巧用参数方程加工椭圆曲线

Machining elliptic curves using parameter equations

分析了宏程序的编程思路,讨论了椭圆参数方程的形式,重点对参数方程中参数φ(又叫离心角)的含义进行了研究,并推导出了参数φ与椭圆几何夹角θ的关系式.通过公式可以正确的计算出椭圆曲线加工的起点和终点对应的参数φ值,从而得到宏程序编程循环的起止点.通过典型零件的加工验证了关系式的适用性和通用性.正确的使用椭圆参数方程,正确的理解参数φ的含义,才能加工出满足要求的产品.

The programming method for macro programs is analyzed, the form of the parameter equation for an ellipse dis- cussed, the meaning of the parameter ~p （ also called eccentric angle ） described, and an equation between the parameter φ and the elliptic angle θ deduced in the paper. The values of the parameters φ corresponding to the beginning and end of the elliptic curves are worked out in terms of the equation. The starting and ending points of the cycle for the macro program can thus be determined. The applicability and generality of the equation has been proved in machining typical parts. No qualified parts would be fabricated without using the elliptic parameter equation and correctly understanding the meaning of the parameter φ.