The purpose of this work is to develop approaches to accommodate thickness in origami-based deployable arrays with a high ratio of deployed-to-stowed diameter. The origami flasher model serves as a basis for demonstrating the approach. A thickness-accommodating mathematical model is developed to describe the flasher. Practical modifications are presented for the creation of physical models and two options are proposed: allowing the panels to fold along their diagonals or applying a membrane backing with specified widths at fold-lines. The mathematical model and hardware modifications are employed to create several physical models. The results are general and apply to a range of applications. An example is provided by the application that motivated the work: a deployable solar array for space applications. The model is demonstrated in hardware as a 1/20th scale prototype with a ratio of deployed-to-stowed diameter of 9.2 (or 1.25 m deployed outer diameter to 0.136 m stowed outer diameter).

References

References
1.
Tachi
,
T.
,
2010
, “
Geometric Considerations for the Design of Rigid Origami Structures
,”
Proceedings of IASS Symposium on Spatial Structures—Permanent and Temporary
.
2.
Tachi
,
T.
,
2011
, “
Rigid Foldable Thick Origami
,”
Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education
.
3.
Trautz
,
M.
, and
Kunstler
,
A.
,
2009
, “
Deployable Folded Plate Structures: Folding Patterns Based on 4-Fold-Mechanism Using Stiff Plates
,”
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium
.
4.
Hoberman
,
C.
,
1991
, “
Reversibly Expandable Structures
,” U.S. Patent No. 4,981,732.
5.
Hoberman
,
C.
,
1993
, “
Curved Pleated Sheet Structures
,” U.S. Patent No. 5,234,727.
6.
Hoberman
,
C.
,
2010
, “
Folding Structures Made of Thick Hinged Sheets
,” U.S. Patent No. 7,794,019.
7.
Faist
,
K. A.
, and
Wiens
,
G. J.
,
2010
, “
Parametric Study on the Use of Hoberman Mechanisms for Reconfigurable Antenna and Solar Arrays
,”
Proceedings of IEEE Aerospace Conference
, Paper No. #1172.
8.
Miura
,
K.
,
1980
, “
Method of Packaging and Deployment of Large Membranes in Space
,”
Proceedings of 31st Congress International Astronautical Federation
, pp.
1
10
.
9.
Miura
,
K.
, and
Natori
,
M.
,
1985
, “
2-D Array Experiment on Board a Space Flyer Unit
,”
Space Sol. Power Rev.
,
5
(
4
), pp.
345
356
.
10.
Sternberg
,
S.
,
2010
, “
Symmetry Issues in Collapsible Origami
,”
Symmetry: Cult. Sci.
,
21
(
4
), pp.
345
364
.
11.
Guest
,
S.
, and
Pellegrino
,
S.
,
1992
, “
Inextensional Wrapping of Flat Membranes
,”
Proceedings of the First International Seminar on Structural Morphology
, pp.
203
215
.
12.
Nojima
,
T.
,
2002
, “
Origami Modeling of Functional Structures Based on Organic Patterns
,” Master's thesis, Graduate School of Kyoto University, Kyoto, Japan
.
13.
De Focatiis
,
D. S.
, and
Guest
,
S.
,
2002
, “
Deployable Membranes Designed From Folding Tree Leaves
,”
Philos. Trans. R. Soc. London
,
Ser. A
,
360
, pp.
227
238
.10.1098/rsta.2001.0928
14.
Lang
,
R. J.
,
1997
,
Origami in Action
,
St. Martin's Griffin
, New York.
15.
Shafer
,
J.
,
2001
,
Origami to Astonish and Amuse
,
St. Martin's Griffin
, New York.
16.
Shafer
,
J.
,
2010
,
Origami Ooh La La! Action Origami for Performance and Play
,
CreateSpace Independent Publishing Platform
, US.
17.
Chiang
,
C. H.
,
1984
, “
On the Classification of Spherical Four-Bar Linkages
,”
Mech. Mach. Theory
,
19
, pp.
283
287
.10.1016/0094-114X(84)90061-2
18.
Lang
,
R. J.
,
2012
, “
Mathematica 8 Notebook
,” Available at: http://www.langorigami.com/science/computational/eyeglass_flashers/eyeglass_flasher_13_ma8.nb
19.
NASA Technology Roadmaps
,
2012
, “
TA12: 2.1.3 Flexible Material Systems
,” Available at: http://www.nasa.gov/pdf/501625main_TA12-ID_rev6_NRC-wTASR.pdf
20.
NASA Research Announcement NNL12A3001N
,
2011
, “
Game Changing Opportunities in Technology Development
,” Available at: http://prod.nais.nasa.gov/cgi-bin/eps/synopsis.cgi?acqid=152634
21.
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