Compliant mechanisms are able to transfer motion, force, and energy using a monolithic structure without discrete hinge elements. The geometric design freedoms and multimaterial capability offered by the PolyJet 3D printing process enables the fabrication of compliant mechanisms with optimized topology. The inclusion of multiple materials in the topology optimization process has the potential to eliminate the narrow, weak, hingelike sections that are often present in single-material compliant mechanisms and also allow for greater magnitude deflections. In this paper, the authors propose a design and fabrication process for the realization of 3-phase, multiple-material compliant mechanisms. The process is tested on a 2D compliant force inverter. Experimental and numerical performance of the resulting 3-phase inverter is compared against a standard 2-phase design.

References

References
1.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley
,
New York, NY
.10.1007/978-1-4471-4510-3_7
2.
Vogel
,
S.
,
1995
, “
Better Bent Than Broken
,”
Discover
,
16
(
5
), pp.
62
67
.
3.
Aguirre
,
M. E.
, and
Frecker
,
M.
,
2010
, “
Design and Optimization of Hybrid Compliant Narrow-Gauge Surgical Forceps
,”
ASME
2010 Conference on Smart Materials
, Adaptive Structures and Intelligent Systems, Department of Mechanical and Nuclear Engineering, Pennslyvania State University, University Park, PA, Sept. 28–Oct. 1, pp.
779
788
.10.1115/SMASIS2010-3732
4.
Stratasys,
2013
, “
Objet 350 Connex: Build Mid-Size Prototypes in Multiple Materials
,” http://stratasys.com/3d-printers/design-series/precision/objet-connex350
5.
Sigmund
,
O.
,
1997
, “
On the Design of Compliant Mechanisms Using Topology Optimization
,”
Mech. Struct. Mach.
,
25
(
4
), pp.
493
524
.10.1080/08905459708945415
6.
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.
,
119
(
2
), pp.
238
245
.10.1115/1.2826242
7.
Challis
,
V. J.
,
Roberts
,
A. P.
,
Grotowski
,
J. F.
,
Zhang
,
L.-C.
, and
Sercombe
,
T. B.
,
2010
, “
Prototypes for Bone Implant Scaffolds Designed Via Topology Optimization and Manufactured by Solid Freeform Fabrication
,”
Adv. Eng. Mater.
,
12
(
11
), pp.
1106
1110
.10.1002/adem.201000154
8.
Challis
,
V. J.
,
Guest
,
J. K.
,
Grotowski
,
J. F.
, and
Roberts
,
A. P.
,
2012
, “
Computationally Generated Cross-Property Bounds for Stiffness and Fluid Permeability Using Topology Optimization
,”
Int. J. Solids Struct.
,
49
(
23–24
), pp.
3397
3408
.10.1016/j.ijsolstr.2012.07.019
9.
Andreassen
,
E.
,
Lazarov
,
B. S.
, and
Sigmund
,
O.
,
2014
, “
Design of Manufacturable 3D Extremal Elastic Microstructure
,”
Mech. Mater.
,
69
(
1
), pp.
1
10
.10.1016/j.mechmat.2013.09.018
10.
Brackett
,
D.
,
Ashcroft
,
I.
, and
Hague
,
R.
,
2011
, “
Topology Optimization for Additive Manufacturing
,”
22nd Annual International Solid Freeform Fabrication Symposium
, Austin, TX, Aug. 8–10, pp.
348
362
.
11.
Brackett
,
D.
,
Ashcroft
,
I.
, and
Hague
,
R.
,
2011
, “
A Dithering Based Method to Generate Variable Volume Lattice Cells for Additive Manufacturing
,”
22nd Annual International Solid Freeform Fabrication Symposium
, Austin, TX, Aug. 8–10, pp.
671
679
.
12.
Aremu
,
A.
,
Ashcroft
,
I.
,
Wildman
,
R.
,
Hague
,
R.
,
Tuck
,
C.
, and
Brackett
,
D.
,
2011
, “
A Hybrid Algorithm for Topology Optimization of Additive Manufactured Structures
,”
22nd Annual International Solid Freeform Fabrication Symposium
, Austin, TX, Aug. 8–10, pp.
279
289
.
13.
Maute
,
K.
, and
Ramm
,
E.
,
1995
, “
Adaptive Topology Optimization
,”
Struct. Optim.
,
10
(
2
), pp.
100
112
.10.1007/BF01743537
14.
Stainko
,
R.
,
2006
, “
An Adaptive Multilevel Approach to the Minimal Compliance Problem
,”
Commun. Numer. Methods Eng.
,
22
(
2
), pp.
109
118
.10.1002/cnm.800
15.
Guest
,
J. K.
, and
Smith Genut
,
L. C.
,
2010
, “
Reducing Dimensionality in Topology Optimization Using Adaptive Design Variable Fields
,”
Int. J. Numer. Methods Eng.
,
81
(
8
), pp.
1019
1045
.10.1002/nme.2724
16.
Watts
,
D. M.
, and
Hague
,
R.
,
2006
, “
Exploiting the Design Freedom of RM
,”
17th Annual International Solid Freeform Fabrication Symposium
, Austin, TX, Aug. 14–16, pp.
656
667
.
17.
Sigmund
,
O.
, and
Petersson
,
J.
,
1998
, “
Numerical Instabilities in Topology Optimization: A Survey on Procedures Dealing With Checkerboards, Mesh-Dependencies and Local Minima
,”
Struct. Optim.
,
16
(
1
), pp.
68
75
.10.1007/BF01214002
18.
Wang
,
H. V.
, and
Rosen
,
D. W.
,
2001
,
Computer-Aided Design Methods for the Additive Fabrication of Truss Structures
,
Georgia Institute of Technology
,
Atlanta, GA
.
19.
Wang
,
H. V.
, and
Rosen
,
D. W.
,
2006
, “
An Automated Design Synthesis Method for Compliant Mechanisms With Application to Morphing Wings
,”
ASME Mechanisms and Robotics Conference
, Philadelphia, PA, Sept. 10–13, pp.
1
9
.
20.
Wang
,
H. V.
,
Chen
,
Y.
, and
Rosen
,
D. W.
,
2005
, “
A Hybrid Geometric Modeling Method for Large Scale Conformal Cellular Structures
,”
ASME Computers and Information in Engineering Conference
, Long Beach, CA, Sept. 24–28, pp.
421
427
.
21.
Graf
,
G. C.
,
2009
,
Development of Specialized Base Primitives for Meso-Scale Conforming Truss Structures
,
Georgia Institute of Technology
,
Atlanta, GA
.
22.
Graf
,
G. C.
,
Chu
,
J.
,
Engelbrecht
,
S.
, and
Rosen
,
D. W.
,
2009
, “
Synthesis Methods for Lightweight Lattice Structures
,”
ASME
International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, San Diego, CA, Aug. 30–Sept. 2, pp.
579
589
.10.1115/DETC2009-86993
23.
Chu
,
J.
,
Engelbrecht
,
S.
,
Graf
,
G.
, and
Rosen
,
D. W.
,
2010
, “
A Comparison of Synthesis Methods for Cellular Structures With Application to Additive Manufacturing
,”
Rapid Prototyping J.
,
16
(
4
), pp.
459
472
.10.1108/13552541011049298
24.
Rosen
,
D. W.
,
2007
, “
Computer-Aided Design for Additive Manufacturing of Cellular Structures
,”
Comput.-Aided Des. Appl.
,
4
(
5
), pp.
585
594
.10.1080/16864360.2007.10738493
25.
Chu
,
C.
,
Graf
,
G.
, and
Rosen
,
D. W.
,
2008
, “
Design for Additive Manufacturing of Cellular Structures
,”
Comput.-Aided Des. Appl.
,
5
(
5
), pp.
686
696
.10.3722/cadaps.2008.686-696
26.
Chen
,
Y.
, and
Wang
,
S.
,
2008
, “
Computer-Aided Product Design With Performance-Tailored Mesostructures
,”
Comput.-Aided Des. Appl.
,
5
(
1–4
), pp.
1
11
.10.1016/j.cam.2007.06.033
27.
Li
,
Y.
,
Chen
,
Y.
, and
Zhou
,
C.
,
2009
, “
Design of Flexible Skin for Target Displacements Based on Meso-Structures
,”
ASME
International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, San Diego, CA, Aug. 30–Sept. 2, pp.
1
14
.10.1115/DETC2009-87137
28.
Maheshwaraa
,
U.
,
Bourell
,
D.
, and
Seepersad
,
C. C.
,
2007
, “
Design and Freeform Fabrication of Deployable Structures with Lattice Skins
,”
Rapid Prototyping J.
,
13
(
4
), pp.
213
225
.10.1108/13552540710776160
29.
Hiller
,
J. D.
, and
Lipson
,
H.
,
2009
, “
Multimaterial Topological Optimization of Structures and Mechanisms
,”
11th Annual Conference on Genetic and Evolutionary Computation
, New York, July 8–12, pp.
1521
1528
.
30.
Hiller
,
J. D.
, and
Lipson
,
H.
,
2009
, “
Design Automation for Multi-Material Printing
,”
20th Annual International Solid Freeform Fabrication Symposium
, Austin, TX, Aug. 3–5, pp.
279
287
.
31.
Bendsøe
,
M. P.
,
1989
, “
Optimal Shape Design as a Material Distribution Problem
,”
Struct. Optim.
,
1
(
4
), pp.
193
202
.10.1007/BF01650949
32.
Bendsøe
,
M. P.
, and
Sigmund
,
O.
,
1999
, “
Material Interpolation Schemes in Topology Optimization
,”
Arch. Appl. Mech.
,
69
(
9–10
), pp.
635
654
.10.1007/s004190050248
33.
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.
,
23
(
1
), pp.
49
62
.10.1007/s00158-001-0165-z
34.
Saxena
,
A.
,
2005
, “
Topology Design of Large Displacement Compliant Mechanisms with Multiple Materials and Multiple Output Ports
,”
Struct. Multidiscip. Optim.
,
30
(
6
), pp.
477
490
.10.1007/s00158-005-0535-z
35.
Saxena
,
A.
,
2002
, “
On Multiple-Material Optimal Compliant Topologies: Discrete Variable Parameterization Using Genetic Algorithm
,”
ASME
International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Montreal, QC, Canada, Sept. 29,–Oct. 2, pp.
1
12
.10.1115/DETC2002/MECH-34209
36.
Bailey
,
S. A.
,
Cham
,
J. G.
,
Cutkosky
,
M. R.
, and
Full
,
R. J.
,
1999
, “
Biomimetic Robotic Mechanisms via Shape Deposition Manufacturing
,”
Robotics Research: The 9th International Symposium
, Snowbird, UT, Oct. 9–12, pp.
403
410
.
37.
Rajagopalan
,
S.
,
Goldman
,
R.
,
Shin
,
K.-H.
,
Kumar
,
V.
,
Cutkosky
,
M.
, and
Dutta
,
D.
,
2001
, “
Representation of Heterogeneous Objects During Design, Processing and Freeform-Fabrication
,”
Mater. Des.
,
22
(
3
), pp.
185
197
.10.1016/S0261-3069(00)00065-0
38.
Bejgerowski
,
W.
,
Gerdes
,
J. W.
,
Gupta
,
S. K.
, and
Bruck
,
H. A.
,
2011
, “
Design and Fabrication of Miniature Compliant Hinges for Multi-Material Compliant Mechanisms
,”
Int. J. Adv. Manuf. Technol.
,
57
(
5–8
), pp.
437
452
.10.1007/s00170-011-3301-y
39.
Bejgerowski
,
W.
,
Gerdes
,
J. W.
,
Gupta
,
S. K.
,
Bruck
,
H. A.
, and
Wilkerson
,
S.
,
2010
, “
Design and Fabrication of a Multi-Material Compliant Flapping Wing Drive Mechanism for Miniature Air Vehicles
,”
ASME
International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Montreal, QC, Canada, Aug. 15–18, pp.
69
80
.10.1115/DETC2010-28519
40.
Gouker
,
R. M.
,
Gupta
,
S. K.
,
Bruck
,
H. A.
, and
Holzschuh
,
T.
,
2006
, “
Manufacturing of Multi-Material Compliant Mechanisms Using Multi-Material Molding
,”
Int. J. Adv. Manuf. Technol.
,
30
(
11
), pp.
1049
1075
.10.1007/s00170-005-0152-4
41.
Rajkowski
,
J. E.
,
Gerratt
,
A. P.
,
Schaler
,
E. W.
, and
Bergbreiter
,
S.
,
2009
, “
A Multi-Material Milli-Robot Prototyping Process
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
, IEEE Computer Society, Mechanical Engineering Department, Institute for Systems Research, University of Maryland, College Park, MD, Oct. 11–15, pp.
2777
2782
.
42.
Vogtmann
,
D. E.
,
Gupta
,
S. K.
, and
Bergbreiter
,
S.
,
2011
, “
A Systematic Approach to Designing Multi-Material Miniature Compliant Mechanisms
,”
ASME
International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Washington, DC, Aug. 28–31, pp.
211
221
.10.1115/DETC2011-48410
43.
Gaynor
,
A. T.
,
Guest
,
J. K.
, and
Moen
,
C. D.
,
2012
, “
Reinforced Concrete Force Visualization and Design Using Bilinear Truss-Continuum Topology Optimization
,”
J. Struct. Eng.
,
139
(
4
), pp.
607
618
.10.1061/(ASCE)ST.1943-541X.0000692
44.
Amir
,
O.
, and
Sigmund
,
O.
,
2013
, “
Reinforcement Layout Design for Concrete Structures Based on Continuum Damage and Truss Topology Optimization
,”
Struct. Multidiscip. Optim.
,
47
(
2
), pp.
157
174
.10.1007/s00158-012-0817-1
45.
Yang
,
Y.
,
Moen
,
C. D.
, and
Guest
,
J. K.
, “
Three-dimensional Force Flow Paths and Reinforcement Design in Concrete via Stress-dependent Truss-continuum Topology Optimization
,”
ASCE Journal of Engineering Mechanics.
10.1061/(ASCE)EM.1943-7889.0000819
46.
Carlo
,
H. J.
,
Patrick Spicer
,
J.
, and
Rivera-Silva
,
A.
,
2012
, “
Simultaneous Consideration of Scalable-Reconfigurable Manufacturing System Investment and Operating costs
,”
ASME J. Manuf. Sci. Eng.
,
134
(
1
), p.
011003
.10.1115/1.4005305
47.
Pang
,
L.
, and
Kishawy
,
H. A.
,
2012
, “
Modified Primary Shear Zone Analysis for Identification of Material Mechanical Behavior During Machining Process Using Genetic Algorithm
,”
ASME J. Manuf. Sci. Eng.
,
134
(
4
), p.
041003
.10.1115/1.4006768
48.
Deuser
,
B. K.
,
Tang
,
L.
,
Landers
,
R. G.
,
Leu
,
M. C.
, and
Hilmas
,
G. E.
,
2013
, “
Hybrid Extrusion Force-Velocity Control Using Freeze-Form Extrusion Fabrication for Functionally Graded Material Parts
,”
ASME J. Manuf. Sci. Eng.
,
135
(
4
), p.
041015
.10.1115/1.4024534
49.
Keshavarz Panahi
,
A.
,
Mianajiy
,
H.
,
Miandoabchi
,
E.
, and
Hussaini Fareed
,
M.
,
2013
, “
Optimization of the Powder Injection Molding Process Parameters Using the Sequential Simplex Algorithm and Sensitivity Analysis
,”
ASME J. Manuf. Sci. Eng.
,
135
(
1
), p.
011006
.10.1115/1.4023301
50.
Bryan
,
A.
,
Hu
,
S. J.
, and
Koren
,
Y.
,
2013
, “
Assembly System Reconfiguration Planning
,”
ASME J. Manuf. Sci. Eng.
,
135
(
4
), p.
041005
.10.1115/1.4024288
51.
Park
,
H. S.
, and
Anh
,
T. V.
,
2012
, “
Development of Evolutionary Method for Optimizing a Roll Forming Process of Aluminum Parts
,”
ASME J. Manuf. Sci. Eng.
,
134
(
2
), p.
021012
.10.1115/1.4005804
52.
Leng
,
J.
,
Li
,
Z.
,
Guest
,
J. K.
, and
Schafer
,
B. W.
,
2013
, “
Shape Optimization of Cold-Formed Steel Columns With Manufacturing Constraints and Limited Number of Rollers
,”
Proceedings of the Structural Stability Research Council
, Annual Stability Conference, St. Louis, MO, Apr. 16–20, pp.
1
19
.
53.
Hofmann
,
D.
,
Huang
,
H.
, and
Reinhart
,
G.
,
2013
, “
Automated Shape Optimization of Orienting Devices for Vibratory Bowl Feeders
,”
ASME J. Manuf. Sci. Eng.
,
135
(
5
), p.
051017
.10.1115/1.4025089
54.
Svanberg
,
K.
,
1987
, “
The Method of Moving Asymptotes—A New Method for Structural Optimization
,”
Int. J. Numer. Methods Eng.
,
24
(
2
), pp.
359
373
.10.1002/nme.1620240207
55.
Guest
,
J. K.
,
Prévost
,
J. H.
, and
Belytschko
,
T.
,
2004
, “
Achieving Minimum Length Scale in Topology Optimization Using Nodal Design Variables and Projection Functions
,”
Int. J. Numer. Methods Eng.
,
61
(
2
), pp.
238
254
.10.1002/nme.1064
56.
Guest
,
J. K.
,
2009
, “
Topology Optimization With Multiple Phase Projection
,”
Comput. Methods Appl. Mech. Eng.
,
199
(
1–4
), pp.
123
135
.10.1016/j.cma.2009.09.023
57.
Guest
,
J. K.
,
Asadpoure
,
A.
, and
Ha
,
S.-H.
,
2011
, “
Eliminating Beta-Continuation From Heaviside Projection and Density Filter Algorithms
,”
Struct. Multidiscip. Optim.
,
44
(
4
), pp.
443
453
.10.1007/s00158-011-0676-1
58.
Buhl
,
T.
,
Pedersen
,
C.
, and
Sigmund
,
O.
,
2000
, “
Stiffness Design of Geometrically Nonlinear Structures Using Topology Optimization
,”
Struct. Multidiscip. Optim.
,
19
(
2
), pp.
93
104
.10.1007/s001580050089
59.
Bruns
,
T. E.
, and
Tortorelli
,
D. A.
,
2001
, “
Topology Optimization of Non-Linear Elastic Structures and Compliant Mechanisms
,”
Comput. Methods Appl. Mech. Eng.
,
190
(
26–27
), pp.
3443
3459
.10.1016/S0045-7825(00)00278-4
60.
Sigmund
,
O.
,
2009
, “
Manufacturing Tolerant Topology Optimization
,”
Acta Mechanica Sinica/Lixue Xuebao
,
25
(
2
), pp.
227
239
.10.1007/s10409-009-0240-z
61.
Jansen
,
M.
,
Lombaert
,
G.
,
Diehl
,
M.
,
Lazarov
,
B. S.
,
Sigmund
,
O.
, and
Schevenels
,
M.
,
2013
, “
Robust Topology Optimization Accounting for Misplacement of Material
,”
Struct. Multidiscip. Optim.
,
47
(
3
), pp.
317
333
.10.1007/s00158-012-0835-z
62.
Schevenels
,
M.
,
Lazarov
,
B. S.
, and
Sigmund
,
O.
,
2011
, “
Robust Topology Optimization Accounting for Spatially Varying Manufacturing Errors
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
49–52
), pp.
3613
3627
.10.1016/j.cma.2011.08.006
63.
Luo
,
J.
,
Luo
,
Z.
,
Chen
,
S.
,
Tong
,
L.
, and
Yu Wang
,
M.
,
2008
, “
A New Level Set Method for Systematic Design of Hinge-Free Compliant Mechanisms
,”
Comput. Methods Appl. Mech. Eng.
,
198
(
2
), pp.
318
331
.10.1016/j.cma.2008.08.003
You do not currently have access to this content.