Lu Qian This email address is being protected from spambots. You need JavaScript enabled to view it.1

1School of Mechanical Engineering, Yancheng Institute of Technology, Yancheng City, Jiangsu Province 224051, P.R. China


Received: July 28, 2015
Accepted: October 8, 2015
Publication Date: December 1, 2015

Download Citation: ||  


To optimize the flexible micro-displacement amplification mechanism, it is necessary to design the flexure hinge parametrically. A new general structural parameter was proposed, the effect law of to the compliance coefficients of different types of flexure hinges was discussed, and the compliance features of the commonly used flexure hinges were compared horizontally. Conversely, based on the influence analysis of the compliance features, a new parameter λ, the compliance ratio, was proposed, and the main form of sensitivity in the output displacement of the flexure hinges with different λ was analyzed. An actual flexible micro-displacement amplification mechanism with two stage levers was taken as an example, which achieved the type selection by making use of the parameters ε and λ, and the amplification ratio of the flexible mechanism was also validated by FEM simulation and experiment. Under the same driven force (10N), the amplification ratio k before and after optimization based on the parameters of ε and λ are 6.72 and 8.96, respectively; while the experiment results are 6.28 and 8.88, respectively. The simulation and experiment results show that the working range of flexible amplification mechanism could be enhanced effectively based on flexure hinges with the parameters ε and λ. It is feasible and correct to design the flexible amplification mechanism parametrically by the structure parameters of the flexure hinges, and it is helpful to optimize this type of flexible amplification mechanism.

Keywords: Flexure Hinge, Flexible Amplification Mechanism, Structure Parameter, Compliance Ratio, Parametric Design


  1. [1] Xu, Q. S., “Design, Testing and Precision Control of a Novel Long-stroke Flexure Micro-positioning System,” Mechanism and Machine Theory, Vol. 70, No. 6, pp. 209224 (2013). doi: 10.1016/j.mechmachtheory.2013. 07.016
  2. [2] Li, Q. X., Wang, D. S., Li, Y. H., Design of Modern Precision Instruments, Tsinghua University Press, Beijing, pp. 156162 (2004).
  3. [3] Zhang, D., Gao, Z., Malosio, M., et al., “ANovel Flexure Parallel Micromanipulator Based on Multi-level Displacement Amplifier with/without Symmetrical Design,” International Journal of Mechanics and Materials in Design, Vol. 8, No. 4, pp. 311325 (2012). doi: 10. 1007/s10999-012-9197-3
  4. [4] Bhagat, U., Shirinzadeh, B., Clark, L., et al., “Design and Analysis of a Novel Flexure-based 3-DOF Mechanism,” Mechanism and Machine Theory, Vol. 74, No. 4, pp. 173187 (2014). doi: 10.1016/j.mechmach theory.2013.12.006
  5. [5] Choi, S. B., Han, S. S., Han, Y. M., et al., “A Magnification Device for Precision Mechanisms Featuring Piezoactuators and Flexure Hinges: Design and Experimental Validation,” Mechanism and Machine Theory, Vol. 42, No. 9, pp. 11841198 (2007). doi: 10.1016/j. mechmachtheory.2006.08.009
  6. [6] Do, T. N., Tjahjowidodo, T., Lau, M. W. S., et al., “Hysteresis Modeling and Position Control of Tendonsheath Mechanism in Flexible Endoscopic Systems,” Mechatronics, Vol. 24, No. 1, pp. 1222 (2014). doi: 10.1016/j.mechatronics.2013.11.003
  7. [7] Meng, Q. L., Li, Y. M. and Xu, J., “A Novel Analytical Model for Flexure-based Proportion Compliant Mechanisms,” Precision Engineering, Vol. 38, No. 3, pp. 449457 (2014). doi: 10.1016/j.precisioneng.2013.12. 001
  8. [8] Kim, J. J., Choi, Y. M., Ahn, D., et al., “A Millimeterrange Flexure-based Nano-positioning Stage Using a Self-guided Displacement Amplification Mechanism,” Mechanism and Machine Theory, Vol. 50, No. 2, pp. 109120 (2012). doi: 10.1016/j.mechmachtheory.2011. 11.012
  9. [9] Bi, S. S., Zhao, S. S. and Zhao, X. F., “Dimensionless Design Graphs for Three Types of Annulus-shaped Flexure Hinges,” Precision Engineering, Vol. 34, No. 3, pp. 659666 (2013). doi: 10.1016/j.precisioneng.2010. 01.002
  10. [10] Lobontiu, N., “Compliance-based Matrix Method for Modeling the Quasi-Static Response of Planar Serial Flexure-hinge Mechanisms,” Precision Engineering, Vol. 38, No. 3, pp. 639650 (2014). doi: 10.1016/j. precisioneng.2014.02.014
  11. [11] Lobontiu, N. and Cullin, M., “In-plane Elastic Response of Two-segment Circular-axis Symmetric Notch Flexure Hinges: the Right Circular Design,” Precision Engineering, Vol. 37, No. 3, pp. 542555 (2013). doi: 10.1016/j.precisioneng.2012.12.007
  12. [12] Bolzmacher, C., Bauer, K., Schmid, U., et al., “Displacement Amplification of Piezoelectric Microactuators with a Micromachined Leverage Unit,” Sensors and Actuators A: Physical, Vol. 157, No. 1, pp. 6167 (2010). doi: 10.1016/j.sna.2009.10.014
  13. [13] Ma, H. W., Yao, S. M., Wang, L. Q., et al., “Analysis of the Displacement Amplification Ratio of Bridge-type Flexure Hinge,” Sensors and Actuators A: Physical, Vol. 132, No. 6, pp. 730736 (2006). doi: 10.1016/j. sna.2005.12.028
  14. [14] Xu, Q. S. and Li, Y. M., “Analytical Modeling, Optimization and Testing of a Compound Bridge-type Compliant Displacement Amplifier,” Mechanism and Machine Theory, Vol. 46, No. 2, pp. 183200 (2011). doi: 10.1016/j.mechmachtheory.2010.09.007
  15. [15] Choi, K. B., Lee, J. J. and Hata, S., “A Piezo-driven Compliant Stage with Double Mechanical Amplification Mechanisms Arranged in Parallel,” Sensors and Actuators A: Physical, Vol. 161, No. 12, pp. 173181 (2010). doi: 10.1016/j.sna.2010.05.027
  16. [16] Yu, Y. Q., Feng, Z. L. and Xu, Q. P., “A Pseudorigid-body 2R Model of Flexural Beam in Compliant Mechanisms,” Mechanism and Machine Theory, Vol. 55, No. 9, pp. 1833 (2012). doi: 10.1016/j.mechma chtheory.2012.04.005
  17. [17] Yu, Z. Y., Yao, X. X. and Song, X. D., “Design of Micro-displacement Amplifier Based on Flexure Hinges,” Chinese Journal of Scientific Instrument, Vol. 30, No. 9, pp. 18181822 (2009).
  18. [18] Zhao, L., Gong, Y. and Hua, Y. Y., “Compliance Matrix Analysis of Corner-filleted Flexure Hinge,” China Mechanical Engineering, Vol. 24, No. 18, pp. 2462 2468 (2013).
  19. [19] Tian, Y., Shirinzadeh, B., Zhang, D., et al., “Three Flexure Hinges for Compliant Mechanism Designs Based on Dimensionless Graph Analysis,” Precision Engineering, Vol. 34, No. 1, pp. 92100 (2010). doi: 10. 1016/j.precisioneng.2009.03.004
  20. [20] Lu, Q., Cui, Z. and Chen, X. F., “Fuzzy Multi-objective Optimization for Movement Performance of Deep-notch Elliptical Flexure Hinges,” Review of Scientific Instrument, Vol. 86, No. 6 (2015). doi: 10.1063/1.4922914
  21. [21] Zhao, L., Gong, Y. and Hua, Y. Y., “Compliance Matrix Analysis of Corner-filleted Flexure Hinge,” China Mechanical Engineering, Vol. 24, No. 18, pp. 2462 2468 (2013).
  22. [22] Zuo, X. Y. and Liu, X. M., “Calculation and Analysis of Rotational Stiffness for Three Types of Flexure Hinges,” Chinese Journal of Scientific Instrument, Vol. 27, No. 12, pp. 17251728 (2006).
  23. [23] Zhao, H. W., Wu, B. D. and Cao, D. B., “Mechanical Performance of Right-Angle Flexure Hinge,” Nanotechnology and Precision Engineering, Vol. 5, No. 2, pp. 143147 (2007).