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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
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Figures

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Fig. 1

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

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Fig. 2

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

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Fig. 3

Flexible segment with external in-plane loads and displacements

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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

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Fig. 5

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

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Fig. 6

Antisymmetric serpentine flexure hinge

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Fig. 7

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

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Fig. 8

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

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Fig. 9

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

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Fig. 10

Variation of axial compliance with R2

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Fig. 11

Variation of axial compliance with l3

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Fig. 12

Variation of axial compliance with R4

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Fig. 13

Variation of axial compliance with α5

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Fig. 14

Variation of axial compliance with t

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Fig. 15

Variation of axial compliance with w

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Fig. 16

Translation stage with two identical serpentine hinges

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Fig. 17

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

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