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.

References

References
1.
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
.10.1016/j.precisioneng.2008.05.001
2.
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
.10.1016/j.precisioneng.2009.06.007
3.
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
.10.1109/TMECH.2010.2052107
4.
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
.10.1109/TASE.2012.2198918
5.
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
.10.1016/S0141-6359(97)00064-0
6.
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
.10.1016/j.ijmachtools.2006.07.007
7.
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
.10.1016/j.sna.2008.04.018
8.
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
.10.1016/j.sna.2005.12.028
9.
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
.10.1016/j.compstruc.2003.07.003
10.
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
.10.1063/1.1148842
11.
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
.10.1016/j.ymssp.2008.06.007
12.
Mohd-Zubir
,
M. N.
, and
Shirinzadeh
,
B.
,
2009
, “
Development of a High Precision Flexure-Based Microgripper
,”
Precis. Eng.
,
33
(
4
), pp.
362
370
.10.1016/j.precisioneng.2008.10.003
13.
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
.
14.
Trylinski
,
V.
,
1971
,
Fine Mechanisms and Precision Instruments
,
Pergamon Press
,
Oxford, UK
.
15.
Sydenham
,
P. H.
,
1984
, “
Elastic Design of Fine Mechanism in Instruments
,”
J. Phys.
,
17
(
11
), pp.
922
930
.
16.
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
.10.1117/12.218653
17.
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
.10.1080/15397730701673304
18.
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
.10.1109/ICRA.2012.6224758
19.
Awtar
,
S.
,
2004
, “
Synthesis and Analysis of Parallel Kinematic XY Flexure Mechanisms
,” Sc.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
20.
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
.10.1115/1.1900149
21.
Paros
,
J. M.
, and
Weisbord
,
L.
,
1965
, “
How to Design Flexure Hinges
,”
Mach. Des.
,
37
(
11
), pp.
151
156
.
22.
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
.10.1115/1.1372190
23.
Smith
,
S. T.
,
Badami
,
V. G.
,
Dale
,
J. S.
, and
Xu
,
Y.
,
2000
, “
Elliptical Flexure Hinges
,”
Rev. Sci. Instrum.
,
68
(
3
), pp.
1474
1483
.10.1063/1.1147635
24.
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
.10.1115/1.4004441
25.
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
.10.1016/S0094-114X(02)00002-2
26.
Chen
,
G.
,
Liu
,
X.
,
Gao
,
H.
, and
Jia
,
J.
,
2009
, “
A Generalized Model for Conic Flexure Hinges
,”
Rev. Sci. Instrum.
,
80
(
5
), p.
055106
.10.1063/1.3137074
27.
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
.10.1016/j.precisioneng.2009.10.002
28.
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
.
29.
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
.10.1080/15397734.2012.722887
30.
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
.10.1080/15397734.2014.899152
31.
Lobontiu
,
N.
, “
In-Plane Compliances of Planar Flexure Hinges With Serially-Connected Straight- and Circular-Axis Segments
,”
ASME J. Mech. Des.
136
(12), p. 122301.10.1115/1.4028276
32.
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
.10.1016/j.mechmachtheory.2014.06.002
33.
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
.10.1016/j.precisioneng.2008.08.001
34.
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
.10.1063/1.3656075
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