According to restraints given by constant-length of links, the constrained equations are established, and the system of nonlinear equations is then obtained to solve the function generating synthesis problem of spherical four-bar linkages. Consequently, this system is transformed into a saddle-point programming problem. By considering the constraint on length coordination, transmission angle, and to avoid branch defect, the constrained optimization model is thus constructed to formulate the approximately function generating synthesis of spherical four-bar linkages, which can be solved by the differential evolution (DE) algorithm. The constraint violation, weakly and strongly infeasible solution are defined to guide the search process. According to these concepts, an improved feasibility rule is presented to handle constraints and a feasibility-rule-based DE (FRDE) algorithm is formed to approach constrained optimization problems. The FRDE algorithm is tested against four benchmark problems and the results indicate that the presented algorithm outperforms the compared ones in term of reliability and robustness. Orientating optimization synthesis of mechanisms, it is studied to develop an FRDE algorithm with repair strategies (FRRDE) which integrates the repair operators into the FRDE algorithm. Five real cases of synthesis are given to show that this model and approach is valid and feasible, and the proposed FRRDE algorithm performs better in term of final results than compared algorithms.