CNC工具機傳統是用直線或圓弧的刀具路徑去加工，而這些路徑命令通常是以G碼來表示加工的命令，但近幾年來由於加工形狀的複雜化，工件需要更先進的幾何曲線，參數式曲線就常被來描述複雜的曲線和曲面，但通常加工時欲達到所需的精度，就必須將加工路徑以許多的直線的命令來趨近，因此會造成許多短線段，這不但會增加工具機記憶體的需求，在高速度和高精度的需求下，也容易因為急跳度過大容易造成工具機停擺甚至於損害或是因速度不平均，造成加工表面不平滑。近年來發展出一些以NURBS曲線為基底的控制器，就是為了改善此一問題，不但能減少工具機記憶體的使用，刀具的運動也更為平滑，所以加工高速度高精度也更容易去實現。
本論文提出若干關於實現參數式曲線加工命令的方法，主要是利用平滑的參數式軌跡路徑來改善傳統因短線段引起的種種問題，尤其在現今工具機追求高精度、高速度時更為重要。我們引入一些實現平滑軌跡路徑的方法，包括如何用參數式曲線在不失精度的前提下去擬合欲加工的路徑，這做法是為了配合現今大多數的電腦輔助設計軟體(CAM)還是使用短線段去趨近參數式刀具路徑的解決方法，而這些擬合的方法有插補(interpolation)方式的擬合和趨近(approximation)方式的擬合，這兩種方法各有優缺點，其中趨近方式的擬合可以有效的減少輸入的短線段資料。在本論文之後實做一參數式插值器(interpolator)，其中插值器負責把我們已經規劃好的參數式刀具路徑，解析成工具機各軸的運動命令，工具機各軸的馬達再利用這些命令去加工出我們希望的工件。當然，我們最後希望利用這些方法在工具機上實現高速度、高精度的高性能加工方法。

CNC machine tools have typically used linear and circular segments to generate tool paths. These segments are inputted to the controller by command data known as G-code. More recently, part geometry has become more complex requiring the use of more advanced curve geometries. Parametric curves are becoming more popular in design systems and these curves are approximated by a large number of linear segments before sending them to the controller. Unfortunately, to achieve the desired tolerance, a large number of very small line segments are produced. These can be prohibitive given memory capabilities of the CNC machine tools. In addition, the shortness of the linear segments can cause machine to halt because jerk of the machine tool is too large. To solve the problems, several NURBS interpolation methods have been developed. These methods can reduce the amount of data required by controllers and allow tools to move more smoothly. So it is easily to realize machining at high speed and high precise.
The purpose of this paper is to present several methods to implement NURBS interpolation. To begin with, this paper proposes two methods which fit line tool paths with interpolation and approximation. The purpose generates smooth parametric contour paths for solving the unsmooth problem resulted from massive short lines. Finally, this paper uses a PC-based controller as a real application for verifying machining results.

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