In this article, a Stackelberg game theoretic approach is used for multi-objective optimal synthesis of four-bar mechanisms for path generation. Two objective functions, namely, tracking error (TE) and transmission angle’s deviation from 90° (TA), are considered as leader and follower, respectively. In this way, a new analytical approach is presented to provide a function of rational reaction set (RRS) of the follower. Consequently, the multi-objective optimal synthesis of four-bar mechanism is therefore cast into a single-objective optimal synthesis using only the leader variables and the obtained nonlinear algebraic equation representing the RRS of the follower. The superiority of using such game theoretic method of Stackelberg is demonstrated for three cases of synthesis of four-bar mechanisms for path generation.
