This paper presents a new design of a deployable one degree-of-freedom (DOF) mechanism. Polygonal rigid-link designs are first investigated. Then, belt-driven links are considered in order to maximize the expansion ratio while avoiding flattened ill-conditioned parallelogram configurations. The planar basic shape of the proposed design is a triangle. Hence, virtually any planar or spatial surface can be created by assembling such faces. For architecture and telescopic applications, the cupola assembly is investigated. The advantages of this approach are discussed, and the scalability is demonstrated. Finally, a prototype is built for illustration purposes.

References

References
1.
Ishii
,
K.
,
2000
,
Structural Design of Retractable Roof Structures
,
WIT Press
,
Southampton, UK
.
2.
Gantes
,
C.
,
2001
,
Deployable Structures: Analysis and Design
,
WIT Press
,
New York
.
3.
Imbriale
,
W. A.
,
Gao
,
S.
, and
Boccia
,
L.
,
2012
,
Space Antenna Handbook
,
Wiley
,
Chichester, UK
.
4.
Pellegrino
,
S.
,
2001
,
Deployable Structures
, Vol.
412
,
Springer-Verlag
,
Wien, Austria
.
5.
Hoberman
,
C.
,
1991
, “
Radial Expansion/Retraction Truss Structures
,” U.S. Patent No. 5,024,031.
6.
Wei
,
G.
, and
Dai
,
J. S.
,
2012
, “
Synthesis of a Family of Regular Deployable Polyhedral Mechanisms (DPMs)
,”
Latest Advances in Robot Kinematics
, Springer, New York, pp.
123
130
.
7.
Korkmaz
,
K.
,
2005
, “
Generation of a New Type of Architectural Umbrella
,”
Int. J. Space Struct.
,
20
(
1
), pp.
35
41
.
8.
Lopatina
,
A.
, and
Morozov
,
E.
,
2009
, “
Modal Analysis of the Thin-Walled Composite Spoke of an Umbrella-Type Deployable Space Antenna
,”
Compos. Struct.
,
88
(
1
), pp.
46
55
.
9.
Wei
,
X.-Z.
,
Yao
,
Y.-A.
,
Tian
,
Y.-B.
, and
Fang
,
R.
,
2006
, “
A New Method of Creating Expandable Structure for Spatial Objects
,”
Proc. Inst. Mech. Eng., Part C
,
220
(
12
), pp.
1813
1818
.
10.
Kiper
,
G.
,
Soylemez
,
E.
, and
Kisisel
,
A. O.
,
2008
, “
A Family of Deployable Polygons and Polyhedra
,”
Mech. Mach. Theory
,
43
(
5
), pp.
627
640
.
11.
Agrawal
,
S.
, and
Kumar
,
S.
,
2002
, “
Polyhedral Single Degree-of-Freedom Expanding Structures: Design and Prototypes
,”
ASME J. Mech. Des.
,
124
(
3
), pp.
473
478
.
12.
Kovacs
,
F.
,
Tarnai
,
T.
,
Fowler
,
P.
, and
Guest
,
S.
,
2004
, “
A Class of Expandable Polyhedral Structures
,”
Int. J. Solids Struct.
,
41
(
3–4
), pp.
1119
1137
.
13.
Wohlhart
,
K.
,
1995
, “
New Overconstrained Spheroidal Linkages
,”
9th World Congress on the Theory of Machines and Mechanism
, Milan, Italy, Aug. 29–Sept. 5, Vol.
1
, pp.
149
154
.
14.
Gosselin
,
C.
, and
Gagnon-Lachance
,
D.
,
2006
, “
Expandable Polyhedral Mechanisms Based on Polygonal One-Degree-of-Freedom Faces
,”
Proc. Inst. Mech. Eng., Part C
,
220
(
7
), p.
1011
.
15.
Wohlhart
,
K.
,
2008
, “
Double-Ring Polyhedral Linkages
,”
First Conference on Interdisciplinary Applications in Kinematics
, Lima, Perú, Jan. 9–11, pp.
1
17
.
16.
Phillips
,
J.
,
1984/1990
,
Freedom Machinery
, Vol. 1,
Cambridge University Press
, Cambridge,
UK
.
17.
Guest
,
S.
, and
Fowler
,
P.
,
2005
, “
A Symmetry-Extended Mobility Rule
,”
Mech. Mach. Theory
,
40
(
9
), pp.
1002
1014
.
18.
Loeb
,
A.
,
1991
,
Space Structures
,
Birkhauser
,
Basel, Germany
.
19.
Gogu
,
G.
,
2005
, “
Chebyshev-Grübler-Kutzbachs Criterion for Mobility Calculation of Multi-Loop Mechanisms Revisited Via Theory of Linear Transformations
,”
Eur. J. Mech. A/Solids
,
24
(
3
), pp.
427
441
.
20.
Hartenberg
,
R.
, and
Denavit
,
J.
,
1964
,
Kinematic Synthesis of Linkages
,
McGraw-Hill
,
New York
.
21.
Ballia
,
S. S.
, and
Chanda
,
S.
,
2002
, “
Transmission Angle in Mechanisms (Triangle in Mech)
,”
Mech. Mach. Theory
,
37
(
2
), pp.
175
195
.
22.
Tao
,
D.
,
1964
,
Applied Linkage Synthesis
,
Addison-Wesley
, Reading,
MA
.
23.
Gosselin
,
C. M.
,
Sefrioui
,
J.
, and
Richard
,
M. J.
,
1992
, “
Solutions polynomiales au problème de la cinématique directe des manipulateurs parallèles plans à trois degrés de liberté
,”
Mech. Mach. Theory
,
27
(
2
), pp.
107
119
.
24.
Birglen
,
L.
,
Laliberté
,
T.
, and
Gosselin
,
C.
,
2008
,
Underactuated Robotic Hands
, Vol.
40
,
Springer-Verlag
,
Wien, Austria
.
25.
St-Onge
,
D.
, and
Gosselin
,
C.
,
2014
, “
Deployable Mechanisms for Small to Medium-Sized Space Debris Removal
,”
65th International Astronautical Congress, (IAC-14), Space Debris Symposium
, Toronto, Canada, Sept. 29–Oct. 3, p.
11
.
26.
Li
,
J.
,
Yan
,
S.
,
Guo
,
F.
, and
Guo
,
P.
,
2013
, “
Effects of Damping, Friction, Gravity, and Flexibility on the Dynamic Performance of a Deployable Mechanism With Clearance
,”
J. Mech. Eng. Sci.
,
227
(
8
), pp.
1
13
.
27.
Wohlhart
,
K.
,
2007
, “
Cupola Linkages
,”
12th IFToMM World Congress
, Besançon, France, June 18–21, pp.
319
324
.
28.
Posamentier
,
A. S.
,
2012
,
The Glorious Golden Ratio
,
Prometheus Books
,
Amherst, NY
.
29.
Wei
,
G.
, and
Dai
,
J.
,
2014
, “
Reconfigurable and Deployable Platonic Mechanisms With a Variable Revolute Joint
,”
Advances in Robot Kinematics
,
Springer
,
Cham, Switzerland
, pp.
485
495
.
30.
Laliberté
,
T.
,
Gosselin
,
C.
, and
Côté
,
G.
,
2001
, “
A Rapid Prototyping Framework for Fast and Cost-Effective Design of Robotic Mechanism Prototypes
,”
IEEE Rob. Autom. Mag.
,
8
(
3
), pp.
43
52
.
31.
Hongwei
,
G.
,
Jing
,
Z.
,
Rongqiang
,
L.
, and
Zongquan
,
D.
,
2013
, “
Effects of Joint on Dynamics of Space Deployable Structure
,”
Chin. J. Mech. Eng.
,
26
(
5
), pp.
861
872
.
32.
Britvec
,
S.
,
1995
,
Stability and Optimization of Flexible Space Structures
,
Birkhauser
,
Basel, Germany
.
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