Abstract

Origami tessellations belong to a type of origami in which repetitive units are used. Stacking sheets of these origami tessellations is a fabrication technique to construct mechanical cellular meta-materials. Almost all crease-stackable origami tessellations investigated to date are based on the Miura-ori and its derivatives, which contain only four-crease vertices. Such origami tessellations typically have a single degree-of-freedom (DOF), and the stacked origami tessellations retain that DOF. In this paper, we explore the possibility of creating stackable origami using origami tessellations that are not based on the Miura-ori. A novel origami tessellation called the origami claw tessellation (OCT) is proposed. This tessellation contains both four and six-crease vertices and has multiple DOFs. It is purposely designed so that the tessellation is crease-stackable. Moreover, we demonstrate that the crease-stacked OCTs have only a single DOF due to the mechanical coupling between the layers, a feature that has never been previously explored in stackable origami. Our findings have been proven analytically and validated using physical models. This work could inspire more research into using other exotic origami tessellations to create multi-layered cellular meta-materials.

References

1.
Yellowhorse
,
A. D.
, and
Howell
,
L. L.
,
2019
, “
Regular 2D and 3D Linkage-Based Origami Tessellations
,”
ASME 2019 International Design Engineering Technical Conferences
,
Anaheim, CA
,
Aug. 18–19
, pp.
1
10
.
2.
Miura
,
K.
,
1985
, “
Method of Packaging and Deployment of Large Membranes in Space
,”
The Institute of Space and Astronautical Science Report
,
618
, pp.
1
9
.
3.
Nishiyama
,
Y.
,
2012
, “
Miura Folding: Applying Origami to Space Exploration
,”
Int. J. Pure Appl. Math.
,
79
(
2
), pp.
269
279
. 1311-8080
4.
Evans
,
T. A.
,
Lang
,
R. J.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2015
, “
Rigidly Foldable Origami Gadgets and Tessellations
,”
R. Soc. Open Sci.
,
2
(
9
), pp.
1
18
.
5.
Gattas
,
J. M.
,
Wu
,
W.
, and
You
,
Z.
,
2013
, “
Miura-Based Rigid Origami: Parameterizations of First-Level Derivative and Piecewise Geometries
,”
ASME J. Mech. Des.
,
135
(
11
), p.
111011
.
6.
Tachi
,
T.
,
2009
, “
Generalization of Rigid Foldable Quadrilateral Mesh Origami
,”
Proceedings of the International Association for Shell and Spatial Structures Symposium 2009
,
Valencia, Spain
,
Sept. 28–Oct. 2
, pp.
2287
2294
.
7.
Schenk
,
M.
, and
Guest
,
S. D.
,
2011
, “Origami Folding: A Structural Engineering Approach,”
Origami5
,
P.
Wang-Iverson
,
R. J.
Lang
,
and M.
Yim
, eds.,
A. K. Peters
,
New York
, pp.
291
303
.
8.
Hull
,
T. C.
,
2013
, “The Combinatorics of Flat Folds: A Survey,”
Origami3
,
T. C.
Hull
, ed.,
A K Peters
,
Natick, MA
, pp.
29
38
.
9.
Sareh
,
P.
, and
Guest
,
S. D.
,
2013
, “
Minimal Isomorphic Symmetric Variations on the Miura Fold Pattern
,”
Proceedings of the First Conference Transformables 2013
,
Seville, Spain
,
Sept. 18–20
.
10.
Lang
,
R. J.
,
2018
,
Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami
,
CRC Press
,
Boca Raton
, pp.
29
34
.
11.
Sareh
,
P.
, and
Guest
,
S. D.
,
2015
, “
Design of Isomorphic Symmetric Descendants of the Miura-Ori
,”
Smart Mater. Struct.
,
24
(
8
), pp.
1
12
.
12.
Sareh
,
P.
, and
Guest
,
S. D.
,
2015
, “
A Framework for the Symmetric Generalization of the Miura-Ori
,”
Int. J. Space Struct.
,
30
(
2
), pp.
141
152
.
13.
Schenk
,
M.
, and
Guest
,
S. D.
,
2013
, “
Geometry of Miura-Folded Metamaterials
,”
PNAS
,
110
(
9
), pp.
3276
3281
.
14.
Gattas
,
J. M.
, and
You
,
Z.
,
2015
, “
Geometric Assembly of Rigidly-Foldable Morphing Sandwich Structures
,”
Eng. Struct.
,
94
(
1
), pp.
149
159
.
15.
Filipov
,
E. T.
,
Tachi
,
T.
, and
Paulino
,
G. H.
,
2015
, “
Origami Tubes Assembled Into Stiff, Yet Reconfigurable Structures and Metamaterials
,”
PNAS
,
112
(
40
), pp.
12321
12326
.
16.
Callens
,
S. J. P.
, and
Zadpoor
,
A. A.
,
2017
, “
From Flat Sheets to Curved Geometries: Origami and Kirigami Approaches
,”
Mater. Today
,
21
(
3
), pp.
241
264
.
17.
Chen
,
Y.
,
Feng
,
H.
,
Ma
,
J.
,
Peng
,
R.
, and
You
,
Z.
,
2016
, “
Symmetric Waterbomb Origami
,”
Proc. R. Soc. A
,
472
(
2190
), pp.
1
20
.
18.
Hull
,
T. C.
,
2015
, “Counting Mountain-Valley Assignments for Flat-Folds,”
Origami6
,
K
Miura
,
T
Kawasaki
,
T
Tachi
,
R.
Uehara
,
R. J.
Lang
, and
P.
Wang-Iverson
, eds.,
American Mathematical Society
,
Providence
, pp.
3
10
.
19.
Farnham
,
J.
,
Hull
,
T. C.
, and
Rumbolt
,
A.
,
2022
, “
Rigid Folding Equations of Degree-6 Origami Vertices
,”
Proc. R. Soc. A
,
478
(
2260
), pp.
1
19
.
20.
Gan
,
W. W.
, and
Pellegrino
,
S.
,
2006
, “
Numerical Approach to the Kinematic Analysis of Deployable Structures Forming a Closed Loop
,”
Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci.
,
220
(
7
), pp.
1045
1056
.
21.
Chen
,
Y.
,
Peng
,
R.
, and
You
,
Z.
,
2015
, “
Supplementary Material for Origami of Thick Panels
,”
Science
,
349
(
6246
), pp.
396
400
.
22.
Beggs
,
J. S.
,
1966
,
Advanced Mechanism
,
The Macmillan Company
,
New York
, pp.
132
136
.
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