Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2016, Article ID 5602142, 11 pages
http://dx.doi.org/10.1155/2016/5602142
Research Article

Empirical Compliance Equations for Constant Rectangular Cross Section Flexure Hinges and Their Applications

Manufacturing Engineering Institute, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

Received 7 November 2015; Accepted 13 March 2016

Academic Editor: Dane Quinn

Copyright © 2016 Tiemin Li 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. N. Lobontiu, Compliant Mechanisms: Design of Flexure Hinges, CRC Press, New York, NY, USA, 2010.
  2. Y. Tian, B. Shirinzadeh, D. Zhang, and Y. Zhong, “Three flexure hinges for compliant mechanism designs based on dimensionless graph analysis,” Precision Engineering, vol. 34, no. 1, pp. 92–100, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. M. N. M. Zubir, B. Shirinzadeh, and Y. Tian, “Development of a novel flexure-based microgripper for high precision micro-object manipulation,” Sensors and Actuators A: Physical, vol. 150, no. 2, pp. 257–266, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. Y. Li and Q. Xu, “A novel design and analysis of a 2-DOF compliant parallel micromanipulator for nanomanipulation,” IEEE Transactions on Automation Science and Engineering, vol. 3, no. 3, pp. 247–254, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. Y. Li and Q. Xu, “Design of a new decoupled XY flexure parallel kinematic manipulator with actuator isolation,” in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '08), pp. 470–475, IEEE, Nice, France, September 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. Q. Xu, “Design and development of a flexure-based dual-stage nanopositioning system with minimum interference behavior,” IEEE Transactions on Automation Science and Engineering, vol. 9, no. 3, pp. 554–563, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. L.-J. Lai, G.-Y. Gu, and L.-M. Zhu, “Design and control of a decoupled two degree of freedom translational parallel micro-positioning stage,” Review of Scientific Instruments, vol. 83, no. 4, Article ID 045105, 2012. View at Publisher · View at Google Scholar · View at Scopus
  8. Y. Li, S. Xiao, L. Xi, and Z. Wu, “Design, modeling, control and experiment for a 2-DOF compliant micro-motion stage,” International Journal of Precision Engineering and Manufacturing, vol. 15, no. 4, pp. 735–744, 2014. View at Publisher · View at Google Scholar · View at Scopus
  9. P. R. Ouyang, R. C. Tjiptoprodjo, W. J. Zhang, and G. S. Yang, “Micro-motion devices technology: the state of arts review,” International Journal of Advanced Manufacturing Technology, vol. 38, no. 5-6, pp. 463–478, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. Y. K. Yong and T.-F. Lu, “The effect of the accuracies of flexure hinge equations on the output compliances of planar micro-motion stages,” Mechanism and Machine Theory, vol. 43, no. 3, pp. 347–363, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. Y. K. Yong and T.-F. Lu, “Comparison of circular flexure hinge design equations and the derivation of empirical stiffness formulations,” in Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM '09), pp. 510–515, Singapore, July 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. J. M. Paros, “How to design flexure hinges,” Machine Design, vol. 37, pp. 151–156, 1965. View at Google Scholar
  13. Y. Wu and Z. Zhou, “Design calculations for flexure hinges,” Review of Scientific Instruments, vol. 73, no. 8, pp. 3101–3106, 2002. View at Publisher · View at Google Scholar · View at Scopus
  14. W. O. Schotborgh, F. G. M. Kokkeler, H. Tragter, and F. J. A. M. Van Houten, “Dimensionless design graphs for flexure elements and a comparison between three flexure elements,” Precision Engineering, vol. 29, no. 1, pp. 41–47, 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. N. Lobontiu, E. Garcia, M. Hardau, and N. Bal, “Stiffness characterization of corner-filleted flexure hinges,” Review of Scientific Instruments, vol. 75, no. 11, pp. 4896–4905, 2004. View at Publisher · View at Google Scholar · View at Scopus
  16. N. Lobontiu, J. S. N. Paine, E. Garcia, and M. Goldfarb, “Corner-filleted flexure hinges,” Journal of Mechanical Design, vol. 123, no. 3, pp. 346–352, 2001. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. M. Tseytlin, “Notch flexure hinges: an effective theory,” Review of Scientific Instruments, vol. 73, no. 9, pp. 3363–3368, 2002. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Acer and A. Sabanovic, “Comparison of circular flexure hinge compliance modeling methods,” in Proceedings of the IEEE International Conference on Mechatronics (ICM '11), pp. 271–276, IEEE, Istanbul, Turkey, April 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. Q. Meng, Y. Li, and J. Xu, “New empirical stiffness equations for corner-filleted flexure hinges,” Mechanical Sciences, vol. 4, no. 2, pp. 345–356, 2013. View at Publisher · View at Google Scholar · View at Scopus
  20. S. T. Smith, V. G. Badami, J. S. Dale, and Y. Xu, “Elliptical flexure hinges,” Review of Scientific Instruments, vol. 68, no. 3, pp. 1474–1483, 1997. View at Publisher · View at Google Scholar · View at Scopus
  21. N. Lobontiu, J. S. N. Paine, E. Garcia, and M. Goldfarb, “Design of symmetric conic-section flexure hinges based on closed-form compliance equations,” Mechanism and Machine Theory, vol. 37, no. 5, pp. 477–498, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  22. G.-M. Chen, J.-Y. Jia, and Z.-W. Li, “Right-circular corner-filleted flexure hinges,” in Proceedings of the IEEE Conference on Automation Science and Engineering, pp. 249–253, IEEE, Edmonton, Canada, August 2005. View at Publisher · View at Google Scholar · View at Scopus
  23. S. Linß, T. Erbe, and L. Zentner, “On polynomial flexure hinges for increased deflection and an approach for simplified manufacturing,” in Proceedings of the 13th World Congress in Mechanisms and Machine Science, pp. 1–9, Guanajuato, Mexico, June 2011.
  24. Q. Xu, “New flexure parallel-kinematic micropositioning system with large workspace,” IEEE Transactions on Robotics, vol. 28, no. 2, pp. 478–491, 2012. View at Publisher · View at Google Scholar · View at Scopus
  25. Q. 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
  26. N. Lobontiu and E. Garcia, “Analytical model of displacement amplification and stiffness optimization for a class of flexure-based compliant mechanisms,” Computers and Structures, vol. 81, no. 32, pp. 2797–2810, 2003. View at Publisher · View at Google Scholar · View at Scopus
  27. H.-W. Ma, S.-M. Yao, L.-Q. Wang, and Z. Zhong, “Analysis of the displacement amplification ratio of bridge-type flexure hinge,” Sensors and Actuators A: Physical, vol. 132, no. 2, pp. 730–736, 2006. View at Publisher · View at Google Scholar · View at Scopus
  28. Q. Xu and Y. Li, “Analytical modeling, optimization and testing of a compound bridge-type compliant displacement amplifier,” Mechanism and Machine Theory, vol. 46, no. 2, pp. 183–200, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  29. G. Ye, W. Li, Y.-Q. Wang, X.-F. Yang, and L. Yu, “Kinematics analysis of bridge-type micro-displacement mechanism based on flexure hinge,” in Proceedings of the IEEE International Conference on Information and Automation (ICIA '10), pp. 66–70, IEEE, Harbin, China, June 2010. View at Publisher · View at Google Scholar · View at Scopus