中文摘要：

针对目前圆弧插补与椭圆弧插补在适用范围、计算效率与精度方面的问题，通过引入微分模型表达空间圆弧与椭圆弧，提出了基于微分模型的空间圆弧与椭圆弧插补方法，能实现空间任意圆弧与椭圆弧的插补。在空间圆弧插补中能实现零径向误差与零速度波动。在空间椭圆弧插补中能实现零径向误差与较低的速度波动。同时，该方法的插补过程统一了圆弧和椭圆弧的正逆插补，无需象限判断，因此插补流程简单高效。另外，该方法采用的插补点递推公式能转换为一系列简单的四则运算，因此插补计算效率高。仿真对比分析表明了该方法相对于目前的方法具有很大的优越性。最后，在自主开发的数控平台上实现了该方法并完成了试件的加工。

英文摘要：

To improve the application range, computational efficiency and accuracy of current circular arc and elliptic arc interpolation, the differential model was introduced to represent the spatial circular arc and elliptic arc, and the corresponding interpolation methods were proposed with the ability of interpolating arbitrary spatial circular arcs and elliptic arcs. In spatial circular arc interpolation, zero radial error and zero feedrate fluctuation can be achieved. In spatial elliptic are interpolation, zero radial error and relative low feedrate fluctuation can be achieved. Meanwhile, the method unified the clockwise and anticlockwise interpolation of circular arc and elliptic arc interpolation with no quadrant judgment process, thus the algorithm flows were very simple and efficient. The recursion formulas for generating sampling points in the proposed methods can be deformed to a computational efficiency can be obtained. The simulation and series of simple arithmetics, thus high comparison analysis demonstrated the proposed methods were superior to other methods. Finally, the methods were implemented on a selfdeveloped open CNC platform, which were successfully applied to workpiece machining. The feasibility and applicability of the proposed methods were verified by simulation and experimental results.