為因應未來高精度與高進給的自由曲面加工要求，本文開發多軸交叉耦合預補償法(MCCPM)做為複合型五軸工具機的控制核心，其構型是由六軸史都華平台搭配X-Y table，此工具機具備有平台高精密定位等優點，同時X-Y table更可以彌補平台工作空間不足的缺點。文中所設計的加工規劃可以有效擴大CCPM的運用範圍，此外，所提出的線上插補器設計除了能有效減低在加工過程中電腦的計算負擔外，高階自由曲線的運用概念更使得工具機的加工能力大為提升。其中定義的方向輪廓誤差與方向預補償更是一大突破，使得MCCPM可以達到在曲面加工時的表面精度要求；為配合自由曲線的特性，我們適當修正速度預補償的定義，考慮到預補償的補償方向，經由電腦模擬加工得到不錯的精度，特別是修正後的速度預補償能夠在軌跡急速轉彎時，其輪廓誤差不至於有太大擴張。

In order to achieve the request of high precision and high feed-rate in the future, the Multi-axis Cross-Coupled Pre-compensation method (MCCPM) is developed in this study for compound five-axis machine tools. The machine is composed of 6DOF Stewart -platform and X-Y table, it has the advantage of precise location of the platform and X-Y table can offset the defect of insufficient workspace. The processed planning proposed can enlarge the application of CCPM, the interpolator proposed can effective to reduce the load of PC under process, and the application of free-form curve increase the processed capability of the machine. Besides, the orientation contour error and the orientation pre-compensation are defined in this study and let MCCPM can achieve the request for the precision of processed surface. Furthermore, we modify pre-compensation for the characteristic of free-form surface and consider the direction of compensation. It has great precision by PC simulations. Especially when the trajectory is quick to change direction, the contour error not has large variation.

中文摘要 i
Abstract ii
致謝 iii
Contents iv
List of Tables vi
List of Figures vii
Nomenclature ix
Chapter.1 緒論 01
Chapter.2 MCCPM的基礎觀念 05
2.1 六自由度史都華平台的特性 05
2.1.1 逆向運動解 05
2.1.2 前向運動解 07
2.1.3 運動解的數值分析法 07
2.1.4 奇異曲面與工作空間 08
2.2 交叉耦合預補償法在兩軸工具機的使用 11
Chapter.3 MCCPM針對五軸CNC工具機的加工規劃 12
3.1 機構簡介 12
3.2 MCCPM針對五軸加工機的加工規劃 13
3.3 插補器設計-位置與方向軌跡的規劃 13
3.4 插補器設計-數學模式 15
3.4.1 標準五軸工具機模式的軌跡產生 15
3.4.2 複合型五軸工具機的軌跡產生 17
3.5 線上即時插補 18
Chapter.4多軸交叉耦合預補償控制器規劃 22
4.1 輪廓誤差模式 23
4.1.1 空間路徑輪廓誤差 24
4.1.2 方向輪廓誤差 25
4.2 預補償模式 28
4.2.1 空間路徑預補償 28
4.2.2 加工方向預補償 29
4.3 複合式五軸加工機的輪廓誤差與預補償 32
4.4 多軸交叉耦合預補償的演算步驟 36
Chapter.5 MCCPM模擬 40
5.1 史都華平台與X-Y table 的協調 41
5.2 MCCPM模擬 44
Chapter.6 結論 57
參考文獻 58

01. Y. Koren, “Cross-coupled biaxial computer control for manufacturing systems”, ASME Trans Journal of Dynamic System, Measurement and Control, Vol.102, No.4, 1980, p265-272
02. Y. Koren and Ch.-Ch. Lo, “Variable gain cross coupling control for contouring”, Annals of the CIRP, Vol.40, 1991, p371-374
03. Zong-Mu Yeh, “A cross-coupled bistage fuzzy controller for biaxis servomechanism control”, Fuzzy Sets and Systems 97, 1998, p265-275
04. Hua-Yi Chuang and Chang-Huan Liu, ”Cross-coupled adaptive feedrate control for multiaxis machine tool”, Journal of Dynamic Systems, Measurement and Control, Vol.113, 1991, p451-457
05. Y.S. Tarng, H.Y. Chuang and W.T. Hsu, “Intelligent cross-coupled fuzzy federate controller design for CNC machine tools based on genetic algorithms”, International Journal of Machine Tools & Manufacture 39, 1999, p1673-1692
06. K. Srinivasan, P.K. Kulkarni, “Cross-coupled control of biaxial feed drive servomechanisms”, Journal of Engineering for Industry, Vol.111, 1989, p140-148
07. YAW-SHIH SHIEH, AN-CHEN LEE, and CHIN-SHENG CHEN, “Cross-coupled biaxial step control for CNC EDM”, International Journal of Machine Tools & Manufacture, Vol.36, No.12, 1996, p1363-1383
08. JIH-HUA CHIN and TSUNG-CHING LIN, “Cross-coupled precompensation method for the contouring accuracy of computer numerically controlled machine tools”, International Journal of Machine Tools & Manufacture 37, 1997, No.7, p947-967
09. JIH-HUA CHIN and SHIN-TYI LIN, “The path precompensation method for flexible arm robot”, Robotics & Computer-Integrated Manufacturing, Vol.13, No.3, 1997, p203-215
10. Chin, J. H. and Lin, H. W., "The algorithms of the cross-coupled precompensation method for generating the involute-type scrolls" ASME J. Dynamic Systems, Measurement, and Control, March, Vol.121, 1999, pp.96-104
11. Chang-de Zhang, Shin-Min Song, “Forward kinematics of a class of parallel (Stewart) platforms with closed-form solutions”, Proceedings of the IEEE International Conference on Robots and Automation, p2676-2681, 1993
12. Z. Jason Geng and Leonard S. Haynes, “A 3-2-1 kinematics configuration of a Stewart platform and its application to six degree of freedom pose measurements”, Robotics & Computer-Integrated Manufacturing, Vol.11, No.1, p23-34, 1994
13. Xinhua Zhao, etc. “A successive approximation algorithm for the direct position analysis of parallel manipulators”, Mechanism and Machine Theory 35, p1095-1101, 2000
14. Partrick Huynh, etc. “Maximum velocity analysis of parallel manipulators”, IEEE International Conference on Robotics and Automation, p3268-3273, 1997
15. Timo Ropponen, etc. “Accuracy analysis of a modified Stewart platform manipulator”, IEEE International Conference on Robotics and Automation, p521-525, 1995
16. Jian Wang, etc. “On the accuracy of a Stewart platform- I. The effect of manufacturing tolerances”, IEEE International Conference on Robotics and Automation, p725-731, 1993
17. Oren Masory, etc. “On the accuracy of a Stewart platform- II. Kinematic calibration and compensation”, IEEE International Conference on Robotics and Automation, p114-120, 1993
18. Zhe Wang, etc. “A study on workspace, boundary workspace analysis and workpiece positioning for parallel machine tools”, Mechanism and Machine Theory 36, p605-622, 2001
19. S. Bhattacharya, etc. “Comparison of an exact and an approximate method of singularity avoidance in platform type parallel manipulators”, Mechanism and Machine Theory 33, No.7, p965-974, 1998
20. W. Khalil, D. Murareci “Kinematics analysis and singular configurations of a class of parallel robots”, Mathmatics and Computers in Simulation, Vol.41, p377-390, 1996
21. Vladimir Portman, "Deterministic metrology of platform-type machine tools", International Journal of Machine Tools & Manufacture 40, p1423-1442, 2000
22. Vladimir T. Portman, Ben-Zion Sandle, Eliahu Zahavi, "Rigid 6-DOF parallel platform for precision 3-D micromanipulation", International Journal of Machine Tools & Manufacture 41, p1229-1250, 2001
23. E.L.J. Bohez, “Five-axis milling machine tool kinematic chain design and analysis”, International Journal of Machine Tools & Manufacture 42, p505-520, 2002
24. Jianxin Pi, Edward Red and Greg Jensen, “Grind-free tool path generation for five-axis surface machining”, Computer Integrated Manufacturing Systems Vol.11, No.4, p337-350, 1998
25. Jae-Hee Kim, etc. “Development of a trajectory generation method for a five-axis NC machine”, Mechanism and Machine Theory 36, 983-996, 2001
26. C-C. Lo, “Efficient cutter-path planning for five-axis surface machining with a flat-end cutter”, Computer-Aided Design 31, 557-566, 1999
27. Chih-Ching Lo, ”Real-time generation and control of cutter path for 5-axis CNC machining”, International Journal of Machine Tools & manufacture Vol.39, 471-488, 1999
28. Y. Koren, ”Five-Axis surface interpolators”, Annals of CIRP, Vol.44, 1995
29. 蔡和其, ”Path Precompensation Algorithm for robotic machining of spatial curves and surfaces”, Institute of Mechanical Engineering, National Chiao-Tung., Taiwan, ROC., Master’s Thesis, 1992
30. 劉燿睿, ”The development of the cross-coupled precompensation method for tracking higher order curves”, Institute of Mechanical Engineering, National Chiao-Tung., Taiwan, ROC., Master’s Thesis, 1996
31. 林胡偉, ”The algorithms of the cross-coupled precompensation method for generating the involute-type scrolls” , Institute of Mechanical Engineering, National Chiao-Tung., Taiwan, ROC., Master’s Thesis, 1997
32. 林錦輝, ”The development of fuzzy logic controller for contour control using cross-coupled precompensation method” , Institute of Mechanical Engineering, National Chiao-Tung., Taiwan, ROC., Master’s Thesis, 1999
33. 江仁傑, “Improvement of flight simulator through motion control on hydraulic cylinder” , Institute of Mechanical Engineering, National Chiao-Tung., Taiwan, Master’s Thesis, 2000
34. 謝振揚, ”The influence of hydraulics in motion simulation system” , Institute of Mechanical Engineering, National Chiao-Tung., Taiwan, ROC., Master’s Thesis, 2001
35. KUNWOO LEE, “Principles of CAD/CAM/CAE system”, Addison Wesley, 1999
36. M.L. James, etc. “Applied numerical methods for digital computation”, Harper Collins, 1993, fourth edition