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Research Papers: Mechanisms and Robotics

Planar Flexible Hinges With Curvilinear-Axis Segments for Mechanisms of In-Plane and Out-of-Plane Operation

[+] Author and Article Information
Nicolae Lobontiu

Mechanical Engineering Department,
School of 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 July 28, 2014; final manuscript received October 6, 2014; published online November 14, 2014. Assoc. Editor: Ettore Pennestri.

J. Mech. Des 137(1), 012302 (Jan 01, 2015) (15 pages) Paper No: MD-14-1451; doi: 10.1115/1.4028792 History: Received July 28, 2014; Revised October 06, 2014; Online November 14, 2014

The new design class and related analytic compliance-matrix model of planar flexible hinges with curvilinear longitudinal axes is presented here. The proposed approach enhances and generalizes the existing design and modeling variants dedicated to straight-axis and circular-axis hinge configurations. In-plane and out-of-plane small-displacement compliances are derived for standalone curvilinear-axis hinges as well as for hinges that are formed by serially connecting several curvilinear- and straight-axis segments. The general algorithm is further utilized to derive the compliance model of symmetric hinges, which utilizes a reduced number of compliances defining half the hinge. To illustrate the modeling/design procedure, a new flexible hinge is introduced and studied whose half portion comprises a constant-thickness parabolic-axis segment and a straight-axis segment of elliptically varying thickness. The resulting analytical compliances are validated by finite element simulation (FEA). Two compliant mechanisms that incorporate the new hinge design are studied in terms of specific performance qualifiers.

Copyright © 2015 by ASME
Topics: Hinges , Stress
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Figures

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Fig. 1

Configuration of planar flexible hinges: (a) deep flexible hinge with in-plane loads and deformations and (b) shallow flexible hinge with out-of-plane loads and deformations

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Fig. 2

Skeleton representation of planar flexible hinges with: (a) straight-axis, (b) circular-axis, and (c) segments of straight and circular axes

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Fig. 3

New planar flexible hinges in skeleton representation: (a) single-segment, polynomial-axis design, (b) single-segment, higher-order spline-axis design, (c) design formed of a curved-axis segment smoothly connected to a straight-axis segment, and (d) multiple-segment symmetric design

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Fig. 4

Free-fixed curvilinear-axis flexible hinge: (a) skeleton representation with free-end loads and displacements and (b) planar geometry

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Fig. 5

Free-fixed straight-axis flexible hinge with geometry, loads, and deformations

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Fig. 6

Planar curvilinear-axis flexible hinge in global reference frame under the action of load displaced from its free end

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Fig. 7

Planar multiple-segment serial flexible hinge with load applied at its free end

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Fig. 8

Skeleton representation of a general symmetric multiple-segment flexible hinge

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Fig. 9

Symmetric flexible hinge with half portion formed of parabolic-axis constant-thickness segment 1 and straight-axis right elliptically filleted segment 2

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Fig. 10

Planar geometry in local reference frames of: (a) parabolic-axis segment 1 and (b) straight-axis, right elliptically corner-filleted segment 2

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Fig. 11

Finite element half model with loads and deformations

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Fig. 12

Percentage relative error of compliance ratio r in terms of minimum thickness t

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Fig. 13

Percentage relative error of compliance ratio r in terms of minimum thickness lx1 and ap

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Fig. 14

Percentage relative error of compliance ratio r in terms of minimum thickness a and b

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Fig. 15

In-plane rotary compliance as a function of the parabolic parameters lx1 and ap

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Fig. 16

In-plane rotary compliance as a function of the elliptic parameters a and b

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Fig. 17

In-plane rotary compliance as a function of the minimum thickness t

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Fig. 18

Displacement–amplification, planar-motion, symmetric device with four identical flexure hinges of parabolic- and straight-axis design: (a) schematic representation; (b) detail of a flexure hinge with load and boundary conditions

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Fig. 19

Symmetric stage with four identical flexible hinges of parabolic- and straight-axis design for out-of-plane motion: (a) top view configuration and (b) side view of a flexible hinge with load and boundary conditions

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