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標題: NURBS曲線偏置及口袋型模穴刀具路徑產生
Offsetting NURBS curves and tool-path generation for pockets
作者: 施浚龍
Shih, Jiunn-Long
關鍵字: NURBS curves;NURBS曲線;Offsetting;Piecewise Bezier curves;Pocketing;Tool path generation;偏置;分段Bezier曲線;口袋型模穴加工;刀具路徑產生
出版社: 機械工程學系
本論文的目的是在於發展一有效率且強健的計算高次NURBS偏置曲線之方法,並且對它在建構口袋型模穴之NURBS格式刀具路徑之應用作探討。有關自由曲線的偏置,其基本操作程序包括:(1) 對一給定的原始曲線,求取其直線嵌合複合線;(2) 對直線嵌合複合線作偏置,以便得到正確偏置的線性近似表示;(3) 根據線性近似表示的偏置,重新建構高次連續的偏置曲線。經由所提出的方法及設定不同的偏置條件,而有三種不一樣的曲線偏置結果產生。其中之一可以得到以G1連續的分段Bezier曲線所表示之偏置曲線;其二可以得到C2連續的B-spline曲線型式之偏置;而最後一種偏置條件,會產生單邊的近似偏置,並以C1連續的分段Bezier曲線來表示。與文獻上所記載的偏置計算方法不同的是,這個方法可以根據Bezier曲線的凸殼性質及位置誤差累積的觀念,去估計全域性的偏置接近誤差。而且因為只需要線性的幾何計算,因此該方法是相當有效率的且強健的。特別是,此方法適足以對口袋型模穴加工中,有關NURBS格式刀具路徑產生的複雜問題,提供一完全的解決之道。這一方面的應用之所以能夠獲致巨大的成功,主要是基於該方法可以得到全域可控制誤差的偏置曲線,以及在最初線性近似偏置被求出時,即可消除會產生過切的自交迴圈。因此,沒有過切與尖點的高次連續刀具路徑,可以很容易地被產生出來。

This research aims to develop an efficient and robust method for computing higher-degree continuity offsets of NURBS curves and to investigate its application on constructing NURBS-format tool paths for pocketing. The basic steps for offsetting freeform curves are: (1) computing the line-fitting curve of a given progenitor curve; (2) constructing a linear approximating offset by offsetting the line-fitting curve exactly; and (3) reconstructing a higher-degree continuous offset curve based on the offset line-fitting curve. Under different offsetting conditions, three kinds of offsetting results can be obtained using this proposed method. One of them will generate offset curves with G1 continuity using piecewise Bezier curves; another one will have offsets with C2 continuity in integral B-spline form; and the last one, which is a novel attempt for NURBS offsetting, will obtain one-sided offset approximations in form of C1 piecewise Bezier curves. Unlike previous offset computation methods, the proposed method can estimate the offset approximation errors with global accuracy based on the convex hull property of Bezier curves and the idea of cumulative position error. And since all operations involved in offsetting are linear geometric calculations, the method is very efficient and robust. In particular, this offsetting method is able to precisely provide a total solution to the complicated problem of NURBS-format tool path generation for pocketing. The enormous success behind this application is largely due to the fact that the method can obtain offset curves with globally controllable error and self-intersecting loops can be eliminated as early as when the initially linear approximation offsets are obtained. Hence, higher-degree continuous tool paths can be generated easily with no overcutting or cusps.
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