This paper presents an approach based on parameterized compliance for type synthesis of flexure mechanisms with serial, parallel, or hybrid topologies. The parameterized compliance matrices have been derived for commonly used flexure elements, which are significantly influenced by flexure parameters including material and geometric properties. Different parameters of flexure elements generate different degree of freedom (DOF) characteristic of types. Enlightened by the compliance analysis of flexure elements, a parameterization approach with detailed processes and steps is introduced in this paper to help analyze and synthesize flexure mechanisms with the case study as serial chains, parallel chains, and combination hybrid chains. For a hybrid flexure, the results of finite element (FE) modeling simulations are compared to analytical compliance elements characteristic. Under linear deformations, the maximum compliance errors of analytical models are less than 6% compared with the FE models. The final goal of this work is to provide a parameterized approach for type synthesis of flexure mechanisms, which is used to configure and change the parameters of flexure mechanisms to achieve the desired DOF requirements of types initially.

References

References
1.
Midha
,
A.
,
Norton
,
T. W.
, and
Howell
,
L. L.
,
1994
, “
On the Nomenclature, Classification, and Abstractions of Compliant Mechanisms
,”
ASME J. Mech. Des.
,
116
(
1
), pp.
270
279
.10.1115/1.2919358
2.
Howell
,
L. L.
,
2001
,
Compliance Mechanisms
,
Wiley-Interscience
,
New York, NY
.
3.
Sin
,
J.
,
Popa
,
D.
, and
Stephanou
,
H.
,
2002
, “
Model Based Automatic Fiber Alignment
,”
Proceeding of the Fiber Optic Automation 2002 Conference
, San Diego, CA.
4.
Moody
,
M. V.
,
Paik
,
H. J.
, and
Canavan
,
E. R.
,
2002
, “
Three-Axis Superconducting Gravity Gradiometer for Sensitive Gravity Experiments
,”
Rev. Sci. Instrum.
,
73
(
11
), pp.
3957
3974
.10.1063/1.1511798
5.
Bono
,
M.
, and
Hibbard
,
R.
,
2007
, “
A Flexure-Based Tool Holder for Sub-μm Positioning of a Single Point Cutting Tool on a Four-Axis Lathe
,”
Precis. Eng.
,
31
(
2
), pp.
169
176
.10.1016/j.precisioneng.2006.03.007
6.
Masters
,
N. D.
, and
Howell
,
L. L.
,
2003
, “
A Self-Retracting Fully Compliant Bistable Micromechanism
,”
J. Microelectromech. Syst.
,
12
(
3
), pp.
273
280
.10.1109/JMEMS.2003.811751
7.
Ball
,
R. S.
,
1900
,
A Treatise on the Theory of Screw
,
Cambridge University Press
,
Cambridge, UK
.
8.
Hunt
,
K. H.
,
1978
,
Kinematic Geometry of Mechanisms
,
Oxford University Press
,
New York
.
9.
Phillips
,
J.
,
1984
,
Freedom in Machinery
(Volume
1
, Introducing Screw Theory),
Cambridge University Press
,
Cambridge, MA
.
10.
Phillips
,
J.
,
1990
,
Freedom in Machinery
(Volume
2
, Screw Theory Exemplified),
Cambridge University Press
,
Cambridge, MA
.
11.
Loncaric
,
J.
,
1987
, “
Normal Forms of Stiffness and Compliance Matrix
,”
J. Rob. Autom.
,
3
(
6
), pp.
567
572
.10.1109/JRA.1987.1087148
12.
Lipkin
,
H.
, and
Timothy
,
P.
,
1992
, “
Geometrical Properties of Modelled Robot Elasticity: Part I—Decomposition
,” Robotics, Spatial Mechanisms, and Mechanical Systems: ASME Design Technical Conferences, 22nd Biennal Mechanisms Conference, Scottsdale, AZ, Sept. 13–16, pp.
179
185
.
13.
Lipkin
,
H.
, and
Timothy
,
P.
,
1992
, “
Geometrical Properties of Modelled Robot Elasticity: Part II—Center of Elasticity
,” Robotics, Spatial Mechanisms, and Mechanical Systems: ASME Design Technical Conferences, 22nd Biennal Mechanisms Conference, Scottsdale, AZ, Sept. 13–16, pp.
187
193
.
14.
Pigoski
,
T.
,
Griffis
,
M.
, and
Duffy
,
J.
,
1998
, “
Stiffness Mappings Employing Different Frames of Reference
,”
Mech. Mach. Theory
,
33
(
6
), pp.
825
838
.10.1016/S0094-114X(97)00083-9
15.
Selig
,
J. M.
,
2000
, “
The Spatial Stiffness Matrix From Simple Stretched Springs
,”
IEEE International Conference
on Robotics and Automation (
ICRA '00
), San Francisco, CA, Apr. 24–28, pp.
3314
3319
10.1109/ROBOT.2000.845218.
16.
Huang
,
S. G.
, and
Schimmels
,
J. M.
,
2000
, “
The Bounds and Realization of Spatial Compliances Achieved With Simple Serial Elastic Mechanisms
,”
IEEE Trans. Rob. Autom.
,
16
(
1
), pp.
99
103
.10.1109/70.833197
17.
Huang
,
S. G.
, and
Schimmels
,
J. M.
,
1998
, “
The Bounds and Realization of Spatial Stiffness Achieved With Simple Springs Connected in Parallel
,”
IEEE Trans. Rob. Autom.
,
14
(
3
), pp.
466
475
.10.1109/70.678455
18.
Guerinot
,
E.
,
Magleby
,
S. P.
,
Howell
,
L. L.
, and
Todd
,
R. H.
,
2005
, “
Compliant Joint Design Principals for High Compressive Load Situation
,”
ASME J. Mech. Des.
,
127
(
4
), pp.
774
781
.10.1115/1.1862677
19.
Slocum
,
A. H.
,
1992
,
Precision Machine Design
,
Prentice-Hall Inc.
,
Englewood Cliffs, NJ
.
20.
Howell
,
L. L.
, and
Midha
,
A.
,
1995
, “
Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms
,”
ASME J. Mech. Des.
,
117
(
1
), pp.
156
165
.10.1115/1.2826101
21.
Maxwell
,
J. C.
, and
Niven
,
W. D.
,
1890
,
General Considerations Concerning Scientific Apparatus
,
Courier Dover Publications
,
New York
.
22.
Blanding
,
D. L.
,
1999
,
Exact Constraint: Machine Design Using Kinematic Processing
,
American Society of Mechanical Engineers
,
New York
.
23.
Kim
,
C. J.
,
Moon
,
Y. M.
, and
Sridhar
,
K.
,
2008
, “
A Building Block Approach to the Conceptual Synthesis of Compliant Mechanisms Utilizing Compliance and Stiffness Ellipsoids
,”
ASME J. Mech. Des.
,
130
(
2
), p.
022308
10.1115/1.2821387.
24.
Hopkins
,
J. B.
, and
Culpepper
,
M. L.
,
2010
, “
Synthesis of Multi-Degree of Freedom, Parallel Flexure System Concepts Via Freedom and Constraint Topology (FACT). Part I: Principals
,”
Precis. Eng.
,
34
(
2
), pp.
259
270
.10.1016/j.precisioneng.2009.06.008
25.
Su
,
H. J.
,
Dorozhkin
,
D. V.
, and
Vance
,
J. M.
,
2009
, “
A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
1
(
4
), p.
041009
.10.1115/1.3211024
26.
Yu
,
J. J.
,
Li
,
S. Z.
,
Su
,
H. J.
, and
Culpepper
,
M. L.
,
2011
, “
Screw Theory Based Methodology for the Deterministic Type Synthesis of Flexure Mechanisms
,”
ASME J. Mech. Rob.
,
3
(
3
), p.
031008
.10.1115/1.4004123
27.
Su
,
H. J.
,
Shi
,
H. L.
, 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
.10.1115/1.4006441
28.
Li
,
S. Z.
,
Yu
,
J. J.
,
Zong
,
G. H.
, and
Su
,
H.-J.
,
2012
, “
A Compliance-Based Compensation Approach for Designing High-Precision Flexure Mechanism
,”
ASME
Paper No. DETC2012-71018
10.1115/DETC2012-71018.
29.
Young
,
W. C.
, and
Budynas
,
R. G.
,
2001
,
Roark's Formulas for Stress and Strain
,
7th ed.
,
McGraw-Hill
,
New York
.
30.
Zhang
,
Y.
,
Su.
,
H.-J.
, and
Liao
,
Q.
,
2014
, “
Mobility Criteria of Compliance Mechanisms Based on Decomposition of Compliance Matrices
,”
Mech. Mach. Theory
,
79
, pp.
80
93
.10.1016/j.mechmachtheory.2014.04.010
31.
Lin
,
Q.
,
Burdick
,
J. W.
, and
Rimon
,
E.
,
2000
, “
A Stiffness-Based Quality Measure for Compliant Grasps and Fixtures
,”
IEEE Trans. Rob. Autom
,
16
(
6
), pp.
675
688
.10.1109/70.897779
32.
Hopkins
,
J. B.
, and
Culpepper
,
M. L.
,
2011
, “
Synthesis of Precision Serial Flexure Systems Using Freedom and Constraint Topologies (FACT)
,”
Precision Engineering
,
35
(
4
), pp.
638
649
10.1016/j.precisioneng.2011.04.006.
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