UPS+UPR+S并联机构伴随运动及正逆解分析

目的针对二自由度的UPS+UPR+S并联机构对该并联机构是否具有伴随运动以及对该并联机构的位姿正逆解进行分析。方法通过旋转变化矩阵得到相应向量的表达式,并建立约束方程验证是否具有伴随运动。对该机构进行正逆解分析,通过遗传算法求得机构的部分正解并与逆解相互验证,并通过实例进行验证分析,得到最佳个体、最佳适应度、多样性值和每代个体得分结果。结果该机构不存在伴随运动,正解与逆解所得结果相差较小,数据可以相互吻合。正解实例得到的最佳个体为-0.267和0.31,结果与反解相互验证,最佳适应度逐渐减小,获得了每代得分和每代个体得分情况。结论机构不存在伴随运动,性能较好,由正逆解相互吻合可知正逆解的正确性。

Concomitant Motion and Positive and Inverse Solutions of UPS+UPR+S Parallel Mechanism

The work aims to check whether it has the concomitant motion and analyze the positive and inverse solutions of the position and pose with respect to UPS+UPR+S parallel mechanism with two degrees of freedom. The expression of the corresponding vector was obtained by rotating the change matrix, and the constraint equation was established to verify whether there was concomitant motion. The positive and inverse solutions of the mechanism were analyzed, and part of positive solutions of the mechanism were obtained by genetic algorithm and mutually verified with the inverse solutions. An example was given to validate the analysis, and the best individual, the best fitness, the diversity value and the score of individuals of each generation were obtained. There was no concomitant motion in the mechanism, the difference between positive solution and inverse solution was small, and the data could be consistent with each other. The best individuals obtained by positive solution were -0.267 and 0.31, subsequently mutually verified with the inverse solution. The optimal fitness decreased gradually, and the score of each generation and the score of individuals of each generation were obtained. There is no concomitant motion in the mechanism, and the performance is good. As the positive and inverse solutions coincide with each other, the correctness of the positive and inverse solutions can be proved.