零件之「定位」與「夾持」為加工中首要考量的因素，曲面零件因為沒有明顯的平面特徵，所以定位與夾持相當困難。業界常以虎鉗夾持六面體素材來進行加工，但對於曲面零件的夾持往往必須設計專用夾具，甚至必須在曲面上建立能夠定位的平面特徵，此為相當不易且浪費時間的工作。
傳統之3-2-1定位原理時常被運用於規則幾何機械零件之定位與夾持，而這些零件必需具有容易定位與夾持的平面特徵，但當今之消費性產品大都為不規則形狀之曲面造型，沒有明顯的平面可供定位與夾持，因此本論文依X、-X、Y、-Y、Z、-Z六個方向夾45º夾角，以分出六個點群來對應到六面體的六個正交平面，將點群資料分別以X、Y、Z為參考做遞增排序後，刪除因非凸曲面造成不是在最外圍的點資料後，以3-2-1定位原理應用於曲面零件上，找尋適當的定位點與夾持點。最後，以這些參考點設計出一個彈性化夾具來進行夾持驗證，並於加工模擬軟體上模擬三軸加工之可行性。
彈性化的夾具設計能處理不同幾何形狀的曲面零件之夾持，降低專用化夾具設計的時間及人力成本，也能降低設計者加工經驗之門檻，突破設計與製造的鴻溝。

Fixturing and clamping of workpieces are one of the primary factors for machining processes. Lacking of obvious plane features makes it fairly difficult to clamp and locate a mechanical part with free-form surfaces. Clamping process by vises is often used for hexahedral workpieces in industrial applications, but for free-form surfaces, customized fixtures often must be designed for clamping process, and even a plane feature should be designed on a free-form surface part. These tasks are quite difficult and time-consuming.
The traditional 3-2-1 fixturing concept is often used to locate and clamp basic general mechanical parts which are composite by simple plane elements. On the contrary, free-form surfaces rarely include a plane feature so that it is difficult to locate and clamp. Therefore, this thesis classifies 6 groups of points by 45 degree boundary of normal vector on surfaces in six directions which are X, -X, Y, -Y, Z and -Z, similar to the six-axis orthogonal plane on hexahedral workpieces. After that, sort the point data in ascending order by X, Y, and Z to filter the points which are not on the outermost area occurs on a non-convex surface. At last, applying the 3-2-1 concept on a free-form surface and generate fixturing and clamping points by reference of the six point groups. After generating these reference points, a flexible fixture will be designed and after that we can verify those points for 3-axis machining by CAD model design and simulating machining process on computer aided manufacturing software.
Clamping different shape of free-form surfaces by a flexible fixture reduces the time and labor costs on design a customized one, and flexible fixture designing for free-form surfaces not only reduce the difficulty for designer which occur by lacking of processing experience, but also break the barrier between designer and manufacturer.

[1] Hui Wang, Yiming Rong, Hua Li and Price Shaun (2010), “Computer aided fixture design: Recent research and trends,” Computer-Aided Design, Vol. 42, pp. 1085-1094.
[2] Bartholomew O Nnaji, Saqib Alladin and Paul Lyu (1988), ”A framework for a rule-based expert fixturing system for face milling planar surfaces on a CAD system using flexible fixtures,” Journal of Manufacturing Systems,Vol. 7, pp. 193-207.
[3] Cai-Hua Xionga, You-Fu Lib, Y. Kevin Rongc and You-Lun Xiong (2002), “Qualitative analysis and quantitative evaluation of fixturing”, Robotics and Computer Integrated Manufacturing, Vol. 18, pp. 335-342.
[4] Van-Duc Nguyen (1988) ,“Constructing Force-Closure Grasps,” International Journal of Robotics Research, Vol.7, pp. 3-16.
[5] Xanthippi Markenscoff, Luqun Ni and Christos H. Papadimitriou (1990), “The Geometry of Grasping,” International Journal of Robotics Research, Vol. 9, pp. 61-74.
[6] J. Loncaric (1987), “Normal Forms of Stiffness and Compliance Matrices,” IEEE Journal on Robotics and Automation, Vol. 3, pp. 567-572.
[7] Y. Wu, Y. Rong, W. Ma, S.R. LeClair (1998), “Automated modular Fixture planning:Accuracy, clamping, and accessibility analyses”, Robotics and Computer-Integrated Manufacturing, Vol. 14,pp. 1-15.
[8] 邱至意，「3D曲面模型網格化之研究」(2010)，碩士論文，國立中央大學，機械工程研究所，桃園市。
[9] Y Zheng and Chee-Meng Chew (2010), “A geometric approach to automated fixture layout design,” Computer-Aided Design, Vol. 42, pp. 202-212.
[10] Y. Zheng, M.C. Lin and D. Manocha (2011), “Efficient simplex comptation for fixture layout design,” Computer-Aided Design, Vol. 43, pp. 1307-1318
[11] Chantal Wentink, A Frank Van Der Stappen and Mark Overmars (1996), “Algorithms for Fixture Design,” Algorithms for Robotic Motion and Manipulation, Editors: J-P. Laumond and M.H. Overmars, A K Peters/CRC Press.
[12] Y. Wu, Y. Rong, W. Ma and S.R. LeClair (1998), “Automated modular Fixture planning: Geometric analysis,” Robotics and Computer-Integrated Manufacturing, Vol. 14, pp. 17-26.
[13] H. Asada (1985), “Kinematic analysis of workpart fixturing for flexible assembly with automatically reconfigurable fixtures,” IEEE Journal on Robotics and Automation, Vol. 1, pp. 86-94.