基于牛顿迭代的6-UPS并联机构运动学正解的研究  

The Forward Kinematics Analysis of 6-UPS Parallel Mechanism Based on Newton Iteration

作　　者：刘芳华[1,2] 张星[2] 魏玉平[2] 吴洪涛[1] 

机构地区：[1]南京航空航天大学机电学院,江苏南京210016 [2]江苏科技大学机械工程学院,江苏镇江212003

出　　处：《机械设计与制造》2013年第5期173-176,共4页Machinery Design & Manufacture

基　　金：国防科工委"十一五"预研基金(C4220062501);航空科学基金(H0608-012);江苏省数字化制造技术重点实验室基金(HGDML0909)

摘　　要：对自制的6-UPS并联机构的运动学问题进行了分析,利用数值法对该机构的运动学正解进行深入研究。通过运动学反解计算,在旋转矩阵和驱动杆长约束条件下,建立了运动学正解的数学模型,通过化简得到一组六个只含有三个姿态变量的非线性方程组;利用Mathematica软件求解上述方程,利用牛顿迭代法引入所有有效初值求解上述方程组得到正解结果,避免由于初值选取不当产生的漏解现象,并绘出对应的机构装配简图。经算例验证,方法使得算法的收敛速度以及高效寻找全部解得到很好的提高。The research of the mechanism kinematics based on the homemade 6-UPS parallel mechanism is analyzed with the numerical method.The kinematics mathematical model is established by the inverse kinematics calculation,the rotation matrix and the length of driving rod.A group of six nonlinear equations only containing three attitude variables is got by simplifying the model.The above equations are solved by the software Mathematica,and the positive solution results are obtained by using Newton iteration method which joins the initial value of all effective results,and the leakage solution of the improper initial value is avoided.Then the corresponding mechanism assembly sketches are drawn.The example shows that the algorithm convergence speed and high efficiency for all solutions are well improved by this method.

关 键 词：6-UPS并联机构 运动学正解 数值法 牛顿迭代 

分 类 号：TH16[机械工程—机械制造及自动化] TH12