本論文的研究對象為一新型六自由度混合式精密定位平台（專利申請中）。其構型設計首先是就水平運動（XY軸）機構各加上一楔形行程縮小裝置，以縮小其致動器之定位誤差而成一水平運動（XY軸）定位平台；再者，在水平運動（XY軸）定位平台上加裝一精密旋轉伺服平台以控制垂直旋轉（γ）軸；最後，在精密旋轉伺服平台上裝置一並聯式三自由度運動機構（α、β和Z軸），而成本論文所研究的六自由度精密定位平台。
　　為使後續研究能精確控制此定位平台，首先對其進行逆向、順向運動解的推導。接者，定義其並聯式三自由度定位平台的誤差源，並依據所設定的誤差源來建立其逆向、順向運動解誤差模型。最後，進行誤差參數的靈敏度分析，以作為設計人員訂定尺寸公差的參考依據。並且，由分析結果得知：當Y0軸之定位精度較不易受誤差影響。所以若此六自由度定位平台應用於AWG (Arrayed Waveguide Grating)及光纖陣列對位時，依分析結果建議其載具平台上光學元件的夾持方位為其光軸與X0軸平行較佳。

　　A new type of six-DOF composite precision positioning stage is the object of study in this thesis. This precision stage has a horizontal motion (X and Y axes) stage which is made by horizontal motion (X and Y axes) mechanism and wedge-shaped mechanism that reduce positioning error. Furthermore, an accurate rotary servo stage which controls the vertical rotary axis (γ axis) is designed on the horizontal motion (X and Y axes) stage. Then, this precision stage of this thesis is accomplished by arranging a three degree of freedom (α、β and Z axses) parallel kinematic mechanism on the accurate rotary servo stage.
　　In order to exactly control this positioning stage, the inverse and forward kinematic solutions are solved, firstly. Then, the fabricating error parameters of 3-DOF parallel kinematic postioning stage are defined and considered with the inverse/forward kinematic solutions, so that the error can be established. Finally, the errors sensitivity are analyzed and regarded as the designer's reference material. According to the result of analysis, the positioning accuracy of Y0-axis is not easily affected by fabricating errors. Therefore, it is the best choice for the optical axis of AWG (Arrayed Waveguide Grating) or fiber array on the loading stage are parallelled with X0-axis if this six-DOF positioning stage is applied to couple AWG with fiber array.

1. T. Saito, T. Ota, T. Toratani, and Y. Ono, “16-ch Arrayed Waveguide Grating Module with 100-GHz Spacing,” Furukawa Review, No.19, pp.47-52, 2000.
2. S. Ma, M. Jiang, J. Gao, and L. Lu, “New Progress of Coupling Technologies between High Density Array Fiber and Waveguides,” Changchun Suruga Seiki Co., Ltd., 2001.
3. J. Hasegawa, T. Saito, H. Koshi, and K. Kashihara, “Development of a Heater-control AWG Module,” Furukawa Review, No.22, pp.1-5, 2002.
4. J. Zheng and L. Lu, “Automatic Alignment System for AWGs,” Changchun Suruga Seiki Co., Ltd., 2001.
5. 趙玉麟, “光電計畫先期參與4X2.5G機構設計報告,” 工業技術研究院電子工業研究所, 民國90年。
6. 簡志賢, 黃相宇, “奈米對光平台與微細夾持技術,” 機械工業雜誌, 240期, pp.228-237, 民國92年。
7. “光電科技產業動態調查：我國與全球光電產業及技術動態調查報告,”財團法人光電科技工業協進會, 民國92年。
8. N. Henmi, K. Sato, S. Wada, and A. Shimokohbe, “A Six-degrees of Freedom Fine Motion Mechanism,” Mechatronics, Vol. 2 No. 5, pp. 445-457, 1992.
9. P. Gao, and S. M. Swei, “A Six-degree-of-freedom Micro-manipulator Based on Piezoelectric Translators,” Nanotechnology, No.10, pp.447-452, 1999.
10. R. C. Merkle, “A New Family of Six Degrees of Freedom Positional Devices,” Nanotechnology, No.8, pp.47-52, 1997.
11. T. Nomura, and R. Suzuki, “Six-axis Controlled Nanometer-order Positioning Stage for Microfabrication,” Nanotechnology, No.3, pp.21-28, 1992.
12. 白尉芬, 次奈米級三維六次元雷射測長與即時控制系統研究之初步成果, 碩士論文, 國立清華大學物理學系, 民國87年。
13. 蔡奇陵, 六自由度超精密奈米定位平台研製, 碩士論文, 國立臺灣大學機械工程學系, 民國90年。
14. 吳冬立, 並聯式六自由度奈米級微定位平台研製, 碩士論文, 國立臺灣大學機械工程學系, 民國91年。
15. 陳家豪, 奈米級精密定位平台之最佳位移解析度及軌跡圓之分析與量測, 碩士論文, 國立臺灣大學機械工程學系, 民國92年。
16. D. Stewart, “A Platform with Six Degrees of Freedom,” Proceedings of the Institution of Mechanical Engineering, Vol. 180, pp. 371-386, 1965.
17. K. M. Lee, and D. K. Shah, “Dynamic Analysis of a Three-degrees-of- freedom In-parallel Actuated Manipulator,” IEEE Journal of Robotics and Automation, Vol. 4, No. 3, pp. 361-367, 1988.
18. J. Denavit, and R. S. Hartenberg, “A Kinematic Notation for Lower Pair Mechanisms Based on Matrices,” ASME, Journal of Applied Mechanics, Vol.22, pp. 215-221, 1955.
19. P. M. Ferreira, and C.R. Liu, “An Analytical Quadratic Model for the Geometric Error of a Machine Tool,” Journal of Manufacturing Systems, Vol. 5, No.1. pp. 51-63, 1986.
20. K. F. Eman, and B. T. Wu, “A Generalized Geometric Error Model for Multi-axis Machines,” Annals of CIRP, Vol. 36, No.1, pp. 253-256, 1987.
21. O. Masory, J. Wang, and H. Zhuang, “On the Accuracy of a Stewart Platform-Part II Kinematic Calibration and Compensation,” Proceedings of the 1993 IEEE, International Conference on Robotics and Automation, pp. 725-731, 1993.
22. J. Wang, and O. Masory, “On the Accuracy of a Stewart Platform-Part I The Effect of Manufacturing Tolerances”, Proceedings of the 1993 IEEE, International Conference on Robotics and Automation, pp. 114-120, 1993.
23. K. H. Hunt, Kinematic Geometry of Mechanisms, Oxford University press, London, 1978.
24. H. Asada, and J.-J. E. Slotine, Robot Analysis and Control, John Wiley and Sons, Inc., 1986.
25. J. Fauvel, “Algorithms in the Pre-calculus Classroom: Who was Newton- Raphson?,” Mathematics in School 27, pp. 45-47, 1998.