Comparison of circular flexure hinge design equations and the derivation of empirical stiffness formulations

Flexure hinges are commonly used in many applications which require precise and smooth motions in the nanometer scale. There were various formulations derived using different methods to calculate the stiffness of circular flexure hinges. This article compares these equations with FEA predictions. The limitation of these equations at different t/R (R is the radius and t is the neck thickness) ratios are revealed. Based on the limitations of these design equations, a guideline to select the most accurate equations for hinge design calculations is presented. In addition to the review and comparisons, general empirical stiffness equations in the x- and y-direction were formulated in this study (with errors less than 3% when compared to FEA simulations) for a wide range of t/R ratios (0.05 ≤ t/R ≤ 0.8).

[1]  D. K. Bowen,et al.  Design and assessment of monolithic high precision translation mechanisms , 1987 .

[2]  W. O. Schotborgh,et al.  Dimensionless design graphs for flexure elements and a comparison between three flexure elements , 2005 .

[3]  E. C. Teague,et al.  Piezodriven 50‐μm range stage with subnanometer resolution , 1978 .

[4]  Stuart T. Smith,et al.  ELLIPTICAL FLEXURE HINGES , 1997 .

[5]  P. Gao,et al.  A new piezodriven precision micropositioning stage utilizing flexure hinges , 1999 .

[6]  Nicolae Lobontiu,et al.  Corner-Filleted Flexure Hinges , 2001 .

[7]  Yuen Kuan Yong,et al.  Design, Identification, and Control of a Flexure-Based XY Stage for Fast Nanoscale Positioning , 2009, IEEE Transactions on Nanotechnology.

[8]  Nicolae Lobontiu,et al.  Design of symmetric conic-section flexure hinges based on closed-form compliance equations , 2002 .

[9]  J. M. Paros,et al.  Flexure Pivots to Replace Knife Edge and Ball Bearing , 1965 .

[10]  Karl Johan Åström,et al.  Design and Modeling of a High-Speed AFM-Scanner , 2007, IEEE Transactions on Control Systems Technology.

[11]  G M Whitesides,et al.  The art of building small. , 2001, Scientific American.

[12]  Nicolae Lobontiu,et al.  Compliant Mechanisms: Design of Flexure Hinges , 2002 .

[13]  Zhaoying Zhou,et al.  Design calculations for flexure hinges , 2002 .

[14]  Murti V. Salapaka,et al.  High bandwidth nano-positioner: A robust control approach , 2002 .

[15]  Santosh Devasia,et al.  A Survey of Control Issues in Nanopositioning , 2007, IEEE Transactions on Control Systems Technology.

[16]  T. Ando,et al.  High-speed Atomic Force Microscopy for Capturing Dynamic Behavior of Protein Molecules at Work , 2005 .

[17]  Musa Jouaneh,et al.  Modeling and control of a micro-positioning tower , 1997 .

[18]  J. Paros.  How to design flexure hinges , 1965 .

[19]  Y. Tseytlin.  Notch flexure hinges: An effective theory , 2002 .

[20]  I. Her,et al.  A Linear Scheme for the Displacement Analysis of Micropositioning Stages with Flexure Hinges , 1994 .

[21]  Tien-Fu Lu,et al.  Review of circular flexure hinge design equations and derivation of empirical formulations , 2008 .

[22]  Tien-Fu Lu,et al.  The effect of the accuracies of flexure hinge equations on the output compliances of planar micro-motion stages , 2008 .