This paper presents a number of systematically designed compliant topologies and discusses how the intrinsic kinematic behavior can be extracted from them. This is then applied to the number synthesis of linkages. Many techniques developed for number synthesis of linkages enumerate numerous possible kinematic chains, but few can select the best configuration among them. A systematic computational approach that can select the best configuration based on kinetostatic design specifications is presented here. This is a serendipitous result that transpired when two well-developed design techniques for compliant mechanisms were combined. A number of examples with nonintuitive design specifications are included to illustrate the new approach to the number synthesis. The examples also illustrate that the kinematic behavior is aptly captured in the elastic mechanics-based topology optimization method to compliant mechanism design. Dimensional synthesis is also accomplished in the same procedure, which is an added benefit of this approach.

1.
Erdman, A. G., and Sandor, G. N., 1997, Mechanism Design: Analysis and Synthesis, Vol. 1, Third Edition, Prentice Hall, Englewood Cliffs, New Jersey.
2.
Olson
,
D. G.
,
Erdman
,
A. G.
, and
Riley
,
D. R.
,
1985
, “
A Systematic Procedure for Type Synthesis of Mechanisms with Literature Review
,”
Mech. Mach. Theory
,
20
(
4
), pp.
285
295
.
3.
Kota, S., Ananthasuresh, G. K., Olson, D. G., Soni, A. H., Sathyadev, S., and Shirkodaie, A., 1993, “Chapter 3: Type Synthesis and Creative Design,” Modern Kinematics: Developments in the Last Forty Years, A. G. Erdman, ed., John Wiley & Sons, New York.
4.
Titus, J. E., Erdman, A. G., and Riley, D. R., 1990, “Techniques for Type Synthesis of Mechanisms,” NSC-CSF Joint Seminar on Recent Developments in Machine Design, National Cheng Kung University, Taiwan, Taiwan 70101, November 11–12, 1990.
5.
Freudenstein
,
F.
,
1967
, “
The Basic Concepts of Polya’s Theory of Enumeration with Application to the Structural Classification of Mechanisms
,”
J. Mec.
,
3
, pp.
275
290
.
6.
Mruthyunjaya
,
T. S.
, and
Raghavan
,
M. R.
,
1984
, “
Computer-Aided Analysis of the Structure of Kinematic Chains
,”
Mech. Mach. Theory
,
19
, pp.
357
368
.
7.
Erdman, A. G., Nelson, E., Peterson, J., and Bowen, J., 1980, “Type and Dimensional Synthesis of Casement Window Mechanisms,” ASME paper no. 80-DET-78.
8.
Waldron, K. J., and Kinzel, G. L., 1999, Kinematics, Dynamics, and Design of Machinery, John Wiley & Sons Inc., New York.
9.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Oxford University Press.
10.
De Sa
,
S.
, and
Roth
,
B.
,
1981
, “
Kinematic Mappings. Part 1: Classification of Algebraic Motions in the Plane
,”
ASME J. Mech. Des.
,
103
, pp.
585
591
.
11.
Freudenstein
,
F.
, and
Maki
,
E. R.
,
1983
,
ASME J. Mech. Des.
,
105
, p.
259
259
.
12.
Rankers
,
H.
,
1978
, “
An Alternate Method for Synthesis of the Slider Crank Inversion
,”
Mech. Mach. Theory
,
13
, pp.
395
406
.
13.
Erdman
,
A. G.
,
Thomson
,
T. R.
, and
Riley
,
D. R.
,
1986
, “
Type Selection of Robot and Gripper Kinematic Topology Using Expert Systems
,”
Int. J. Robot. Res.
,
5
(
2
), pp.
183
189
.
14.
Soni
,
A. H.
,
Dado
,
M. H. F.
, and
Weng
,
Y.
,
1988
, “
An Automated Procedure for Intelligent Mechanism Selection and Dimensional Synthesis
,”
ASME J. Mech. Des.
,
110
, pp.
130
137
.
15.
Hoetzel
,
D. A.
, and
Chieng
,
W. H.
,
1990
, “
Knowledge-Based Approaches for Creative Synthesis of Mechanisms
,”
Comput.-Aided Des.
,
22
(
1
), pp.
57
67
.
16.
Kota
,
S.
,
Erdman
,
A. G.
,
Riley
,
D. R.
,
Esterline
,
A.
, and
Slagle
,
J. R.
,
1988
, “
A Network-Based Expert System for Intelligent Design of Mechanisms
,”
Artificial Intelligence in Engineering Design, Analysis, and Manufacturing
,
2
(
1
), pp.
17
32
.
17.
Frecker
,
M. I.
,
Ananthasuresh
,
G. K.
,
Nishiwaki
,
S.
,
Kikuchi
,
N.
, and
Kota
,
S.
,
1997
, “
Topological Synthesis of Compliant Mechaisms Using Multicriteria Optimization
,”
ASME J. Mech. Des.
,
119
, pp.
238
245
.
18.
Saxena
,
A.
, and
Ananthasuresh
,
G. K.
,
2000
, “
On an Optimal Property of Compliant Topologies
,”
Structural and Multidisciplinary Optimization
,
19
, pp.
36
49
.
19.
Howell
,
L. L.
, and
Midha
,
A.
,
1996
, “
A Loop-Closure Theory for the Analysis and Synthesis of Compliant Mechanisms
,”
ASME J. Mech. Des.
,
118
, pp.
121
125
.
20.
Howell
,
L. L.
, and
Midha
,
A.
,
1995
, “
Parametric Deflection Approximation for End-Loaded, Large-Deflection Beams in Compliant Mechanisms
,”
ASME J. Mech. Des.
,
117
(
1
), pp.
156
165
.
21.
Mettlach, G. A., and Midha, A., 1996, “Using Burmester Theory in the Design of Compliant Mechanisms,” CD-ROM Proc. of the 1996 ASME Design Engineering Technical Conferences, 96-DETC/MECH-1181.
22.
Sigmund
,
O.
,
1997
, “
On the Design of Compliant Mechanisms Using Topology Optimization
,”
Mechanics of Structures and Machines
25
(
4
), pp.
495
526
.
23.
Nishiwaki
,
S.
,
Frecker
,
M. I.
,
Min
,
S.
, and
Kikuchi
,
N.
,
1998
, “
Topology Optimization of Compliant Mechanisms Using the Homogenization Method
,”
Int. J. Numer. Methods Eng.
,
42
, pp.
535
559
.
24.
Bendsøe
,
M. P.
, and
Kikuchi
,
N.
,
1988
, “
Generating Optimal Topologies in Structuural Design Using a Homogenization Method
,”
Comput. Methods Appl. Mech. Eng.
,
71
, pp.
197
224
.
25.
Rozvany
,
G. I. N.
,
Bendsøe
,
M. P.
, and
Kirsch
,
U.
,
1995
, “
Layout Optimization of Structures
,”
Appl. Mech. Rev.
,
48
, pp.
41
119
.
26.
Yin, L., and Ananathasuresh, G. K., 2001, “Topology Optimization of Compliant Mechanisms with Multiple Materials Using a Peak Function Material Interpolation Scheme,” Structural and Multidisciplinary Optimization, in press.
27.
Burns, R. H., and Crossley, F. R. E., 1968, “Kinetostatic Synthesis of Flexible Link Mechanisms,” ASME Paper No. 66-Mech-5.
28.
Howell, L. L., 2002, Compliant Mechanisms, John Wiley and Sons, New York.
29.
Saxena
,
A.
, and
Kramer
,
S. N.
,
1998
, “
A Simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End Forces and Moments
,”
ASME J. Mech. Des.
,
120
(
3
), pp.
392
400
.
30.
Kimball, C., Tsai, L. W., DeVoe, D., and Maloney, J., 2000, “Modeling and Batch Fabrication of Spatial Micro-Manipulators,” CD-ROM Proc. of 2000 ASME Design Engineering technical Conferences, Paper no. DETC00/MECH-14116.
31.
Howell
,
L. L.
, and
Midha
,
A.
,
1994
, “
A Method for the Design of Compliant Mechanisms with Small length flexural pivots
,”
ASME J. Mech. Des.
,
116
(
1
), pp.
280
290
.
32.
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
.
33.
Ananthasuresh, G. K., and Howell, L. L., 1996, “Case Studies and a Note on the Degrees-of-Freedom in Compliant Mechanisms,” CD-ROM Proc. of 1996 ASME Design Engineering technical Conferences, Paper no. 96-DETC/MECH-1217.
34.
Saxena, A., and Ananthasuresh, G. K., 2000, “PennSyn: A Topology Synthesis Software for Compliant Mechanisms,” CD-ROM Proc. of 2000 ASME Design Engineering technical Conferences, Paper no. DETC00/MECH-14139.
35.
Saxena
,
A.
, and
Ananthasuresh
,
G. K.
,
2001
, “
Topology Optimization of Compliant Mechanisms with Strength Considerations
,”
Mechanics of Structures and Machines
29
, pp.
199
222
.
36.
Lyon
,
S. M.
,
Evans
,
M. S.
,
Erickson
,
P. A.
, and
Howell
,
L. L.
,
1999
, “
Prediction of the First Modal Frequency of Compliant Mechanisms Using the Pseudo-Rigid-Body Model
,”
ASME J. Mech. Des.
,
121
(
2
), pp.
309
313
.
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