空间自由曲线形状误差计算的迭代逼近法

An Approximation Method for Estimating the Form Devlation of the Free Space Curve

提出了一种新的空间自由曲线轮廓形状误差计算方法─—迭代逼近法，基本原理是：在小误差条件下，把空间理论曲线离散为一系列小直线段，用点到直线的距离，构造实测点到理论曲线距离的近似解析公式；经多次循环迭代，最终获得的形状误差是最小区域意义下的近似。实验表明本算法运行过程稳定，结果准确可靠；算法的平均相对误差在５％的范围内。

The free space curve is increasingly widely used. So far , however, no satisfactorymethod is available for the inspection and calculation of its form deviation,Anew method forestimating such deviation is proposed. The basic principle is as follows:(1) Under the con-dition of small deviation)the theoretical space curve is discretized to a series of short linesegments;(2) An approximate analytic formula for calculating the distance from a measur-ing point to the theoretical curve is generated;(3)With the least square method, a differen-tiaI translation matrix of coordination is obtained;(4) The form deviation finally obtained byiterative optimization is a good approximation of the curve deviation in the sense of the leastzone. Experimental results show that the method proposed runs steadily and the results areaccurate and reliable. The average relative error inspected is less than 5%.