摘要
本論文將針對一利用撓性鉸鍊及壓電致動器的XY精密定位平台進行分析、測試與實驗。此平台可減低撓性鉸鍊上的應力集中現象及在兩致動軸間獲得較低的干涉量。本文利用矩陣的關係式推導出風箱式撓性鉸鍊(bellow-type flexure hinges)機構的特性，並使用電腦解析軟體驗證。使用步階訊號測試平台的基本特性，X軸方向最大位移量為1.3微米，干涉量50奈米，Y軸方向最大位移量0.8微米，干涉量11奈米；若改成使用斜坡訊號驅動，則可在X軸得到最大位移量1.2微米及45奈米干涉量，在Y軸有最大位移量0.9微米和35奈米的干涉量。平台的等效應力與等效應變的分佈，可藉由有限元素軟體模擬得到。參照XY平台的特性測試結果，進行平台的定位實驗，可將目標物(target object)定位在與預定位移誤差10奈米以內的範圍。

Abstract
This paper reports about a precision positioning XY stage utilizing flexure hinges and piezoelectric actuators. XY stage was designed with the aim of reducing the stress-concentration of flexure hinges and the low interference between two actuating axes. Utilized the expression of matrix to figure out the properties of the bellow-type flexure hinges, and proved these by mathematical software. Experiments demonstrated that the stage actuated by a stairstep driving signal with maximum displacement 1.3μm and interference 50nm along X axis; along Y axis with maximum displacement 0.8μm and interference 11nm. The stage actuated by a ramp signal with maximum displacement 1.2μm and interference 45nm along X axis; along Y axis with maximum displacement 0.9μm and interference 35nm. The finite element method (FEM) was used to analyse the stress-concentration of the stage. and the simulated results were compared with the experiments. Referred to the testing results, the target object could be moved in the aimed position accurately.

摘要 8
ABSTRACT 9
符號說明 10
第一章 緒論 13
1-1 前言 13
1-2 奈米定位系統的歷史發展 14
1-3 研究目的 16
1-4 論文架構 17
第二章 奈米定位裝置介紹 18
2-1 壓電元件介紹 18
2-1-1 壓電效應發現 18
2-1-2 壓電元件的應用 18
2-1-3 壓電致動器的分類 19
2-1-4 壓電元件的基本特性 20
2-2 微奈米定位系統分類介紹 22
2-3-1利用靜態特性的定位裝置 22
2-2-2 利用動態特性的定位裝置 24
2-3-3 壓電元件與其他機械元件構成的定位裝置 25
第三章 XY超精密定位平台介紹與理論推導 28
3-1 XY定位平台介紹 28
3-2 XY平台剛性矩陣推導 30
3-2-1 撓性鉸鍊介紹 30
3-2-2 撓性鉸鍊基本剛性值推導 31
3-2-2 位移轉換矩陣推導 32
3-2-3 XY平台的剛性矩陣推導 38
3-2-4 XY平台的特徵值與特徵向量 46
3-3 XY平台動態特性推導 51
3-3-1 動態方程式推導 51
3-3-2 XY平台動態特性分析 52
第四章 XY平台相關實驗 56
4-1 實驗設備的架構 56
4-2 XY定位平台特性測試 57
4-2-1 測試方式 57
4-2-1 階梯式步階驅動訊號 58
4-2-2 斜坡驅動訊號 61
4-2-3 XY定位平台的步階響應 64
4-3 XY定位平台的應力與應變 65
4-3-1 建構XY定位平台的模組 66
4-3-2 XY定位平台的有限元素分析 66
4-4 XY平台定位控制 71
4-4-1 控制方法 71
4-4-2 實驗結果 71
第五章 總結 76
5-1 結論 76
5-2 未來展望 77
參考文獻 78

[1] 張所鋐, “奈米定位技術及應用”, 奈微米工程－精密製程與量測技術, 滄海書局, 2002, pp.247-320.
[2] 吳東權, “奈米科技”, 機械月刊, 2004, 346期, 文6-7.
[3] 黒澤富蔵 「ナノ計測への招待」,日本精密工學會,2003.
[4] 巫鎮華、王維漢, “奈米定位平台在奈米科技的應用”, 機械月刊, 2004, 346期, 文6-7.
[5] G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, “Surface Studies by Scanning Tunneling Microscopy”, Physical Review Letters, 49, 1982, pp.57-61.
[6] G. Binnig, C. F. Quate, and Ch. Gerber, “Atomic Force Microscope”, Physical Review Letters, 56, 1986, pp.930-933.
[7] D. M. Eigler, and E. K. Schweizer, “Positioning single atoms with a scanning tunnelling microscope”, Nature, Vol. 344, 1990, pp.524-526.
[8] Hideki Kawakatsu and Toshiro Higuchi, “A dual tunneling-unit scanning tunneling microscope”, Journal of Vacuum Science & Technology. A 8 (1), 1990, pp.319-323.
[9] N. Mikoshiba, S. Morita, and Y. Ishigame, “Multilayer Piezoelectric Actuators for Scanning Tunneling Microscope”, Japanese Journal of Applied Physics, Vol. 26, 1987, pp.200-202.
[10] S. H. Chang, C. K. Tseng, and H. C. Chien, “An Ultra-Precision XYθZ Piezo-Micropositioner PartⅠ：Design and Analysis”, IEEE Transaction on Ultrasonic, Ferroelectrics, and Frequency Control, Vol. 46, no. 4, 1999, pp.897-905.
[11] S. H. Chang, C. K. Tseng, and H. C. Chien, “An Ultra-Precision XYθZ Piezo-Micropositioner PartⅡ：Experiment and Performance”, IEEE Transaction on Ultrasonic, Ferroelectrics, and Frequency Control, Vol. 46, no.4, 1999, pp.906-911.
[12] Y. T. Liu and T. Higuchi, “Precision Positioning Device Utilizing Impact Force of Combined Piezo-Pneumatic Actuator”, IEEE/ASME Transactions on Mechatronics, Vol. 6, no. 4, 2001, pp.467-473.
[13] Y. T. Liu and C. W. Wang, “A self-moving precision positioning stage utilizing impact force of spring-mounted piezoelectric actuator”, Sensors and Actuators A, Vol.102, 2002, pp.83-92.
[14] N. Bonnail, D. Tonneau, G.-A. Capolino, and H. Dallaporta, “Dynamic and Static Responses of a Piezoelectric Actuator at Nanometer Scale Elongations”, IEEE, Vol.1, 2000, pp.293-298.
[15] J. M. Paros and L. Weisbord, “How to Design Flexure Hinges”, Machine Design, Vol.37, 1965, pp.151-156.
[16] S. T. Smith, “Flexures:Element of Elastic Mechanisms”, Gordon and Breach Science Publishers, New York, 2000.
[17] I. Her and J. C. Chang, “A Linear Scheme for the Displacement Analysis of Micropositioning Stages with Flexure Hinges” Transactions of the ASME, Vol. 116, 1994, pp.770-776.
[18] R. Yang, M. Jouaneh, and R. Schweizer, “Design and characterization of a low-profile micropositioning stage”, Precision Engineering, Vol.18, 1996, pp. 20-29.
[19] M. Jouaneh, and R. Yang, “Modeling of flexure-hinge type lever mechanisms”, Precision Engineering, Vol. 27, 2003, pp.407-418.
[20] 劉永田, “壓電元件在精密定位及自動組裝作業上的應用”, 奈微米工程－精密製程與量測技術, 滄海書局, 2002, pp.31-148.
[21] W. P. Manson, “Piezoelectricity, its history and applications”, The Journal of the Acoustical Society of America, 1981, pp.1561-1566.
[22] 內野研二, “演習/压電アクチュエータ”, 森北出版, 1991, pp.31-32.
[23] 小池, 齋藤, 石川, 友田, “積層型压電アクチュエータの作動解析”, 第5回電磁力関連のダイナミックスシンポジウム講演論文集, 1993, pp.376-381.
[24] Y.T. Liu, Y.M. Hwang, B.T. Huang, N. Nishioki, and T. Higuchi, “Testing of a Piezoelectric XY Stage Utilizing Bellow-Type Flexure Hinges, ICMT2003, 2003, Taipei, Taiwan.
[25] 樋口俊郎, 山形豐, “压電素子の急速変形を利用した超精密位置決め機構(第2報)”, 精密工学会誌, Vol.54, 1988, pp.2107-2112.
[26] 岡本泰浩, 吉田龍一, “圧電リニアアクチュエータの開発”, 電子通信学会論文誌, Vol. A, 1997, pp.1751-1756.
[27] 劉永田, “压電素子による衝擊力を用いた精密位置決め機構に関すゐ研究”, 東京大学工学系研究科博士論文, 1999.
[28] A. A. Shabana, “Theory of Vibration”, Spring-Verlag, New York, 1991.