6-UPS交叉杆型并联机床的运动学正解算法

Forward Kinematics Analysis of 6-UPS Parallel Machine Tool with Cross Rod

6-UPS交叉杆型并联机床是Stewart并联机构的改进形式,由于动平台分两层结构,不具有一般Stewart平台的对称性,因此很难有效地获得其运动学正解的解析解。采用罗德里格斯参数描述旋转矩阵,通过分析动平台位置和姿态变量之间的耦合关系,并采用消元方法消去运动基本方程中的位置矢量参数,最终得到了只关于罗德里格斯参数的三元四次方程组。在此基础上,利用牛顿迭代方法,构造出用于求解该方程组的迭代函数。通过对实际的并联机床分析,证明了该方法的正确性和有效性。

6-UPS Cross rod parallel machine tool is an improvement of the Stewart parallel mechanism. As two layers in the moving platform destroy the symmetry of generally Stewart platform, it is difficult to calculate the analytical solutions of the forward kinematics problem efficiently. Lodrigues parameters are used to describe the rotation matrix. Through the analysis of the coupling relationships among the position and orientation variables of the moving platform, and eliminated position vector parameters in the basic motion equations, the 4th order equations which have three parameters are obtained. Thus, with the use of Newton iterative method, the iterated function that solved the equations is constructed. The method is proved correct and effective through the analysis of the actual parallel machine tools.