基于PCA/PSO的3T1R并联机构性能优化

Performance Optimization of 3T1R Parallel Mechanism Based on PCA/PSO

根据少自由度并联机构应用广泛的优点,提出了一种3T1R并联机构,该机构具有构型简单、结构对称、定位精度高等特点,可应用于小范围的精密操作,或者是大范围的搬运、分拣以及喷涂等领域。基于方位特征方程的拓扑分析理论,对该并联机构完成了自由度种类以及数目的分析与验证;基于闭环矢量法完成了运动学模型建立,并通过位置正逆解算例验证了运动学的合理性。基于位置逆解方程利用极限边界搜索法分析了3T1R并联机构可达工作空间;通过速度分析建立了速度雅可比矩阵,并根据该矩阵分析机构的定位精度与可操作度性能指标。利用主成分分析(PCA)与粒子群算法(PSO)对3个性能指标进行优化设计,并对优化结果进行了分析,最终优化后可达工作空间体积从0.2933m3提高到0.4231m3,定位精度误差放大因子从15.5044减小至4.4308,可操作度指数从9.7027减小至1.3996。

Based on the widely used advantages of low degree of freedom parallel mechanisms(PM),a new-type three translation one rotation(3T1R)parallel mechanism was proposed,which had the characteristics of simple configuration,symmetrical structure,and high positioning accuracy.It can be applied to small-scale precision operations,as well as large-scale transportation,sorting,and spraying major industrial fields.Based on the topology analysis theory of orientation characteristic equation,the azimuth feature set of position and orientation characteristic(POC)was obtained,and the type and number of degrees of freedom(DOF)of the parallel mechanism were analyzed and verified.A kinematic model was established based on the closed-loop vector method,and the rationality of kinematics was verified through a positional forward and inverse solution example and the results indicated that the kinematic model was completely correct.The reachable workspace’s three-dimensional point cloud picture of the 3T1R parallel mechanism was analyzed by using the limit boundary search method based on the position inverse solution equation.A velocity Jacobian matrix was established through velocity analysis,and based on it,the positioning accuracy and operability performance indicators of the mechanism were analyzed.The PCA/PSO algorithm was used to optimize the design of the reachable workspace,positioning accuracy and operability as three performance indicators,and the optimization results were compared and analyzed.The final optimized reachable workspace volume was increased from 0.2933m3 to 0.4231m3,the positioning accuracy error amplification factor was decreased from 15.5044 to 4.4308,and the operability index was decreased from 9.7027 to 1.3996.