臺灣博碩士論文加值系統

幾何形狀誤差乃是影響機械零組件及光學元件精密性的主要原因之一，故
表面精度的檢驗則相當重要，然以往提出各種表面精度的研究，均侷限於
直線、平面、圓及圓柱等，故無法有效地應用於光學元件的表面精度之檢
測上，因此本文提出針對圓弧及拋物線型曲線元件的幾何形狀誤差做一研
究，期能有效地解決此兩曲線表面精度之檢測。本文最小區域法之分析，
首先，建立滿足最小區域解之兩準則，再利用最小平方和之定義，由數學
模式推導得到最小平方和曲線方程式，進而求得一組通過兩接觸點(1-1
模式)之平行曲線，其法線之距離稱為最小平方和解(Least-squares
solution)，此兩點稱為控制點(Control point )，經由分別檢查兩控制
點對最小平方和曲線上或下方之各點的夾角，可求得一最小夾角，而相對
此值之點為第三接觸點，此三點接觸稱為1-2或2-1模式，保留此三點繼續
檢查其它各點之切線旋轉角，可求得一最小切線旋轉角，而相對此值之點
為第四接觸點，此已滿足準則一，但須再檢查是否滿足準則二，若否，則
須經由反覆地換點，直至兩準則均滿足為止，即求得圓弧最小區域解，然
拋物線則須經由收斂模式調整後，方能得到所求之拋物線最小區域解。

The purpose of this article is to present a minimum zone method
to estimate the profile error for circular arc and parabola be-
cause the study of the profile error for arc and parabola have
not presented in the past. The minimum zone method proposed in
this article set up the criteria for the minimum zone solution
first,obtained 1-1model from the least-squares method ,utilized
minimum intersectional angle to obtain 2-1 or 1-2model, and
then minimum tangent rotat- ion angle to obtain 2-2model.
Finally, utilized strict rules for data exchange to obtain the
minimum zone solution for circular arc. The minimum zone
solution for parabola was obtained by means of data exchange
and convergent method. Finally, the software which rapidly
displayed the result was developed according to the above
analysis.Comparing with the existing least-squares method
through some examples, it can be shown that the minimum zone
method can provide better result.