中文摘要：

根据杆长限制条件,建立约束方程,进而得出求解球面四杆机构函数综合问题的非线性方程组,并将该方程组的求解转化为鞍点规划问题。以杆长协调、传动角、避免乱支缺陷等为约束条件,提出球面四杆机构近似函数综合的约束优化模型,再应用差分进化（Differential evolution,DE）算法求解该问题。在定义约束违反度和弱、强不可行解的基础上,提出处理约束条件的改进可行性规则,形成求解约束优化问题的可行性规则差分进化（Feasibility-rule-based DE,FRDE）算法。应用4个benchmark约束优化问题测试FRDE算法的优化性能,结果表明,其可靠性和稳健性指标优于对比算法。面向机构优化综合问题,将修复策略融入FRDE算法,发展为带修复策略的FRDE算法（Feasibility-rule-based DE algorithm with repair strategies,FRRDE）。给出5个函数综合实例。结果显示,优化模型和方法可行有效,且FRRDE算法的优化性能好于对比算法。

英文摘要：

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.