This article describes a method for optimizing the synthesis of a four-bar linkage mechanism to generate a definite mathematic function. In this research, the objective function was defined based on the least squares of error between the generated function and the desired function. Because of non-linearity of the objective function and the constraint, SQP method has been used to find the optimal mechanism. This method of optimization is a gradient-based method and its result is more trustable than heuristic methods. In this study, five precision points have been used to synthesize four-bar linkages; therefore, by using this amount of precision points, a set of non-linear equations was obtained for mechanism synthesis. Unlike the previous researches that dimensional parameters are used as optimization variables, precision points distribution was used in current research. The main innovation of this paper is presentation of some directions to have estimative prediction for distribution of precision points in optimal mechanism which maybe useful for designers. These directions were obtained based on the method that presented in current work and regard to shape of desired function and its first and second derivative.

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