Research Papers: Design of Mechanisms and Robotic Systems

In-Plane Compliances of Planar Flexure Hinges With Serially Connected Straight- and Circular-Axis Segments

[+] Author and Article Information
Nicolae Lobontiu

Department of Mechanical Engineering,
University of Alaska Anchorage,
3211 Providence Drive,
Anchorage, AK 99508
e-mail: nlobontiu@uaa.alaska.edu

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 1, 2014; final manuscript received July 23, 2014; published online October 20, 2014. Assoc. Editor: Shorya Awtar.

J. Mech. Des 136(12), 122301 (Oct 20, 2014) (10 pages) Paper No: MD-14-1099; doi: 10.1115/1.4028276 History: Received February 01, 2014; Revised July 23, 2014

The paper introduces a new category of planar flexure hinges that are formed by serially connecting variable cross-sectional segments of straight longitudinal axes with segments of circular longitudinal axes. The small-displacement compliance analytical model is derived for a general hinge configuration using a matrix approach that sums the transformed local-frame compliance matrices of individual component segments. The particular class of antisymmetric flexure hinges is studied using the general model and the corresponding global-frame compliance matrix is calculated as a linear combination of compliances defining the half-hinge configuration. A serpentine (folded) flexure hinge is introduced to illustrate the generic antisymmetric design and model. Finite element simulation is used to validate the analytic compliances of this particular configuration and the compliance sensitivity to geometric parameters variation is further analyzed. The translation stiffnesses of a planar-motion stage with two identical serpentine hinges are calculated based on hinge compliances. The optimum hinge design is subsequently identified, which realizes minimum-resistance motion along the stage axial motion direction.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Paros, J. M., and Weisbord, L., 1965, “How to Design Flexure Hinges,” Mach. Des., 37(27), pp. 151–156.
Smith, S. T., Badami, V. G., Dale, J. S., and Xu, Y., 2000, “Elliptical Flexure Hinges,” Rev. Sci. Instrum., 68(3), pp. 1474–1483. [CrossRef]
Smith, S. T., 2000, Flexures-Elements of Elastic Mechanisms, Gordon and Breach, London.
Lobontiu, N., 2002, Compliant Mechanisms: Design of Flexure Hinges, CRC, Boca Raton.
Lobontiu, N., Paine, J. S. N., Garcia, E., and Goldfarb, M., 2002, “Design of Symmetric Conic-Section Flexure Hinges Based on Closed-Form Compliance Equations,” Mech. Mach. Theory, 37(5), pp. 477–498. [CrossRef]
Chen, G., Liu, X., Gao, H., and Jia, J., 2009, “A Generalized Model for Conic Flexure Hinges,” Rev. Sci. Instrum., 80(5), p. 055106. [CrossRef] [PubMed]
Vallance, R. R., Haghighian, B., and Marsh, E. B., 2008, “A Unified Geometric Model for Designing Elastic Pivots,” Precis. Eng., 32(4), pp. 278–288. [CrossRef]
Linß, S., Erbe, T., and Zentner, L., 2011, “On Polynomial Flexure Hinges for Increased Deflection and an Approach for Simplified Manufacturing,” 13th World Congress in Mechanisms and Machine Science, Guanajato, Mexico, pp. 1–9.
Zelenika, S., Munteanu, M. Gh., and de Bona, F., 2009, “Optimized Flexural Hinge Shapes for Microsystems and High-Precision Applications,” Mech. Mach. Theory, 44(10), pp. 1826–1839. [CrossRef]
Lobontiu, N., Paine, J. S. N., Garcia, E., and Goldfarb, M., 2001, “Corner-Filleted Flexure Hinges,” ASME J. Mech. Des., 123(3), pp. 346–352. [CrossRef]
Chen, G., Liu, X., and Du, Y., 2011, “Elliptical-Arc-Fillet Flexure Hinges: Toward a Generalized Model for Commonly Used Flexure Hinges,” ASME J. Mech. Des., 133(8), p. 081002. [CrossRef]
Lobontiu, N., Cullin, M., Ali, M., and McFerran-Brock, J., 2011, “A Generalized Analytical Compliance Model for Transversely Symmetric Three-Segment Flexure Hinges,” Rev. Sci. Instrum., 82(10), p. 105116. [CrossRef] [PubMed]
Tian, Y., Shirinzadeh, B., and Zhang, D., 2010, “Closed-Form Compliance Equations of Filleted V-Shaped Flexure Hinges for Compliant Mechanism Design,” Precis. Eng., 34(3), pp. 408–418. [CrossRef]
Lobontiu, N., Cullin, M., Petersen, T., Alcazar, J., and Noveanu, S., 2014, “Planar Compliances of Symmetric Notch Flexure Hinges: The Right Circularly Corner-Filleted Parabolic Design,” IEEE Trans. Autom. Sci. Eng., 11(1), pp. 169–176. [CrossRef]
Lobontiu, N., Cullin, M., Ali, M., and Hoffman, J., 2013, “Planar Compliances of Thin Circular-Axis Notch Flexure Hinges With Midpoint Radial Symmetry,” Mech. Based Des. Struct. Mach., 41(2), pp. 202–221. [CrossRef]
Lobontiu, N., and Cullin, M., 2013, “In-Plane Elastic Response of Two-Segment Circular-Axis Symmetric Notch Flexure Hinges: The Right Circular Design,” Precis. Eng., 37(3), pp. 542–555. [CrossRef]
Koster, M., 1998, Constructieprincipes voor het Nauwkeurig Bewegen en Positioneren, Twente University, The Netherlands.
Murin, J., and Kutis, V., 2002, “3D-Beam Element With Continuous Variation of the Cross-Sectional Area,” Comput. Struct., 80(3–4), pp. 329–338. [CrossRef]
Zhang, S., and Fasse, E., 2001, “A Finite-Element-Based Method to Determine the Spatial Stiffness Properties of a Notch Hinge,” ASME J. Mech. Des., 123(1), pp. 141–147. [CrossRef]
Lobontiu, N., and Garcia, E., 2005, “Circular-Hinge Line Element for Finite Element Analysis of Compliant Mechanisms,” ASME J. Mech. Des., 127(4), pp. 766–773. [CrossRef]
Su, H.-J., Shi, H., and Yu, J. J., 2012, “A Symbolic Formulation for Analytical Compliance Analysis and Synthesis of Flexure Mechanisms,” ASME J. Mech. Des., 134(5), p. 051009. [CrossRef]


Grahic Jump Location
Fig. 1

Flexure hinges with (a) straight-axis segment, (b) circular-axis segment, and (c) multiple straight- and circular-axis segments

Grahic Jump Location
Fig. 2

In-plane loads and deformations for (a) straight-axis flexible segment and (b) circular-axis flexible segment

Grahic Jump Location
Fig. 3

Flexible segment with external in-plane loads and displacements

Grahic Jump Location
Fig. 4

General planar flexure hinge composed of n straight-axis segments and m circular-axis segments with in-plane load and deformations at the free end in a global reference frame

Grahic Jump Location
Fig. 5

General flexure hinge formed of two multisegment portions that are placed antisymmetrically with respect to an axis

Grahic Jump Location
Fig. 6

Antisymmetric serpentine flexure hinge

Grahic Jump Location
Fig. 7

Geometry of the antisymmetric serpentine flexure hinge half portion with five different segments and their local reference frames

Grahic Jump Location
Fig. 8

Geometry of variable thickness, circular-axis, and circularly corner-fillet segment

Grahic Jump Location
Fig. 9

Finite element model of a right circularly corner-filleted serpentine flexible hinge with free-end point loading, displacements, and fixed-end

Grahic Jump Location
Fig. 10

Variation of axial compliance with R2

Grahic Jump Location
Fig. 11

Variation of axial compliance with l3

Grahic Jump Location
Fig. 12

Variation of axial compliance with R4

Grahic Jump Location
Fig. 13

Variation of axial compliance with α5

Grahic Jump Location
Fig. 14

Variation of axial compliance with t

Grahic Jump Location
Fig. 15

Variation of axial compliance with w

Grahic Jump Location
Fig. 16

Translation stage with two identical serpentine hinges

Grahic Jump Location
Fig. 17

Right serpentine hinge with (a) x-axis force and displacement and (b) y-axis force and displacement



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In