本研究的目的是設計一個使用低電壓即可致動的XY移動平台，此移動平台利用壓電片作為致動器以進行XY方向的移動控制，掃描範圍之目標為10 µm × 10 µm。為使低操作電壓之實現，本研究採用壓電片進行致動，取代傳統使用壓電疊盤（piezo stack）為致動器，因此本研究可使移動平台的操作電壓有效降低。本研究之操作電壓為10伏特到30伏特，傳統壓電疊盤之操作電壓為100伏特到150伏特，如此便可有效降低移動平台之運作成本與提升操作便利性；為了因應操作電壓變小導致移動量減少的問題，本研究採取以槓桿原理放大位移大小的方向進行解決，以此原理為核心設計移動平台，並做實驗驗證可行性與歸納未來研究的修正方向。本研究之移動平台由兩個步進器組成，其分別控制了X方向與Y方向的移動，其中每個步進器中的主要部件包含有作為致動器的壓電片、當作槓桿的石英Z形桿與作為支點的刀片。在本研究中我們發現，實際移動量與槓桿原理直接推算的量有所差異，我們以ANSYS分析與手算推導公式進行實驗數據的驗證並確認其值有差異的原因為石英Z形桿發生彎曲變形。本研究藉由不同的刀片位置實驗找出最適合的刀片位置，並利用MATLAB繪出整體變形形狀之模型圖。
在得到施力端與抗力端的最適合比值為2: 3後，本研究置放XY方向各12片壓電片作致動，進行XY掃描實現，掃描結果能達到12 µm × 12 µm的移動範圍，也因為本研究之移動量與電壓的對應重現性高，因此未來僅需按照移動量與電壓值的對應即可達到12 µm × 12 µm範圍內的平台移動控制。

In this research, a low voltage XY positioning stage is designed to achieve a desired scanning range of 10 µm × 10 µm using a piezo ceramic disk as the actuator. The purpose of using this type of actuator instead of a piezo stack is because of its low cost and low driving voltage (10 V to 30 V), which is also to develop a low cost micro/nano positioning stage. The positioning stage is assembled using two steppers wherein one stepper has components such as a piezo ceramic disk, a quartz z-beam (z-shaped beam quartz) as cantilever, and a blade as hinge. The mechanism used in the stepper is a lever mechanism to magnify the moving distance of the driving side (piezo ceramic disk). We discovered the moving distance of the driving side did not magnify according to the lever magnification effect. To understand the cause, experiment data, ANSYS simulation, and computational results were compared and analyzed to identify that bending occurred on the z-beam causing the small moving distance. A schematic of the bending shape of the z-beam was shown using the deflection equation, and with Matlab, by plotting the computed deflection value at every point on the z-beam. The relationship of the lever magnification effect and the bending effect was also shown and is in correlation with the experiment data. After the problem was identified, using the best ratio (2:3) of this experiment, we achieved a moving distance of about 12 µm × 12 µm with 12 piezo disk actuators. As a result of gathering the data of moving distance versus voltage, we can identify what driving voltage to apply to achieve a desired moving distance.

Abstract i
中文摘要 ii
Acknowledgement …………………………………………………………………...iii
Contents iv
List of Figures v
List of Tables ix
1. Foreword 1
2. Literature Review 2
2.1. Micro actuator 2
2.1.1. Electromagnetic force 2
2.1.2. Electrostatic force 2
2.1.3. Piezoelectric effect 2
2.2. Micro/nano positioning stage 6
2.2.1. Electromagnetic positioning stage 6
2.2.2. Electrostatic positioning stage 7
2.2.3. Piezo actuated positioning stage 8
2.2.3.1. Monolithic XY positioning stage 8
2.2.3.2. Sectioned XY positioning stage 9
3. Design concept of the low voltage driven XY positioning stage 11
3.1. XY positioning stage 11
3.2. Stepper 11
3.3. Z-beam 12
4. Experiment setup 14
4.1. Piezo disk setup 14
4.2. Experiment setup 1 14
4.3. Experiment setup 2 17
5. Results and Discussion 18
5.1. Measured moving distance 18
5.2. ANSYS results 41
5.3. Computational results 56
6. Conclusion and future prospects 68
6.1. Conclusion 68
6.2. Future prospects 69
Reference 70

[1] K. Deng and E.T. Enikov, “Design and development of a pulsed electromagnetic micro-actuator for 3D virtual tactile displays,” Mechatronics, vol. 20, pp. 503-509, 2010.
[2] L. Petit, C. Prelle, E. Dore, F. Lamarque, and M. Bigerelle, “A Four-Discrete-Position Electromagnetic Actuator: Modeling and Experimentation,” IEEE/ASME Transactions on Mechatronics, vol. 15, pp. 88-96, 2010.
[3] S. He and R.B. Mrad, “Design, Modeling, and Demonstration of a MEMS Repulsive-Force Out-of-Plane Electrostatic Micro Actuator,” Journal of Microelectromechanical Systems, vol. 17, pp. 532-547, 2008.
[4] S. Towfighian, A. Seleim, E.M. Abdel-Rahman, and G.R. Heppler, “A large-stroke electrostatic micro-actuator,” Journal of Micromechanics and Microengineering, vol. 21, pp. 1-12, 2011.
[5] B. Watson, J. Friend, and L. Yeo, “Piezoelectric ultrasonic micro/milli-scale actuators,” Sensors and Actuators A: Physical, vol. 152, pp. 219-233, 2009.
[6] M. Guo, S. Dong, B. Ren, and H. Luo, “A Double-Mode Piezoelectric Single-Crystal Ultrasonic Micro-Actuator,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 57, pp. 2596-2600, 2010.
[7] A.A. Shah, “A FEM-BEM interactive coupling for modeling the piezoelectric health monitoring systems,” Latin American Journal of Solids and Structures, vol. 8, pp. 305-334, 2011.
[8] “Piezoelectric Tube Scanners,” (2015). Retrieved from http://www.piezodrive.com/product-tubes.html
[9] “Piezo Design: Fundamentals of Piezoelectric Actuation,” (2012). Retrieved from http://www.piezo.ws/piezoelectric_actuator_tutorial/Piezo_Design_part3.php#top
[10] W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono, and Y. Tomita, “ A surface motor-driven planar motion stage integrated with an XYθ_Z surface encoder for precision positioning,” Precision Engineering, vol. 28, pp. 329-337, 2004.
[11] X. Liu, K. Kim, and Y. Sun, “A MEMS stage for 3-axis nanopositioning,” Journal of Micromechanics and Microengineering, vol. 17, pp. 1796-1802, 2007.
[12] Y.K. Yong, S.S. Aphale, and S.O.R. Moheimani, “Design, Identification, and Control of a Flexure-Based XY Stage for Fast Nanoscale Positioning,” IEEE Transactions on Nanotechnology, vol. 8, pp. 46-54, 2009.
[13] X. Xiao, L. Pan, P. Liu, X. Tong, and C. Yin, “Comprehensive Optimization of an XY Nano Positioning Stage with Flexure-Hinges and Lever Mechanisms,” IEEE Proceedings of the Nanotechnology Materials and Devices Conference (NMDC), Monterey, California, USA, pp. 368-373, 2010.
[14] H. Tang and Y. Li, “Optimal Design of the Lever Displacement Amplifiers for a Flexure-based Dual-mode Motion Stage,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Kaohsiung, Taiwan, pp. 753-758, 2012.
[15] C.H. Kim and Y.K. Kim, “Micro XY-stage using silicon on a glass substate,” Journal of Micromechanics and Microengineering, vol. 12, pp. 103-107, 2002.
[16] S. Pilot and J. Dong, “Development of a High-Bandwidth XY Nanopositioning Stage for High-Rate Micro-/Nanomanufacturing,” IEEE/ASME Transactions on Mechatronics, vol. 16, pp. 724-733, 2011.
[17] G. Schitter, K.J. Astrom, B.E. DeMartini, P.J. Thurner, K.L. Turner, and P.K. Hansma, “Design and Modeling of a High-Speed AFM-Scanner,” IEEE Transactions on Control Systems Technology, vol. 15, pp. 906-915, 2007.
[18] K.K. Leang and A.J. Fleming, “High-Speed Serial-Kinematic SPM Scanner: Design and Drive Considerations,” Asian Journal of Control, vol. 11, pp. 144-153, 2009.
[19] S. Gonda, T. Kurosawa, and Y. Tanimura, “Mechanical performances of a symmetrical, monolithic three-dimensional fine-motion stage for nanometrology,” Measurement Science and Technology, vol. 10, pp. 986-993, 1999.
[20] I. Martinez, “Properties of Solids,” Department of Motor Propulsion and Thermo Fluid Dynamics, Universidad Politécnica de Madrid (2015). Retrieved from
http://webserver.dmt.upm.es/~isidoro/dat1/eSol.pdf
[21] ANSYS document “SOLID186,” Element Reference (2015).