Abstract: An approximate circle-point of the moving rigid body in spherical motion is defined, and the approach of adaptive circle fitting is presented with respect to spherical curves .Then, the optimum synthesis of spherical four-bar linkages for function generation can be converted into an adaptive curve fitting. Thus, the mathematical model of saddle-point programming for this problem is established with the corresponding optimum algorithms proposed. Theoretically, it is provided that the existence of the best solution and the convergence of the optimum algorithms to optimum synthesis for function generation of spherical four-bar linkages. Genetic algorithms are adopted to solve problems such as selecting initial points, capturing global optimal solution. Finally, examples are given to show the feasibility and the validity for the approach.

Key words: Function generation, Optimal synthesis, Spherical mechanisms