Mechanical Design of High-Speed Nanopositioning Systems

Chapter

Abstract

The performance of a nanopositioning system is tightly coupled to the quality of the mechanical design. Good mechanical design will minimize most position errors and improve overall accuracy and performance. Poor mechanical design, on the other hand, can lead to more errors than the issues associated with the electronics, control system, and other components. In this chapter, an overview of mechanical design is presented, where the emphasis on flexure-guided nanopositioning stages for high-speed nanopositioning. The discussions will focus on systems driven by piezoelectric actuators such as plate-stacks, which are readily available from a number of commercial suppliers. Design examples of parallel- and serial-kinematic scanners are presented to illustrate the design process.

Keywords

Resonance Frequency Piezoelectric Actuator Effective Stiffness Total Strain Energy Flexure Hinge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgements

Y. K. Yong would like to acknowledge Prof. Reza Moheimani for many years of support, guidance, and valuable feedback, her colleagues at the Laboratory for Dynamics and Control of Nanosystems for providing meaningful discussions and creating an incredible research environment, and the University of Newcastle for their commitment to a young researcher. She also wishes to thank the Australian Research Council for supporting her research work. K.K. Leang acknowledges A.J. Fleming for many years of collaboration and for providing the PiezoDrive amplifiers used in the experiments. Additionally, he thanks the National Science Foundation for supporting his research work.

References

  1. 1.
    N.M. Abbas, D.G. Solomon, M.F. Bahari, A review on current research trends in electrical discharge machining (EDM). Int. J. Mach. Tool. Manuf. 47, 1214–1228 (2007)CrossRefGoogle Scholar
  2. 2.
    C. Acar, A. Shkel, MEMS Vibratory Gyroscopes: Structural Approaches to Improve Robustness, 1st edn. (Springer, New York, 2009). doi:10.1007/978-0-387-09536-3 CrossRefGoogle Scholar
  3. 3.
    T. Ando, N. Kodera, E. Takai, D. Maruyama, S. Kiwamu, A. Toda, A high-speed atomic force microscope for studying biological macromolecules. Proc. Natl. Acad. Sci. U. S. A. 98, 12468–12472 (2001)CrossRefGoogle Scholar
  4. 4.
    T. Ando, N. Kodera, T. Uchihashi, A. Miyagi, R. Nakakita, H. Yamashita, K. Matada, High-speed atomic force microscope for capturing dynamic behavior of protein molecules at work. e-J. Surf. Sci. Nanotechnol. 3, 384–392 (2005)Google Scholar
  5. 5.
    T. Ando, T. Uchihashi, T. Fukuma, High-speed atomic force microscopy for nano-visualization of dynamic biomolecular processes. Prog. Surf. Sci. 83(7–9), 337–437 (2008)CrossRefGoogle Scholar
  6. 6.
    T. Ando, T. Uchihashi, N. Kodera, D. Yamamoto, A. Miyagi, M. Taniguchi, H. Yamashita, High-speed AFM and nano-visualization of biomolecular processes. Pflügers Arch. Eur. J. Physiol. 456(1), 211–225 (2008)CrossRefGoogle Scholar
  7. 7.
    APC International Ltd: Piezo-Mechanics: An Introduction. APC International Ltd., Pleasant Gap (2003)Google Scholar
  8. 8.
    A. Bazaei, Y.K. Yong, S.O.R. Moheimani, High-speed Lissajous-scan atomic force microscopy: scan pattern planning and control design issues. Rev. Sci. Instrum. 83(6), 063701 (10pp.) (2012)Google Scholar
  9. 9.
    F. Beer, E.R. Johnston, Mechanics of Materials (McGraw-Hill, New York, 1992)Google Scholar
  10. 10.
    G. Binnig, C.F. Quate, Atomic force microscope. Phys. Rev. Lett. 56(9), 930–933 (1986)CrossRefGoogle Scholar
  11. 11.
    G. Binnig, H. Rohrer, The scanning tunneling microscope. Sci. Am. 253, 50–56 (1986)CrossRefGoogle Scholar
  12. 12.
    G. Borionetti, A. Bazzali, R. Orizio, Atomic force microscopy: a powerful tool for surface defect and morphology inspection in semiconductor industry. Eur. Phys. J. Appl. Phys. 27, 101–106 (2004). doi:10.1051/epjap:2004129 CrossRefGoogle Scholar
  13. 13.
    K.H.J. Buschow, F.R. de Boer, Physics of Magnetism and Magnetic Materials, (Kluwer Academic Publishers, New York, 2004)Google Scholar
  14. 14.
    W.D. Callister, Materials Science and Engineering: An Introduction (Wiley, New York, 1994)Google Scholar
  15. 15.
    F. Cardarelli, Materials Handbook: A Concise Desktop Reference, 2nd edn. (Springer, London, 2000)CrossRefGoogle Scholar
  16. 16.
    R.R. Craig, Mechanics of Materials, 2nd edn. (Wiley, New York, 2000)Google Scholar
  17. 17.
    M.L. Culpepper, G. Anderson, Design of a low-cost nano-manipulator which utilizes a monolithic, spatial compliant mechanism. Precis. Eng. 28(4), 469–482 (2004)CrossRefGoogle Scholar
  18. 18.
    T. Dahlberg, Procedure to calculate deflections of curved beams. Int. J. Eng. Educ. 20(3), 503–513 (2004)Google Scholar
  19. 19.
    N.B. Dahotre, S.P. Harimkar, Laser Fabrication and Machining of Materials (Springer, New York, 2008)Google Scholar
  20. 20.
    S. Devasia, E. Eleftheriou, S.O.R. Moheimani, A survey of control issues in nanopositioning. IEEE Trans. Control Syst. Technol. 15, 802–823 (2007)CrossRefGoogle Scholar
  21. 21.
    G.K. Fedder, Simulation of microelectromechanical systems. Ph.D. thesis, Electrical Engineering and Computer Sciences, University of California at Berkeley (1994)Google Scholar
  22. 22.
    A.J. Fleming, A megahertz bandwidth dual-amplifier for driving piezoelectric actuators and other highly capacitive loads. Rev. Sci. Instrum. 80(1–7), 104701 (2009)Google Scholar
  23. 23.
    A. Fleming, Dual-stage vertical feedback for high-speed scanning probe microscopy. IEEE Trans. Control Syst. Technol. 19(1), 156–165 (2011)CrossRefGoogle Scholar
  24. 24.
    A.J. Fleming, K.K. Leang, Design, Modeling and Control of Nanopositioning Systems (Springer, London, 2014).CrossRefGoogle Scholar
  25. 25.
    P. Gao, S. Swei, Z. Yuan, A new piezodriven precision micropositioning stage utilizing flexure hinges. Nanotechnology 10, 394–398 (1999)CrossRefGoogle Scholar
  26. 26.
    D.C. Handley, T.F. Lu, Y.K. Yong, Workspace investigation of a 3dof compliant micro-motion stage, in The Eighth International Conference on Control, Automation, Robotics and Vision, ICARCV, pp. 1279–1284 (2004)Google Scholar
  27. 27.
    K.H. Ho, S.T. Newman, S. Rahimifard, R.D. Allen, State of the art in wire electrical discharge machining (WEDM). Int. J. Mach. Tools Manuf. 44(12–13), 1247–1259 (2004)CrossRefGoogle Scholar
  28. 28.
    L. Howell, Compliant Mechanisms. (Wiley, New York, 2001)Google Scholar
  29. 29.
    A.D.L. Humphris, B. Zhao, D. Catto, J.P. Howard-Knight, P. Kohli, J.K. Hobbs, High speed nano-metrology. Rev. Sci. Instrum. 82(4), 043710–5 (2011)CrossRefGoogle Scholar
  30. 30.
    D.J. Inman, Engineering Vibration. Prentice Hall Inc., Upper Saddle River (1996)Google Scholar
  31. 31.
    M.S. Johannes, D.G. Cole, R.L. Clark, Atomic force microscope based nanofabrication of master pattern molds for use in soft lithography. Appl. Phys. Lett. 91(12), 123111 (2007)Google Scholar
  32. 32.
    M. Jouaneh, R. Yang, Modeling of flexure-hinge type lever mechanisms. Precis. Eng. 27, 407–418 (2003)CrossRefGoogle Scholar
  33. 33.
    B.J. Kenton, Design, characterization, and control of a high-bandwidth serial-kinematic nanopositioning stage for scanning probe microscopy applications. Master’s thesis, University of Nevada, Reno (2010)Google Scholar
  34. 34.
    B.J. Kenton, A.J. Fleming, K.K. Leang, Compact ultra-fast vertical nanopositioner for improving scanning probe microscope scan speed. Rev. Sci. Instrum. 82(12), 123703 (2011)Google Scholar
  35. 35.
    B.J. Kenton, K.K. Leang, Design and control of a three-axis serial-kinematic high-bandwidth nanopositioner. IEEE/ASME Trans. Mechatron. 17(2), 356–368 (2012)CrossRefGoogle Scholar
  36. 36.
    D. Kim, D. Kang, J. Shim, I. Song, D. Gweon, Optimal design of a flexure hinge-based XYZ atomic force microscopy scanner for minimizing abbe errors. Rev. Sci. Instrum. 76, 073706 (2005)CrossRefGoogle Scholar
  37. 37.
    J.H. Kindt, G.E. Fantner, J.A. Cutroni, P.K. Hansma, Rigid design of fast scanning probe microscopes using finite element analysis. Ultramicroscopy 100, 259–265 (2004)CrossRefGoogle Scholar
  38. 38.
    K.K. Leang, A.J. Fleming, High-speed serial-kinematic AFM scanner: design and drive considerations. Asian J. Control (Special issue on Advanced Control Methods for Scanning Probe Microscopy Research and Techniques) 11(2), 144–153 (2009)Google Scholar
  39. 39.
    D.J. Leo, Engineering Analysis of Smart Material Systems. (Wiley, Hoboken, 2007)Google Scholar
  40. 40.
    D. Leonard, M. Krishnamurthy, C.M. Reaves, S.P. Denbaars, P.M. Petroff, Direct formation of quantum-sized dots from uniform coherent islands of InGaAs on GaAs surfaces. Appl. Phys. Lett. 63(23), 3203–3205 (1993)CrossRefGoogle Scholar
  41. 41.
    Y. Li, Q. Xu, Modeling and performance evaluation of a flexure-based xy parallel micromanipulator. Mech. Mach. Theory 44(12), 2127–2152 (2009)MATHCrossRefGoogle Scholar
  42. 42.
    Y. Li, Q. Xu, Development and assessment of a novel decoupled xy parallel micropositioning platform. IEEE/ASME Trans. Mechatron. 15(1), 125–135 (2010)CrossRefGoogle Scholar
  43. 43.
    H.C. Liaw, B. Shirinzadeh, Neural network motion tracking control of piezo-actuated flexure-based mechanisms for micro-/nanomanipulation. IEEE/ASME Trans. Mechatron. 14(5), 517–527 (2009). doi:10.1109/TMECH.2009.2005491 CrossRefGoogle Scholar
  44. 44.
    N. Lobontiu, Compliant Mechanisms: Design of Flexure Hinges (CRC Press, Boca Raton, 2003)Google Scholar
  45. 45.
    N. Lobontiu, E. Garcia, Analytical model of displacement amplification and stiffness optimization for a class of flexure-based compliant mechanisms. Comput. Struct. 81, 2797–2810 (2003)CrossRefGoogle Scholar
  46. 46.
    N. Lobontiu, E. Garcia, Two-axis flexure hinges with axially-collocated and symmetric notches. Comput. Struct. 81, 1329–1341 (2003)CrossRefGoogle Scholar
  47. 47.
    N. Lobontiu, J.S.N. Paine, E. Garcia, M. Goldfarb, Corner-filleted flexure hinges. Trans. ASME J. Mech. Des. 123, 346–352 (2001)CrossRefGoogle Scholar
  48. 48.
    N. Lobontiu, J.S.N. Paine, E. O’Malley, M. Samuelson, Parabolic and hyperbolic flexure hinges: flexibility, motion precision and stress characterization based on compliance closed-form equations. Precis. Eng. 26, 183–192 (2002)CrossRefGoogle Scholar
  49. 49.
    T.F. Lu, D.C. Handley, Y.K. Yong, C. Eales, A three-DOF compliant micromotion stage with flexure hinges. Ind. Robot 31(4), 355–361 (2004)CrossRefGoogle Scholar
  50. 50.
    H.W. Ma, Y. Shao-Ming, L.Q. Wang, Z. Zhong, Analysis of the displacement amplification ratio of bridge-type flexure hinge. Sens. Actuators A Phys. 132(2), 730–736 (2006)CrossRefGoogle Scholar
  51. 51.
    I.A. Mahmood, S.O.R. Moheimani, Fast spiral-scan atomic force microscopy. Nanotechnology 20(36), 365503 (2009)Google Scholar
  52. 52.
    I.A. Mahmood, S.O.R. Moheimani, B. Bhikkaji, A new scanning method for fast atomic force microscopy. IEEE Trans. Nanotechnol. 10(2), 203–216 (2010)CrossRefGoogle Scholar
  53. 53.
    M. Maroufi, A.G. Fowler, A. Bazaei, S.O.R. Moheimani, High-stroke silicon-on-insulator MEMS nanopositioner: control design for non-raster scan AFM. Rev. Sci. Instrum. 86(2), 023705 (12pp) (2015)Google Scholar
  54. 54.
    R. Merry, N. de Kleijn, M. van de Molengraft, M. Steinbuch, Using a walking piezo actuator to drive and control a high-precision stage. IEEE/ASME Trans. Mechatron. 14(1), 21–31 (2009)CrossRefGoogle Scholar
  55. 55.
    S. Miyake, M. Wang, J. Kim, Silicon nanofabrication by atomic force microscopy-based mechanical processing. J. Nanotechnol. 2014, 102404 (2014)Google Scholar
  56. 56.
    A. Mohammadi, A.G. Fowler, Y.K. Yong, S.O.R. Moheimani, A feedback controlled mems nanopositioner for on-chip high-speed afm. IEEE J. Microelectromech. Syst. 23(3), 610–619 (2014)CrossRefGoogle Scholar
  57. 57.
    S.O.R. Moheimani, Invited review article: accurate and fast nanopositioning with piezoelectric tube scanners: Emerging trends and future challenges. Rev. Sci. Instrum. 79(7), 071101 (2008)Google Scholar
  58. 58.
    B. Mokaberi, A.A.G. Requicha, Compensation of scanner creep and hysteresis for AFM nanomanipulation. IEEE Trans. Autom. Sci. Eng. 5(2), 197–206 (2008)CrossRefGoogle Scholar
  59. 59.
    Newcastle Innovation Ltd., Industry Development Centre, University Drive, Callaghan NSW 2308, Australia: PiezoDrive PDL200 Manual, www.piezodrive.com
  60. 60.
    S.R. Park, A mathematical approach for analyzing ultra precision positioning system with compliant mechanism. J. Mater. Res. Process. Technol. 164–165, 1584–1589 (2005)CrossRefGoogle Scholar
  61. 61.
    J.M. Paros, L. Weisbord, How to design flexure hinges. Mach. Des. 37, 151–156 (1965)Google Scholar
  62. 62.
    J. Peng, X. Chen, Modeling of piezoelectric-driven stick-slip actuators. IEEE/ASME Trans. Mechatron. 16(2), 394–399 (2011)CrossRefGoogle Scholar
  63. 63.
    A.P. Pisano, Y.H. Cho, Mechanical design issues in laterally-driven microstructures. Sens. Actuators A Phys. 23(1–3), 1060–1064 (1990). Proceedings of the 5th International Conference on Solid-State Sensors and Actuators and Eurosensors {III}Google Scholar
  64. 64.
    A.B. Puri, B. Bhattacharyya, An analysis and optimisation of the geometrical inaccuracy due to wire lag phenomenon. Int. J. Mach. Tools Manuf. 43, 151–159 (2003)CrossRefGoogle Scholar
  65. 65.
    M. Rakotondrabe, Y. Haddab, P. Lutz, Development, modeling, and control of a micro-/nanopositioning 2-dof stick-slip device. IEEE/ASME Trans. Mechatron. 14(6), 733–745 (2009)CrossRefGoogle Scholar
  66. 66.
    J.W. Ryu, D.G. Gweon, Error analysis of a flexure hinge mechanism induced by machining imperfection. Precis. Eng. 21, 83–89 (1997)CrossRefGoogle Scholar
  67. 67.
    S. Salapaka, A. Sebastian, J.P. Cleveland, M.V. Salapaka, High bandwidth nano-positioner: A robust control approach. Rev. Sci. Instrum. 73(9), 3232–3241 (2002)CrossRefGoogle Scholar
  68. 68.
    R.B. Salazar, A. Shovsky, H. Schonherr, G.J. Vancso, Dip-pen nanolithography on (bio)reactive monolayer and block-copolymer platforms: Deposition of lines of single macromolecules. Small 2(11), 1274–1282 (2006)CrossRefGoogle Scholar
  69. 69.
    G. Schitter, K.J. Åstrom, B. DeMartini, P.J. Thurner, K.L. Turner, P.K. Hansma, Design and modeling of a high-speed AFM-scanner. IEEE Trans. Control Syst. Technol. 15(5), 906–915 (2007)CrossRefGoogle Scholar
  70. 70.
    G. Schitter, P.J. Thurner, P.K. Hansma, Design and input-shaping control of a novel scanner for high-speed atomic force microscopy. Mechatronics 18, 282–288 (2008)CrossRefGoogle Scholar
  71. 71.
    F. Scire, E. Teague, Piezodriven 50-μm range stage with subnanometer resolution. Rev. Sci. Instrum. 49(12), 1735–1740 (1978)CrossRefGoogle Scholar
  72. 72.
    See Asylum Research: http://asylumresearch.com for information on flexure-based nanopositioning platforms
  73. 73.
    See Mad City Labs Inc: http://www.madcitylabs.com/ for information on flexure-based nanopositioning applications
  74. 74.
    See Park Systems: www.parkafm.com for information on the use of flexure-based nanopositioning platforms in commercially available AFMs
  75. 75.
    E. Shamoto, T. Moriwaki, Ultraprecision diamond cutting of hardened steel by applying elliptical vibration cutting. CIRP Ann. Manuf. Technol. 48(1), 441–444 (1999)CrossRefGoogle Scholar
  76. 76.
    M. Shiga, Invar alloys. Curr. Opin. Solid State Mater. Sci. 1(3), 340–348 (1996). doi:10.1016/S1359-0286(96)80023-4 MathSciNetCrossRefGoogle Scholar
  77. 77.
    V. Shilpiekandula, K. Youcef-Toumi, Dynamic modeling and performance trade-offs in flexure-based positioning and alignment systems, Chapter 25, in Motion Control, ed. by F. Casolo (InTech, Croatia, 2010), pp. 481–496Google Scholar
  78. 78.
    S.T. Smith, Flexures: Elements of Elastic Mechanisms. (Gordon and Breach, New York, 2000)Google Scholar
  79. 79.
    G.T. Smith, Cutting Tool Technology: Industrial Handbook. (Springer, London, 2008)Google Scholar
  80. 80.
    S.T. Smith, V.G. Badami, J.S. Dale, Y. Xu, Elliptical flexure hinges. Rev. Sci. Instrum. 68(3), 1474–1483 (1997)CrossRefGoogle Scholar
  81. 81.
    T.A. Spedding, Z.Q. Wang, Study on modeling of wire EDM process. J. Mater. Process. Technol. 69, 18–28 (1997)CrossRefGoogle Scholar
  82. 82.
    D.J. Taatjes, A.S. Quinn, J.H. Rand, B.P. Jena, Atomic force microscopy: high resolution dynamic imaging of cellular and molecular structure in health and disease. J. Cell. Physiol. 228(10), 1949–1955 (2013)CrossRefGoogle Scholar
  83. 83.
    The World of Micro- and NanoPositioning (PI catalog). Physik Instrumente, Karlsruhe (2005)Google Scholar
  84. 84.
    S.P. Timoshenko, History of Strength of Materials. (McGraw-Hill Book Company, New York, 1953)Google Scholar
  85. 85.
    A.A. Tseng, Advancements and challenges in development of atomic force microscopy for nanofabrication. Nano Today 6(5), 493–509 (2011)CrossRefGoogle Scholar
  86. 86.
    A.A. Tseng, S. Jou, A. Notargiacomo, T. Chen, Recent developments in tip-based nanofabrication and its roadmap. J. Nanosci. Nanotechnol. 8, 2167–2186 (2008)CrossRefGoogle Scholar
  87. 87.
    Y.M. Tseytlin, Notch flexure hinges: an effective theory. Rev. Sci. Instrum. 73(9), 3363–3368 (2002)MathSciNetCrossRefGoogle Scholar
  88. 88.
    T. Tuma, J. Lygeros, V. Kartik, A. Sebastian, A. Pantazi, High-speed multiresolution scanning probe microscopy based on Lissajous scan trajectories. Nanotechnology 23(18), 185501 (2012)Google Scholar
  89. 89.
    S. Wadikhaye, Y.K. Yong, S.O.R. Moheimani, B. Bhikkaji, Control of a piezoelectrically actuated high-speed serial kinematic AFM nanopositioner. Smart Mater. Struct. 22(2), 025030 (12pp.) (2014)Google Scholar
  90. 90.
    C. Wang, V.K. Yadavalli, Investigating biomolecular recognition at the cell surface using atomic force microscopy. Micron 60(0), 5–17 (2014)Google Scholar
  91. 91.
    D.L. White, O.R. Wood, Novel alignment system for imprint lithography. Rev. Sci. Instrum. 18(6), 3552–3556 (2000)Google Scholar
  92. 92.
    K. Wiesauer, G. Springholz, Fabrication of semiconductor nanostructures by nanoindentation of photoresist layers using atomic force microscopy. J. Appl. Phys. 88(12), 7289–7297 (2000)CrossRefGoogle Scholar
  93. 93.
    P. Xu, Y. Jingjun, Z. Guanghua, B. Shusheng, Y. Zhiwei, Analysis of rotational precision for an isosceles-trapezoidal flexural pivot. J. Mech. Des. 130(5), 052302 (9pp.) (2008). doi:10.1115/1.2885507
  94. 94.
    Y.K. Yong, A. Fleming, Piezoelectric actuators with integrated high-voltage power electronics. IEEE/ASME Trans. Mechatron. 20(2), 611–617 (2015)CrossRefGoogle Scholar
  95. 95.
    Y.K. Yong, T.F. Lu, The effect of the accuracies of flexure hinge equations on the output compliances of planar micro-motion stages. Mech. Mach. Theory 43, 347–363 (2008)MATHCrossRefGoogle Scholar
  96. 96.
    Y.K. Yong, T.F. Lu, Kinetostatic modeling of 3-RRR compliant micro-motion stages with flexure hinges. Mech. Mach. Theory 44(6), 1156–1175 (2009)MATHCrossRefGoogle Scholar
  97. 97.
    Y.K. Yong, S.O.R. Moheimani, A compact XYZ scanner for fast atomic force microscopy in constant force contact mode, in IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Montreal (2010)Google Scholar
  98. 98.
    Y.K. Yong, S.O.R. Moheimani, Design of an inertially counterbalanced Z-nanopositioner for high-speed atomic force microscopy. IEEE/ASME Trans. Nanotechnol. 12(2), 137–145 (2013)CrossRefGoogle Scholar
  99. 99.
    Y.K. Yong, T.F. Lu, D.C. Handley, Review of circular flexure hinge design equations and derivation of empirical formulations. Precis. Eng. 32(2), 63–70 (2008)CrossRefGoogle Scholar
  100. 100.
    Y.K. Yong, S. Aphale, S.O.R. Moheimani, Design, identification and control of a flexure-based XY stage for fast nanoscale positioning. IEEE Trans. Nanotechnol. 8(1), 46–54 (2009)CrossRefGoogle Scholar
  101. 101.
    Y.K. Yong, K. Liu, S.O.R. Moheimani, Reducing cross-coupling in a compliant XY nanopositioning stage for fast and accurate raster scanning. IEEE Trans. Control Syst. Technol. 18(5), 1172–1179 (2010)CrossRefGoogle Scholar
  102. 102.
    Y.K. Yong, S.O.R. Moheimani, I.R. Petersen, High-speed cycloid-scan atomic force microscopy. Nanotechnology 21(36), 365503 (2010)Google Scholar
  103. 103.
    Y.K. Yong, B. Bhikkaji, S.O.R. Moheimani, Analog control of a high-speed atomic force microscope scanner, in IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Budapest (2011)Google Scholar
  104. 104.
    Y.K. Yong, S.O.R. Moheimani, B.J. Kenton, K.K. Leang, Invited review article: high-speed flexure-guided nanopositioning: mechanical design and control issues. Rev. Sci. Instrum. 83(12), 121101 (2012)Google Scholar
  105. 105.
    Y.K. Yong, B. Bhikkaji, S.O.R. Moheimani, Design, modeling and FPAA-based control of a high-speed atomic force microscope nanopositioner. IEEE/ASME Trans. Mechatron. 18(3), 1060–1071 (2013)CrossRefGoogle Scholar
  106. 106.
    Y.K. Yong, A. Bazaei, S.O.R. Moheimani, Video-rate Lissajous-scan atomic force microscopy. IEEE Trans. Nanotechnol. 13(1), 85–93 (2014)CrossRefGoogle Scholar
  107. 107.
    W.C. Young, R.G. Budynas, Roark’s Formula for Stress and Strain, 7th edn. (McGraw-Hill, New York, 2002)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of Electrical Engineering and Computer ScienceThe University of NewcastleCallaghanAustralia
  2. 2.Department of Mechanical EngineeringThe University of UtahUTUSA

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