Multimaterial compliant mechanisms enhance the performance of regular single-material compliant mechanisms by adding a new design option, material type variation. This paper introduces a geometric modeling method for multimaterial compliant mechanisms by using multilayer wide curves. Based on the introduced modeling method, a geometric optimization approach for multimaterial compliant mechanisms is proposed. A multilayer wide curve is a curve with variable cross sections and multiple materials. In this paper, every connection in the multimaterial compliant mechanism is represented by a multilayer wide curve, and the whole mechanism is modeled as a set of connected multilayer wide curves. The geometric modeling and the optimization of a multimaterial compliant mechanism are considered as the generation and the optimal selection of the control parameters of the corresponding multilayer wide curves. The deformation and performance of multimaterial compliant mechanisms are evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized, and the practical constraints are imposed during the optimization process. The effectiveness of the proposed geometric modeling and optimization procedures is verified by the demonstrated examples.

1.
Midha
,
A.
,
Norton
,
T. W.
, and
Howell
,
L. L.
, 1994, “
On the Nomenclature, Classification, and Abstractions of Compliant Mechanisms
,”
ASME J. Mech. Des.
1050-0472,
116
(
1
), pp.
270
279
.
2.
Ananthasuresh
,
G. K.
, and
Kota
,
S.
, 1995, “
Designing Compliant Mechanisms
,”
Mech. Eng. (Am. Soc. Mech. Eng.)
0025-6501,
117
(
11
), pp.
93
96
.
3.
Howell
,
L. L.
, 2001,
Compliant Mechanisms
,
Wiley
,
New York
.
4.
Kota
,
S.
,
Ananthasuresh
,
G. K.
,
Crary
,
S. B.
, and
Wise
,
K. D.
, 1994, “
Design and Fabrication of Microelectromechanical Systems
,”
ASME J. Mech. Des.
1050-0472,
116
(
4
), pp.
1081
1088
.
5.
Ananthasuresh
,
G. K.
, 2003,
Optimal Synthesis Methods for MEMS
,
Kluwer Academic
,
Boston
.
6.
Bendsøe
,
M. P.
, and
Sigmund
,
O.
, 2002,
Topology Optimization
,
Springer
,
New York
.
7.
Howell
,
L. L.
, and
Midha
,
A.
, 1994, “
A Method for the Design of Compliant Mechanisms With Small-Length Flexural Pivots
,”
ASME J. Mech. Des.
1050-0472,
116
(
1
), pp.
280
290
.
8.
Howell
,
L. L.
, and
Midha
,
A.
, 1995, “
Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms
,”
ASME J. Mech. Des.
1050-0472,
117
(
1
), pp.
156
165
.
9.
Howell
,
L. L.
, and
Midha
,
A.
, 1996, “
A Loop-Closure Theory for the Analysis and Synthesis of Compliant Mechanisms
,”
ASME J. Mech. Des.
1050-0472,
118
(
1
), pp.
121
125
.
10.
Murphy
,
M. D.
,
Midha
,
A.
, and
Howell
,
L. L.
, 1996, “
The Topological Synthesis of Compliant Mechanisms
,”
Mech. Mach. Theory
0094-114X,
31
(
2
), pp.
185
199
.
11.
Jensen
,
B. D.
, and
Howell
,
L. L.
, 2003, “
Identification of Compliant Pseudo-Rigid-Body Four-Link Mechanism Configurations Resulting in Bistable Behavior
,”
ASME J. Mech. Des.
1050-0472,
125
(
4
), pp.
701
708
.
12.
Jensen
,
B. D.
, and
Howell
,
L. L.
, 2004, “
Bistable Configurations of Compliant Mechanisms Modeled Using Four Links and Translational Joints
,”
ASME J. Mech. Des.
1050-0472,
126
(
4
), pp.
657
666
.
13.
Masters
,
N. D.
, and
Howell
,
L. L.
, 2005, “
A Three Degree-of-Freedom Model for Self-Retracting Fully Compliant Bistable Micromechanisms
,”
ASME J. Mech. Des.
1050-0472,
127
(
4
), pp.
739
744
.
14.
Yu
,
Y.-Q.
,
Howell
,
L. L.
,
Lusk
,
C.
,
Yue
,
Y.
, and
He
,
M.-G.
, 2005, “
Dynamic Modeling of Compliant Mechanisms Based on the Pseudo-Rigid-Body Model
,”
ASME J. Mech. Des.
1050-0472,
127
(
4
), pp.
760
765
.
15.
Guérinot
,
A. E.
,
Magleby
,
S. P.
,
Howell
,
L. L.
, and
Todd
,
R. H.
, 2005, “
Compliant Joint Design Principles for High Compressive Load Situations
,”
ASME J. Mech. Des.
1050-0472,
127
(
4
), pp.
774
781
.
16.
Lobontiu
,
N.
, and
Garcia
,
E.
, 2005, “
Circular-Hinge Line Element for Finite Element Analysis of Compliant Mechanisms
,”
ASME J. Mech. Des.
1050-0472,
127
(
4
), pp.
766
773
.
17.
Zettl
,
B.
,
Szyszkowski
,
W.
, and
Zhang
,
W. J.
, 2005, “
On Systematic Errors of Two-Dimensional Finite Element Modeling of Right Circular Planar Flexure Hinges
,”
ASME J. Mech. Des.
1050-0472,
127
(
4
), pp.
782
787
.
18.
Trease
,
B. P.
,
Moon
,
Y.-M.
, and
Kota
,
S.
, 2005, “
Design of Large-Displacement Compliant Joints
,”
ASME J. Mech. Des.
1050-0472,
127
(
4
), pp.
788
798
.
19.
Suzuki
,
K.
, and
Kikuchi
,
N.
, 1991, “
A Homogenization Method for Shape and Topology Optimization
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
93
, pp.
291
318
.
20.
Ananthasuresh
,
G. K.
,
Kota
,
S.
, and
Kikuchi
,
N.
, 1994, “
Strategies for Systematic Synthesis of Compliant MEMS
,”
ASME Dyn. Syst. Control
,
55
(
2
), pp.
677
686
.
21.
Larsen
,
V. D.
,
Sigmund
,
O.
, and
Bouwstra
,
S.
, 1997, “
Design and Fabrication of Compliant Micromechanisms and Structures With Negative Poisson’s Ratio
,”
J. Microelectromech. Syst.
1057-7157,
6
(
2
), pp.
99
106
.
22.
Sigmund
,
O.
, 1997, “
On the Design of Compliant Mechanisms Using Topology Optimization
,”
Mech. Struct. Mach.
0890-5452,
25
(
4
), pp.
493
524
.
23.
Bruns
,
T. E.
, and
Tortorelli
,
D. A.
, 2001, “
Topology Optimization of Non-Linear Elastic Structures and Compliant Mechanisms
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
190
(
26–27
), pp.
3443
3458
.
24.
Frecker
,
M. I.
,
Ananthasuresh
,
G. K.
,
Nishiwaki
,
S.
,
Kikuchi
,
N.
, and
Kota
,
S.
, 1997, “
Topological Synthesis of Compliant Mechanisms Using Multi-Criteria Optimization
,”
ASME J. Mech. Des.
1050-0472,
119
(
2
), pp.
238
245
.
25.
Joo
,
J.
,
Kota
,
S.
, and
Kikuchi
,
N.
, 2000, “
Topological Synthesis of Compliant Mechanisms Using Linear Beam Elements
,”
Mech. Struct. Mach.
0890-5452,
28
(
4
), pp.
245
280
.
26.
Saxena
,
A.
, and
Ananthasuresh
,
G. K.
, 2001, “
Topology Synthesis of Compliant Mechanisms for Nonlinear Force-Deflection and Curved Path Specifications
,”
ASME J. Mech. Des.
1050-0472,
123
(
1
), pp.
33
43
.
27.
Parsons
,
R.
, and
Canfield
,
S. L.
, 2002, “
Developing Genetic Programming Techniques for the Design of Compliant Mechanisms
,”
Struct. Multidiscip. Optim.
1615-147X,
24
(
1
), pp.
78
86
.
28.
Maddisetty
,
H.
, and
Frecker
,
M.
, 2004, “
Dynamic Topology Optimization of Compliant Mechanisms and Piezoceramic Actuators
,”
ASME J. Mech. Des.
1050-0472,
126
(
6
), pp.
975
983
.
29.
Mankame
,
N. D.
, and
Ananthasuresh
,
G. K.
, 2004, “
A Novel Compliant Mechanism for Converting Reciprocating Translation Into Enclosing Curved Paths
,”
ASME J. Mech. Des.
1050-0472,
126
(
4
), pp.
667
672
.
30.
Chapman
,
C. D.
,
Saitou
,
K.
, and
Jakiela
,
M. J.
, 1994, “
Genetic Algorithms as an Approach to Configuration and Topology Design
,”
ASME J. Mech. Des.
1050-0472,
116
(
4
), pp.
1005
1012
.
31.
Chapman
,
C. D.
, and
Jakiela
,
M. J.
, 1996, “
Genetic Algorithm-Based Structural Topology Design With Compliance and Topology Simplification Considerations
,”
ASME J. Mech. Des.
1050-0472,
118
(
1
), pp.
89
98
.
32.
Jakiela
,
M. J.
,
Chapman
,
C. D.
,
Duda
,
J. W.
,
Adewuya
,
A.
, and
Saitou
,
K.
, 2000, “
Continuum Structural Topology Design With Genetic Algorithms
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
186
(
2
), pp.
339
356
.
33.
Saxena
,
A.
, 2005, “
Synthesis of Compliant Mechanisms for Path Generation Using Genetic Algorithm
,”
ASME J. Mech. Des.
1050-0472,
127
(
4
), pp.
745
752
.
34.
Hull
,
P. V.
, and
Canfield
,
S.
, 2006, “
Optimal Synthesis of Compliant Mechanisms Using Subdivision and Commercial FEA
,”
ASME J. Mech. Des.
1050-0472,
128
(
2
), pp.
337
348
.
35.
Lu
,
K. J.
, and
Kota
,
S.
, 2006, “
Topology and Dimensional Synthesis of Compliant Mechanisms Using Discrete Optimization
,”
ASME J. Mech. Des.
1050-0472,
128
(
5
), pp.
1080
1091
.
36.
Tai
,
K.
,
Cui
,
G. Y.
, and
Ray
,
T.
, 2002, “
Design Synthesis of Path Generating Compliant Mechanisms by Evolutionary Optimization of Topology and Shape
,”
ASME J. Mech. Des.
1050-0472,
124
(
3
), pp.
492
500
.
37.
Zhou
,
H.
, and
Ting
,
K. L.
, 2005, “
Topological Synthesis of Compliant Mechanisms Using Spanning Tree Theory
,”
ASME J. Mech. Des.
1050-0472,
127
(
4
), pp.
753
759
.
38.
Pederson
,
C. B. W.
,
Fleck
,
N. A.
, and
Ananthasuresh
,
G. K.
, 2006, “
Design of a Compliant Mechanism to Modify an Actuator Characteristic to Deliver a Constant Output Force
,”
ASME J. Mech. Des.
1050-0472,
128
(
5
), pp.
1101
1112
.
39.
Crane
,
N. B.
, and
Howell
,
L. L.
, 2004, “
Compliant Floating-Opposing-Arm Centrifugal Clutch
,”
ASME J. Mech. Des.
1050-0472,
126
(
1
), pp.
169
177
.
40.
Canfield
,
S.
, and
Frecker
,
M.
, 2000, “
Topology Optimization of Compliant Mechanical Amplifiers for Piezoelectric Actuators
,”
Struct. Multidiscip. Optim.
1615-147X,
20
(
4
), pp.
269
279
.
41.
Hetrick
,
J. A.
, and
Kota
,
S.
, 1999, “
An Energy Formulation for Parametric Size and Shape Optimization of Compliant Mechanisms
,”
ASME J. Mech. Des.
1050-0472,
121
(
2
), pp.
229
234
.
42.
Xu
,
D.
, and
Ananthasuresh
,
G. K.
, 2003, “
Freeform Skeletal Shape Optimization of Compliant Mechanisms
,”
ASME J. Mech. Des.
1050-0472,
125
(
2
), pp.
253
261
.
43.
Zhou
,
H.
, and
Ting
,
K. L.
, 2006, “
Shape and Size Synthesis of Compliant Mechanisms Using Wide Curve Theory
,”
ASME J. Mech. Des.
1050-0472,
128
(
3
), pp.
551
558
.
44.
Yin
,
L.
, and
Ananthasuresh
,
G. K.
, 2001, “
Topology Optimization of Compliant Mechanisms With Multiple Materials Using a Peak Function Material Interpolation Scheme
,”
Struct. Multidiscip. Optim.
1615-147X,
23
(
1
), pp.
49
62
.
45.
Sigmund
,
O.
, 2001, “
Design of Multiphysics Actuators Using Topology Optimization—Part II: Two-Material Structures
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
190
(
49–50
), pp.
6605
6627
.
46.
Wang
,
M. Y.
, and
Chen
,
S.
, 2005, “
Design of Multi-Material Compliant Mechanisms Using Level Set Methods
,”
ASME J. Mech. Des.
1050-0472,
127
(
5
), pp.
941
956
.
47.
Salomon
,
D.
, 1999,
Computer Graphics and Geometric Modeling
,
Springer
,
New York
.
48.
Farin
,
G.
, 2001,
Curves and Surfaces for CAGD: A Practical Guide
,
Academic
,
New York
.
49.
Mestetskii
,
L. M.
, 2000, “
Fat Curves and Representation of Planar Figures
,”
Comput. Graphics
0097-8493,
24
(
1
), pp.
9
21
.
50.
Optimization Toolbox for Use With Matlab, User’s Guide, Version, 3, 2006, MathWorks, Inc.
51.
Crisfield
,
M. A.
, 1991,
Non-Linear Finite Element Analysis of Solids and Structures
,
Wiley
,
New York
.
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