复杂曲面切割机构运动及误差分析的旋量方法

Kinematics and Errors Analysis of Cutting Machine for Complex-surface Using Screw Theory

针对传统串并联机构分析方法计算烦琐、直观性不强等问题,以复杂曲面切割机为研究对象,在使用旋量方法表示空间刚体运动的基础上,建立了串并联机构的运动学指数积公式的完整表示方法.将4个D-H参数误差等效为误差旋量,建立各关节轴线含有误差旋量的旋量坐标,推导出了含有误差旋量的串并联机构运动学指数积公式,并建立了末端工具坐标系的位姿误差模型.按照上述旋量分析方法,用MATLAB对复杂曲面切割机构进行运动及误差数值计算,并将计算结果与ADAMS仿真结果进行比较.对比结果表明:2组结果的相对误差仅在0.001内,表明了旋量方法在串并联机构分析中应用的正确性.

According to the problems of calculation complexity and abstractness in the traditional analysis methods of serial-parallel mechanism, cutting machine for complex-surface was researched and the complete kinematic product of exponentials formula of serial-parallel mechanism was established based on the screw representation of spatial rigid motion. The errors of 4 D-H parameters were equivalent to error screw, and the practical screw coordinate containing error screw of every joint axis was established. With the practical kinematic product of exponentials formula of serial-parallel mechanism derived, the pose error model of tool coordinate system was established. According to the above screw method, the numerical calculation of cutting machine about kinematic and error was performed with MATLAB and the calculation results were compared with the simulation results of ADAMS. The comparison results show that the relative error of the two groups of calculation results is within the 0. 001 orders of magnitude, which certifies the correctness of screw method＇ s application in the analysis of serial-parallel mechanism.