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Shock and Vibration
Volume 2015 (2015), Article ID 672831, 10 pages
http://dx.doi.org/10.1155/2015/672831
Research Article

Compliance Matrix of a Single-Bent Leaf Flexure for a Modal Analysis

1School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749, Republic of Korea
2Department of Mechanical Engineering, Dong-A University, Busan 604-714, Republic of Korea

Received 22 March 2015; Accepted 4 May 2015

Academic Editor: Chao Tao

Copyright © 2015 Nghia-Huu Nguyen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E.-J. Park, J. Shim, D.-Y. Lee, and J. Lee, “A double-bent planar leaf flexure guide for a nano-scanner,” Journal of the Korean Physical Society, vol. 57, no. 61, pp. 1581–1588, 2010. View at Publisher · View at Google Scholar · View at Scopus
  2. K. Kim, D. Ahn, and D. Gweon, “Optimal design of a 1-rotational DOF flexure joint for a 3-DOF H-type stage,” Mechatronics, vol. 22, no. 1, pp. 24–32, 2011. View at Publisher · View at Google Scholar · View at Scopus
  3. T. T. Y. Koseki, T. Tanikawa, N. Koyachi, and T. Arai, “Kinematic analysis of a translational 3-d.o.f. micro-parallel mechanism using the matrix method,” Advanced Robotics, vol. 16, no. 3, pp. 251–264, 2002. View at Publisher · View at Google Scholar · View at Scopus
  4. J. H. Kim, S. H. Kim, and Y. K. Kwak, “Development and optimization of 3-D bridge-type hinge mechanisms,” Sensors and Actuators A: Physical, vol. 116, no. 3, pp. 530–538, 2004. View at Publisher · View at Google Scholar · View at Scopus
  5. J. W. Ryu, D.-G. Gweon, and K. S. Moon, “Optimal design of a flexure hinge based XYφ wafer stage,” Precision Engineering, vol. 21, no. 1, pp. 18–28, 1997. View at Publisher · View at Google Scholar · View at Scopus
  6. N. Lobontiu and E. Garcia, “Analytical model of displacement amplification and stiffness optimization for a class of flexure-based compliant mechanisms,” Computers & Structures, vol. 81, no. 32, pp. 2797–2810, 2003. View at Publisher · View at Google Scholar · View at Scopus
  7. Y. Li and Q. Xu, “A novel piezoactuated XY stage with parallel, decoupled, and stacked flexure structure for micro-/nanopositioning,” IEEE Transactions on Industrial Electronics, vol. 58, no. 8, pp. 3601–3615, 2011. View at Publisher · View at Google Scholar
  8. D. M. Brouwer, J. P. Meijaard, and J. B. Jonker, “Large deflection stiffness analysis of parallel prismatic leaf-spring flexures,” Precision Engineering, vol. 37, no. 3, pp. 505–521, 2013. View at Publisher · View at Google Scholar · View at Scopus
  9. M. Hayashi and M. Fukuda, “Generation of nanometer displacement using reduction mechanism consisting of torsional leaf spring hinges,” International Journal of Precision Engineering and Manufacturing, vol. 13, no. 5, pp. 679–684, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. J. J. Parise, L. L. Howell, and S. P. Magleby, “Ortho-planar linear-motion springs,” Mechanism and Machine Theory, vol. 36, no. 11-12, pp. 1281–1299, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. S. Fukada and K. Nishimura, “Nanometric positioning over a one-millimeter stroke using a flexure guide and electromagnetic linear motor,” International Journal of Precision Engineering and Manufacturing, vol. 8, pp. 49–53, 2007. View at Google Scholar
  12. Q. S. Xu, “Design and development of a compact flexure-based XY precision positioning system with centimeter range,” IEEE Transactions on Industrial Electronics, vol. 61, no. 2, pp. 893–903, 2014. View at Publisher · View at Google Scholar · View at Scopus
  13. X.-P. S. Su and H. S. Yang, “Design of compliant microleverage mechanisms,” Sensors and Actuators, A: Physical, vol. 87, no. 3, pp. 146–156, 2001. View at Publisher · View at Google Scholar · View at Scopus
  14. 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, no. 1, pp. 46–54, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. J.-J. Kim, Y.-M. Choi, D. Ahn, B. Hwang, D.-G. Gweon, and J. Jeong, “A millimeter-range flexure-based nano-positioning stage using a self-guided displacement amplification mechanism,” Mechanism and Machine Theory, vol. 50, pp. 109–120, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. S. Xiao, Y. Li, and Q. Meng, “Mobility analysis of a 3-PUU flexure-based manipulator based on screw theory and compliance matrix method,” International Journal of Precision Engineering and Manufacturing, vol. 14, no. 8, pp. 1345–1353, 2013. View at Publisher · View at Google Scholar · View at Scopus
  17. N. Lobontiu, “Compliance-based matrix method for modeling the quasi-static response of planar serial flexure-hinge mechanisms,” Precision Engineering, vol. 38, no. 3, pp. 639–650, 2014. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Kujawa, “Torsion of restrained thin-walled bars of open constraint bisymmetric cross-section,” Tast Quarterly, vol. 16, pp. 5–15, 2011. View at Google Scholar
  19. E. J. Sapountzakis, “Bars under torsional loading: a generalized beam theory approach,” ISRN Civil Engineering, vol. 2013, Article ID 916581, 39 pages, 2013. View at Publisher · View at Google Scholar
  20. A. H. Al-HaKeem, Structural analysis of truck chassis frames under longitudinal loads considering bimoment effects [Ph.D. thesis], Cranfield Institute of Technology, Cranfield, UK, 1991.
  21. M. Levinson, “A new rectangular beam theory,” Journal of Sound and Vibration, vol. 74, no. 1, pp. 81–87, 1981. View at Publisher · View at Google Scholar · View at Scopus
  22. J. N. Reddy, C. M. Wang, G. T. Lim, and K. H. Ng, “Bending solutions of Levinson beams and plates in terms of the classical Theories,” International Journal of Solids and Structures, vol. 38, no. 26-27, pp. 4701–4720, 2001. View at Publisher · View at Google Scholar · View at Scopus
  23. C. M. Wang, J. N. Reddy, and K. H. Lee, Shear Deformable Beams and Plates: Relationships with Classical Solutions, Elsevier Science, Oxford, UK, 2000. View at MathSciNet
  24. N. Lobontiu and E. Garcia, Mechanics of Microelectromechanical Systems, Kluwer Academic, New York, NY, USA, 2005.
  25. N. H. Nguyen, B. D. Lim, and D. Y. Lee, “Torsional analysis of a single-bent leaf flexure,” Structural Engineering and Mechanics, vol. 54, no. 1, pp. 189–198, 2015. View at Publisher · View at Google Scholar
  26. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, McGraw-Hill, 2nd edition, 1951. View at MathSciNet
  27. W. D. Pilkey, Analysis and Design of Elastic Beams: Computational Methods, John Wiley & Sons, New York, NY, USA, 2002.
  28. N. H. Nguyen, B. D. Lim, and D. Y. Lee, “Displacement analysis of a single-bent leaf flexure under transverse load,” International Journal of Precision Engineering and Manufacturing, vol. 16, no. 4, pp. 749–754, 2015. View at Publisher · View at Google Scholar