Curved-crease (CC) origami differs from prismatic, or straight-crease origami, in that the folded surface of the pattern is bent during the folding process. Limited studies on the mechanical performance of such geometries have been conducted, in part because of the difficulty in parametrizing and modeling the pattern geometry. This paper presents a new method for generating and parametrizing rigid-foldable, CC geometries from Miura-derivative prismatic base patterns. The two stages of the method, the ellipse creation stage and rigid subdivision stage, are first demonstrated on a Miura-base pattern to generate a CC Miura pattern. It is shown that a single additional parameter to that required for the straight-crease pattern is sufficient to completely define the CC variant. The process is then applied to tapered Miura, Arc, Arc-Miura, and piecewise patterns to generate CC variants of each. All parametrizations are validated by comparison with physical prototypes and compiled into a matlab Toolbox for subsequent work.

References

References
1.
Demaine
,
E.
,
Demaine
,
M.
,
Koschitz
,
D.
, and
Tachi
,
T.
,
2011
, “
Curved Crease Folding: A Review on Art, Design and Mathematics
,”
Proceedings of the IABSE-IASS Symposium: Taller
, Longer, Lighter (IABSE-IASS2011), London, England, Sept. 20–23.
2.
Demaine
,
E.
,
Demaine
,
M.
, and
Koschitz
,
D.
,
2011
, “
Reconstructing David Huffman's Legacy in Curved-Crease Folding
,”
Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education
,
P.
Wang-Iverson
,
R. J.
Lang
, and
M.
Yim
, eds.,
Taylor & Francis Group
, Singapore, pp.
39
52
.
3.
Huffman
,
D. A.
,
1976
, “
Curvature and Creases: A Primer on Paper
,”
IEEE Trans. Comput. C
,
25
(
10
), pp.
1010
1019
.10.1109/TC.1976.1674542
4.
Miura
,
K.
,
1972
, “
Zeta-Core Sandwich—Its Concept and Realization
,”
Institute of Space and Aeronautical Science, University of Tokyo, Report No. 480
, pp.
137
164
.
5.
Heimbs
,
S.
,
2013
, “
Foldcore Sandwich Structures and Their Impact Behaviour: An Overview
,”
Dynamic Failure of Composite and Sandwich Structures, SE-11 (Vol. 192 of Solid Mechanics and Its Applications)
,
Springer
,
Netherlands
, pp.
491
544
.
6.
Saito
,
K.
,
Pellegrino
,
S.
, and
Nojima
,
T.
, “
Manufacture of Arbitrary Cross-Section Composite Honeycomb Cores Based on Origami Techniques
,”
ASME
J. Mech. Des.,
136
(5), p. 051011.10.1115/1.4026824
7.
Schenk
,
M.
, and
Guest
,
S. D.
,
2011
, “
Origami Folding: A Structural Engineering Approach
,”
Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education
,
R. J.
Lang
,
P.
Wang-Iverson
, and
M.
Yim
, eds.,
Taylor & Francis Group
, Singapore, pp.
291
303
.
8.
Gioia
,
F.
,
Dureisseix
,
D.
,
Motro
,
R.
, and
Maurin
,
B.
, “
Design and Analysis of a Foldable/Unfoldable Corrugated Architectural Curved Envelop
,”
ASME J. Mech. Des.
,
134
(
3
), p.
031003
.10.1115/1.4005601
9.
Ma
,
J.
, and
You
,
Z.
,
2014
, “
Energy Absorption of Thin-Walled Square Tubes With a Prefolded Origami Pattern—Part I: Geometry and Numerical Simulation
,”
ASME J. Appl. Mech.
,
81
(
1
), p.
011003
.10.1115/1.4024405
10.
Tachi
,
T.
,
2013
, “
Designing Freeform Origami Tessellations by Generalizing Resch's Patterns
,”
ASME J. Mech. Des.
,
135
(
11
), p.
111006
.10.1115/1.4025389
11.
Davis
,
E.
,
Demaine
,
E. D.
,
Demaine
,
M. L.
, and
Ramseyer
,
J.
,
2013
, “
Reconstructing David Huffman's Origami Tessellations
,”
ASME J. Mech. Des.
,
135
(
11
), p.
111010
.10.1115/1.4025428
12.
Klett
,
Y.
, and
Drechsler
,
K.
,
2011
, “
Designing Technical Tessellations
,”
Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education
,
P.
Wang-Iverson
,
R. J.
Lang
, and
M.
Yim
, eds.,
Taylor & Francis Group
, Singapore, pp.
305
322
.
13.
Bowen
,
L. A.
,
Grames
,
C. L.
,
Magleby
,
S. P.
,
Lang
,
R. J.
, and
Howell
,
L. L.
,
2013
, “
An Approach for Understanding Action Origami as Kinematic Mechanisms
,”
ASME
Paper No. DETC2013-13407.10.1115/DETC2013-13407
14.
Tachi
,
T.
,
2009
, “
Generalization of Rigid-Foldable Quadrilateral-Mesh Origami
,”
J. Int. Assoc. Shell Spatial Struct.
,
50
(
162
), pp.
173
179
.
15.
Nojima
,
T.
, and
Saito
,
K.
,
2006
, “
Development of Newly Designed Ultra-Light Core Structures
,”
JSME Int. J., Ser. A
,
49
(
1
), pp.
38
42
.10.1299/jsmea.49.38
16.
Buri
,
H.
,
Stotz
,
I.
, and
Yves
,
W.
,
2011
, “
Curved Folded Plate Timber Structures
,”
IABSE-IASS Symposium
, vol. CD-ROM IABSE-IASS, London, England.
17.
Tachi
,
T.
,
2011
, “
Rigid-Foldable Thick Origami
,”
Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education
,
P.
Wang-Iverson
,
R. J.
Lang
, and
M.
Yim
, eds.,
Taylor & Francis Group
, Singapore, pp.
253
264
.
18.
Kilian
,
M.
,
Flöry
,
S.
,
Chen
,
Z.
,
Mitra
,
N. J.
,
Sheffer
,
A.
, and
Pottmann
,
H.
,
2008
, “
Curved Folding
,”
ACM Trans. Graphics (TOG)
,
27
(
3
), p.
75
.10.1145/1360612.1360674
19.
Solomon
,
J.
,
Vouga
,
E.
,
Wardetzky
,
M.
, and
Grinspun
,
E.
,
2012
, “
Flexible Developable Surfaces
,”
Computer Graphics Forum
, Vol.
31
,
Wiley Online Library
, pp.
1567
1576
.
20.
Epps
,
G.
, and
Verma
,
S.
,
2013
, “
Curved Folding: Design to Fabrication Process of Robofold
,”
Shape Modeling International
, Bournemouth, UK, July 10–13, pp.
75
83
.
21.
Gattas
,
J.
,
Wu
,
W.
, and
You
,
Z.
, 2013 “
Miura-Base Rigid Origami: Parameterizations of First-Level Derivative and Piecewise Geometries
,”
ASME J. Mech. Des.
135
(
11
), p.
11011
.10.1115/1.4025380
22.
Abbott
,
P.
,
2008
, “
On the Perimeter of an Ellipse
,”
Math. J.
,
11
(
2
), pp.
172
185
.
23.
Edison
,
C. E.
,
2011
, “
Compression and Rotational Limitations of Curved Corrugations
,”
Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education
,
Taylor & Francis Group
, Singapore, pp.
69
79
.
24.
Gattas
,
J.
,
2013
, “
Rigid Origami Toolbox
,” available at http://joegattas.com/rigid-origami-toolbox/
You do not currently have access to this content.