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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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References

Tian, Y., Shirinzadeh, B., and Zhang, D., 2009, “A Flexure-Based Mechanism and Control Metrology for Ultra-Precision Turning Operation,” Precis. Eng., 33(2), pp. 160–166. [CrossRef]
Hopkins, J. B., and Culpeper, M. L., 2010, “Synthesis of Multi-Degree of Freedom, Parallel Flexure System via Freedom and Constraint Topology (FACT)—Part II: Practice,” Precis. Eng., 34(2), pp. 271–278. [CrossRef]
Polit, S., and Dong, J., 2011, “Development of a High-Bandwidth XY Nanopositioning Stage for High-Rate Micro-/Nanomanufacturing,” IEEE/ASME J. Mechatronics, 16(4), pp. 724–733. [CrossRef]
Xu, Q., 2012, “Design and Development of Flexure-Based Dual-Stage Nanopositioning System With Minimum Interference Behavior,” IEEE Autom. Sci. Eng., 9(3), pp. 554–563. [CrossRef]
Ryu, J. W., Gweon, D. G., and Moon, K. S., 1997, “Optimal Design of a Flexure Hinge Based XYθ Wafer Stage,” Precis. Eng., 21(1), pp. 18–28. [CrossRef]
Yao, Q., Dong, J., and Ferreira, P. M., 2007, “Design, Analysis, Fabrication and Testing of a Parallel-Kinematic Micropositioning XY Stage,” Mach. Tools Manuf., 47(6), pp. 946–961. [CrossRef]
Mukhopadhyay, D., Dong, J., Pengwang, E., and Ferreira, P., 2008, “A SOI-MEMS-Based Planar Parallel-Kinematics Nanopositioning Stage,” Sens. Actuators A, 147(1), pp. 340–351. [CrossRef]
Ma, H. W., Yao, S. M., Wang, L. Q., and Zhong, Z., 2006, “Analysis of the Displacement Amplification Ratio of Bridge-Type Flexure Hinge,” Sens. Actuators A, 132(2), pp. 730–736. [CrossRef]
Lobontiu, N., and Garcia, E., 2003, “Analytical Model of Displacement Amplification and Stiffness Optimization for a Class of Flexure-Based Compliant Mechanisms,” Comput. Struct., 81(32), pp. 2797–2810. [CrossRef]
Chang, S. H., and Du, B. C., 1998, “A Precision Piezodriven Micropositioner Mechanism With Large Travel Range,” Rev. Sci. Instrum., 69(4), pp. 1785–1791. [CrossRef]
Tian, Y., Shirinzadeh, B., Zhang, D., and Alici, G., 2009, “Development and Dynamic Modeling of a Flexure-Based Scott–Russell Mechanism for Nano-Manipulation,” Mech. Syst. Signal Process., 23(3), pp. 957–978. [CrossRef]
Mohd-Zubir, M. N., and Shirinzadeh, B., 2009, “Development of a High Precision Flexure-Based Microgripper,” Precis. Eng., 33(4), pp. 362–370. [CrossRef]
Sun, D., and Mills, J. K., 2002, “Manipulating Rigid Payloads With Multiple Robots Using Compliant Grippers,” IEEE/ASME J. Mechatronics, 7(1), pp. 3–34.
Trylinski, V., 1971, Fine Mechanisms and Precision Instruments, Pergamon Press, Oxford, UK.
Sydenham, P. H., 1984, “Elastic Design of Fine Mechanism in Instruments,” J. Phys., 17(11), pp. 922–930.
Vukobratovich, D., Richard, R. M., McNiven, J. P., and Sinclair, L., 1995, “Slit Diaphragm Flexures for Optomechanics,” Proceedings of SPIE: Optomechanical and Precision Instrument Design, San Diego, CA, July 09, Vol. 2542, pp. 2–10. [CrossRef]
Duong, L., and Kazerounian, K., 2007, “Design Improvement of the Mechanical Coupling Diaphragms for Aerospace Applications,” Mech. Based Des. Struct. Mach., 35(4), pp. 467–479. [CrossRef]
Yong, Y. K., and Reza-Mohemani, S. O., 2010, “A z-Scanner Design for High-Speed Scanning Probe Microscopy,” Proceedings of IEEE International Conference on Robotics and Automation, St. Paul, MN, May 14–18, pp. 4780–4785. [CrossRef]
Awtar, S., 2004, “Synthesis and Analysis of Parallel Kinematic XY Flexure Mechanisms,” Sc.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Trease, B. P., Moon, Y.-M., and Kota, S., 2005, “Design of Large-Displacement Compliant Joints,” ASME J. Mech. Des., 127(4), pp.788–798. [CrossRef]
Paros, J. M., and Weisbord, L., 1965, “How to Design Flexure Hinges,” Mach. Des., 37(11), pp. 151–156.
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]
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]
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., 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]
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]
Linβ, 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, Guanajuato, Mexico, June 19–25, pp. 1–9.
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., 2014, “Out-of-Plane (Diaphragm) Compliances of Circular-Axis Notch Flexible Hinges With Midpoint Radial Symmetry,” Mech. Based Des. Struct. Mach., 42(1), pp. 517–537. [CrossRef]
Lobontiu, N., “In-Plane Compliances of Planar Flexure Hinges With Serially-Connected Straight- and Circular-Axis Segments,” ASME J. Mech. Des.136(12), p. 122301. [CrossRef]
Lobontiu, N., 2014, “Compliance-Based Modeling and Design of Straight-Axis/Circular-Axis Flexible Hinges With Small Out-of-Plane Deformations,” Mech. Mach. Theory, 80(C), pp.166–183. [CrossRef]
Chen, G., and Howell, L. L., 2009, “Two General Solutions of Torsional Compliance for Variable Rectangular Cross-Section Hinges in Compliant Mechanisms,” Precis. Eng., 33(3), pp. 268–274. [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]

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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