This paper presents a kinematic procedure to synthesize planar mechanisms, composed of rigid links and revolute joints, capable of approximating a shape change defined by a set of curves. These “morphing curves”, referred to as design profiles, differ from each other by a combination of rigid-body displacement and shape change. Design profiles are converted to piecewise linear curves, referred to as target profiles, that can be readily manipulated. In the segmentation phase, the geometry of rigid links that approximate the shapes of corresponding segments from each target profile is determined. In the mechanization phase, these rigid links are joined together at their end points with revolute joints to form a single chain. Dyads are then added to reduce the number of degrees of freedom (DOF’s) to any desired value, typically 1. The approach can be applied to any number of design profiles that can be approximated with any number of rigid links, which can then be used to construct a mechanism with any number of DOF’s. Naturally, greater difficulty is encountered for larger numbers of design profiles and/or links and for more dramatic changes in shape. The procedure is demonstrated with examples of single-DOF mechanisms approximating shape changes between two and three design profiles.

1.
Monner
,
H. P.
, 2001, “
Realization of an Optimized Wing Camber by Using Formvariable Flap Structures
,”
Aerosp. Sci. Technol.
1270-9638,
5
, pp.
445
455
.
2.
Washington
,
G. N.
, 1996, “
Smart Aperture Antennas
,”
Smart Mater. Struct.
0964-1726,
5
(
6
), pp.
801
805
.
3.
Martin
,
J. W.
,
Main
,
J. A.
, and
Nelson
,
G. C.
, 1998, “
Shape Control of Deployable Membrane Mirrors
,”
ASME Adaptive Structures and Materials Systems Conference
,
Anaheim, CA
, pp.
217
223
.
4.
Austin
,
F.
,
Siclari
,
M. J.
,
Van Nostrand
,
W.
,
Weisensel
,
G. N.
,
Kottamasu
,
V.
, and
Volpe
,
G.
, 1997, “
Comparison of Smart Wing Concepts for Transonic Cruise Drag Reduction
,”
Proc. SPIE
0277-786X,
3044
, pp.
33
40
.
5.
Austin
,
F.
, and
Van Nostrand
,
W.
, 1995, “
Shape Control of an Adaptive Wing for Transonic Drag Reduction
,”
Proc. SPIE
0277-786X,
2447
, pp.
45
55
.
6.
Ameduri
,
S.
,
Esposito
,
C.
, and
Concilio
,
A.
, 2001, “
Active Shape Airfoil Control Through Composite Piezoceramic Actuators
,”
Proc. SPIE
0277-786X,
4327
, pp.
641
650
.
7.
Bart-Smith
,
H.
, and
Risseeuw
,
P. E.
, 2003, “
High Authority Morphing Structures
,”
Proceedings of the ASME International Mechanical Engineering Congress
,
Washington, DC
.
8.
Jardine
,
P.
,
Flanagan
,
J.
,
Martin
,
C.
, and
Carpenter
,
B.
, 1997, “
Smart Wing Shape Memory Alloy Actuator Design and Performance
,”
Proc. SPIE
0277-786X,
3044
, pp.
48
55
.
9.
Martin
,
C. A.
,
Jasmin
,
L.
,
Flanagan
,
J.
,
Appa
,
K.
, and
Kudva
,
J. N.
, 1997, “
Smart Wing Wind Tunnel Model Design
,”
Proc. SPIE
0277-786X,
3044
, pp.
41
47
.
10.
Quackenbush
,
A.
,
Bilanin
,
A.
,
Batcho
,
P.
,
Mckillip
,
R.
, and
Carpenter
,
B.
, 1997, “
Implementation of Vortex Wake Control Using SMA-Actuated Devices
,”
Proc. SPIE
0277-786X,
3044
, pp.
134
146
.
11.
Webb
,
G. V.
,
Lagoudas
,
D. C.
, and
Kulkarini
,
M.
, 1999, “
Adaptive Shape Control for an SMA-Actuated Aerofoil Rib Structure
,”
Proceedings of the ASME International Mechanical Engineering Congress
,
Nashville, TN
, pp.
205
212
.
12.
Angelino
,
M.
, and
Washington
,
G.
, 2001, “
Point Actuated Aperture Antenna Development
,”
Proc. SPIE
0277-786X,
4334
, pp.
147
155
.
13.
Yoon
,
H. S.
, and
Washington
,
G.
, 1998, “
Piezoceramic Actuated Aperture Antennae
,”
Smart Mater. Struct.
0964-1726,
7
(
4
), pp.
537
542
.
14.
Yoon
,
H. S.
,
Washington
,
G.
, and
Theunissen
,
W. H.
, 2000, “
Analysis and Design of Doubly Curved Piezoelectric Strip-Actuated Aperture Antennas
,”
IEEE Trans. Antennas Propag.
0018-926X,
48
(
5
), pp.
755
763
.
15.
Martin
,
J. W.
,
Redmond
,
J. M.
,
Barney
,
P. S.
,
Henson
,
T. D.
,
Wehlburg
,
J. C.
, and
Main
,
J. A.
, 2000, “
Distributed Sensing and Shape Control of Piezoelectric Bimorph Mirrors
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
11
, pp.
744
757
.
16.
Saggere
,
L.
, and
Kota
,
S.
, 1999, “
Static Shape Control of Smart Structures Using Compliant Mechanisms
,”
AIAA J.
0001-1452,
37
, pp.
572
578
.
17.
Saggere
,
L.
, and
Kota
,
S.
, 2001, “
Synthesis of Planar, Compliant Four-Bar Mechanisms for Compliant-Segment Motion Generation
,”
ASME J. Mech. Des.
1050-0472,
123
(
4
), pp.
535
541
.
18.
Lu
,
K. J.
, and
Kota
,
S.
, 2003, “
Design of Compliant Mechanisms for Morphing Structural Shapes
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
14
, pp.
379
391
.
19.
Lu
,
K. J.
, and
Kota
,
S.
, 2005, “
An Effective Method of Synthesizing Compliant Adaptive Structures Using Load Path Representation
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
16
(
4
), pp.
304
317
.
20.
Stubbs
,
M. D.
,
Whittier
,
W. B.
, and
Reinholtz
,
C. F.
, 2004, “
Single Degree-of-Freedom Morphing Wing (Design and Synthesis)
,”
Proceedings of the ASME 2004 Design Engineering Technical Conferences
,
Salt Lake City, UT
.
21.
Erdman
,
A.
,
Sandor
,
G.
, and
Kota
,
S.
, 2001,
Mechanism Design: Analysis and Synthesis
,
4th ed.
,
Prentice-Hall
,
New York
.
22.
Faux
,
I. D.
, and
Pratt
,
M. J.
, 1985,
Computational Geometry for Design and Manufacture
,
Wiley
,
New York
.
23.
Horn
,
B. K. P.
, 1987, “
Closed-Form Solution of Absolute Orientation Using Orthonormal Matrices
,”
J. Opt. Soc. Am. A
0740-3232,
5
(
7
), pp.
1127
1135
.
24.
Horn
,
B. K. P.
, 1987, “
Closed-Form Solution of Absolute Orientation Using Unit Quaternions
,”
J. Opt. Soc. Am. A
0740-3232,
4
(
4
), pp.
629
642
.
25.
Arun
,
K. S.
,
Huang
,
T. S.
, and
Blostein
,
S. D.
, 1987, “
Least-Squares Fitting of Two 3-D Point Sets
,”
IEEE Trans. Pattern Anal. Mach. Intell.
0162-8828,
PAMI-9
(
5
), pp.
698
700
.
26.
Umeyama
,
S.
, 1991, “
Least-Squares Estimation of Transformation Parameters Between Two Point Patterns
,”
IEEE Trans. Pattern Anal. Mach. Intell.
0162-8828,
13
(
4
), pp.
376
380
.
27.
Kinzel
,
E. C.
,
Schmiedeler
,
J. P.
, and
Pennock
,
G. R.
, 2006, “
Kinematic Synthesis for Finitely Separated Positions Using Geometric Constraint Programming
,”
ASME J. Mech. Des.
1050-0472,
128
(
5
), pp.
1070
1079
.
28.
Sarkisyan
,
Y. L.
,
Gupta
,
K. C.
, and
Roth
,
B.
, 1973, “
Kinematic Geometry Associated with the Least-Square Approximation of a Given Motion
,”
ASME J. Eng. Ind.
0022-0817,
95
(
2
), pp.
503
510
.
29.
Chase
,
T. R.
, 2006, “
A Note on the Waldron Construction for Transmission Angle Rectification
,”
ASME J. Mech. Des.
1050-0472,
128
(
3
), pp.
509
512
.
30.
Sun
,
J. W. H.
, and
Waldron
,
K. J.
, 1981, “
Graphical Transmission Angle Control in Planar Linkage Synthesis
,”
Mech. Mach. Theory
0094-114X,
37
(
4
), pp.
385
397
.
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