For a path generation problem, this paper uses the base topology of a single degree-of-freedom (DOF) rigid-body mechanism solution to synthesize fully distributed compliant mechanisms that can trace the same path. Two different strategies are proposed to employ the base topology in the structural optimization so that its design space size can be intelligently reduced from an arbitrary complexity. In the first strategy, dimensional synthesis directly determines the optimal size and shape of the compliant mechanism solution while maintaining the exact base topology. In the second, the base topology establishes an initial mesh network to determine the optimal topology and dimensions simultaneously. To increase the possibility of converging to an optimal design, the objective metrics to evaluate the path generation ability are computed in a novel manner. A section-by-section analysis with a rigid-body transformation is implemented to examine the full path of each candidate mechanism. A two-objective genetic algorithm (GA) is employed to find a group of viable designs that tradeoff minimizing the average Euclidean distance between the desired and actual paths with minimizing the peak distance between corresponding points on those paths. Two synthesis examples generating straight-line and curved paths are presented to demonstrate the procedure's utility.

References

References
1.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley
,
New York
.
2.
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.
,
124
(
3
), pp.
492
500
.10.1115/1.1480818
3.
Mankame
,
N. D.
, and
Ananthasuresh
,
G. K.
,
2007
, “
Synthesis of Contact-Aided Compliant Mechanisms for Non-Smooth Path Generation
,”
Int. J. Numer. Methods Eng.
,
69
(
12
), pp.
2564
2605
.10.1002/nme.1861
4.
Saxena
,
A.
,
2004
, “
Synthesis of Compliant Mechanisms for Path Generation Using Genetic Algorithm
,”
ASME J. Mech. Des.
,
127
(
4
), pp.
745
752
.10.1115/1.1899178
5.
Rai
,
A. K.
,
Saxena
,
A.
, and
Mankame
,
N. D.
,
2006
, “
Synthesis of Path Generating Compliant Mechanisms Using Initially Curved Frame Elements
,”
ASME J. Mech. Des.
,
129
(
10
), pp.
1056
1063
.10.1115/1.2757191
6.
Pedersen
,
C. B. W.
,
Buhl
,
T.
, and
Segmund
,
O.
,
2001
, “
Topology Synthesis of Large-Displacement Compliant Mechanisms
,”
Int. J. Numer. Methods Eng.
,
50
(
12
), pp.
2683
2705
.10.1002/nme.148
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.
,
116
(
1
), pp.
280
290
.10.1115/1.2919359
8.
Zhao
,
K.
, and
Schmiedeler
,
J. P.
,
2016
, “
Using Rigid-Body Mechanism Topologies to Design Shape-Changing Compliant Mechanisms
,”
ASME J. Mech. Rob.
8
(
1
).10.1115/1.4030585
9.
Ullah
,
I.
, and
Kota
,
S.
,
1997
, “
Optimal Synthesis of Mechanisms for Path Generation Using Fourier Descriptors and Global Search Methods
,”
ASME J. Mech. Des.
,
119
(
4
), pp.
504
510
.10.1115/1.2826396
10.
Kempe
,
A. B.
,
1877
,
How to Draw a Straight Line; a Lecture on Linkages
,
Macmillan
,
London
.
11.
Shiakolas
,
P. S.
,
Koladiya
,
D.
, and
Kebrle
,
J.
,
2005
, “
On the Optimum Synthesis of Six-Bar Linkages Using Differential Evolution and the Geometric Centroid of Precision Positions Technique
,”
Mech. Mach. Theory
,
40
(
3
), pp.
319
335
.10.1016/j.mechmachtheory.2004.07.005
12.
Zhou
,
H.
, and
Ting
,
K. L.
,
2005
, “
Path Generation With Singularity Avoidance for Five-Bar Slider–Crank Parallel Manipulators
,”
Mech. Mach. Theory
,
40
(
3
), pp.
371
384
.10.1016/j.mechmachtheory.2004.07.007
13.
Nariman-Zadeh
,
N.
,
Felezi
,
M.
,
Jamali
,
A.
, and
Ganji
,
M.
,
2009
, “
Pareto Optimal Synthesis of Four-Bar Mechanisms for Path Generation
,”
Mech. Mach. Theory
,
44
(
1
), pp.
180
191
.10.1016/j.mechmachtheory.2008.02.006
14.
Murray
,
A. P.
,
Schmiedeler
,
J. P.
, and
Korte
,
B. M.
,
2008
, “
Kinematic Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms
,”
ASME J. Mech. Des.
,
130
(
3
), p.
032302
.10.1115/1.2829892
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