数控随形打磨机器人控制系统中数学方法

介绍了数控随形打磨机器人控制系统中使用的几个数学方法。用3次参数样条曲面拟合模型，以较高的精度，较好地解决了空间自由曲面的光顺拟合问题；用计算机几何的方法重构大型涡轮叶片曲面，可提高叶片的物理学性能；用图形线性变换技术为使用者提供统一的数控编程格式；用图形非线性变换技术，成功地解决了多自由度控制点坐标的变换以及磨头的姿态调节和恒压力磨削等难题。所有这些数学方法都已经过实际运行的验证，是行之有效的，对大型工业机器人的应用研究有一定的参考价值。

Research & Operation on Mathematical Methods used in NC System of Profile followed Grinding Robot

Several mathematic methods used in the numerical control system of profile followed grinding robot are described. Cubic parametric Spline surface function is employed to fit the geometric model of the surface grinded with high precision. Improvement of the physics performance of blade is obtained by reconstructing the large size surface of turbine blade based on calculation geometry. Graphic linear transfer technique is provided to users with unique format of programming. Graphic non linear transfer technique is used to solve some more difficult problems successfully including transformation of the coordinates of comtrolled points in multicoordinates system, adjustment of the attitude of grinding head as well as realization of constant pressure grinding. All these mathematics methods are demonstrated feasible and efficient in actual practice and are valuable in developing large size surface grinding robots.