基于D-H矩阵的Stewart型并联机床位姿误差计算模型  

Modeling of Position and Pose Error of Stewart Machine Tool Based on D-H Transforming Matrix

作　　者：单鹏[1,2] 谢里阳[1] 田万禄[2] 温锦海[2] 

机构地区：[1]东北大学机械工程与自动化学院,沈阳110004 [2]辽宁工业大学机械工程学院,锦州121001

出　　处：《机械工程学报》2010年第17期186-191,共6页Journal of Mechanical Engineering

基　　金：国家高技术研究发展计划资助项目(863计划;2006AA04Z408)

摘　　要：针对6自由度Stewart型并联机床,以D-H变换矩阵为建模工具,建立起包含铰座位姿参数、杆件D-H参数的机床动平台位姿方程。采用矩阵微分方法推导出一个机床位姿误差线性化计算模型。该模型不仅使铰座位姿参数误差、杆件D-H参数误差等几何误差全部进入机床位姿误差计算方程,而且将机床位姿误差与几何误差之间的非线性隐式函数关系简化为线性显式函数关系。基于支链杆长方程建立起一个能描述机床位姿误差与几何误差之间实际映射关系的非线性计算模型,以其作为参考模型对线性化计算模型的有效性进行检验。仿真表明:在小误差条件下,线性化模型可以很好地逼近非线性模型,由于具有形式简洁、分析与计算方便等特点,基于D-H变换矩阵的位姿误差线性化计算模型可用于Stewart型并联机床的精度分析、精度综合及运动学标定。仿真结果还表明:当对机床位姿精度要求较高时,需要考虑杆件的全部D-H参数误差对机床位姿的影响。The kinematical equation of the moving platform of Stewart parallel machine tool is established with D-H transformation matrix,the equation contains the pose parameters of hinge joints and the D-H parameters of component parts in all branches of parallel mechanism. Based on the equation,an new computation model of position-pose error of parallel machine tool is set up by means of the differential method of matrix. It is demonstrated that not only the effects of all geometrical parameter errors on the accuracy of machine tool are reflected in the model,but also the linear,explicit formula are derived approximately from the nonlinear,implicit correlation between machine position-pose error and all geometric errors. To verify the linear model,another model is derived from the length formula of branches of mechanism,which can reflect much exactly the nonlinear correlation between machine position-pose error and all geometric errors. A simulation demonstrates the effectiveness of linear model because its results approximate satisfactorily those of nonlinear model. Therefore the linear model can be applied to Stewart type parallel machine tool in accuracy analysis or integration,and kinematical identification due to its advantages in analysis. The simulation also demonstrates that the influence of all D-H geometric errors on the machine tool position and pose should be considered when high accuracy of the position and pose is required.

关 键 词：Stewart型并联机床 机床位姿误差 D-H变换矩阵 几何误差 

分 类 号：TG659[金属学及工艺—金属切削加工及机床]