This paper proposes a design method to obtain a family of rigidly foldable structures with one degree-of-freedom (DOF). The mechanism of flat-foldable degree-four cones and mutually compatible cones sharing a boundary is interpreted as the mechanism of Bricard's flexible octahedra. By sequentially concatenating compatible cones, one can design horn-shaped rigid-origami mechanisms. This paper presents a method to inversely obtain rigidly foldable horns that follow given space curves. The resulting rigidly foldable horns can be used as building blocks for a transformable cellular structure and attachments to existing rigidly foldable structures.

References

References
1.
Miura
,
K.
,
1970
, “
Proposition of Pseudo-Cylindrical Concave Polyhedral Shells
,”
IASS Symposium on Folded Plates and Prismatic Structures
,
Vienna
,
Austria
, Sept. 28–Oct. 2.
2.
Resch
,
R. D.
, and
Christiansen
,
H.
,
1970
, “
The Design and Analysis of Kinematic Folded Plate Systems
,”
IASS Symposium on Folded Plates and Prismatic Structures
, Vienna, Austria, Sept. 28–Oct. 2.
3.
Balkcom
,
D.
,
2002
, “
Robotic Origami Folding
,” Ph.D. thesis, Carnegie Mellon University, Pittsburgh, PA.
4.
Tachi
,
T.
,
2009
, “
Simulation of Rigid Origami
,” Origami4:
The Fourth International Conference on Origami in Science, Mathematics, and Education
, R. Lang, ed., A. K. Peters, Natick, MA, pp.
175
187
.
5.
Huffman
,
D.
,
1976
, “
Curvature and Creases: A Primer on Paper
,”
IEEE Trans. Comput.
,
C-25
(
10
), pp.
1010
1019
.
6.
Hull
,
T.
,
2006
,
Project Origami
,
A. K. Peters
,
Natrick, MA
.
7.
Tachi
,
T.
,
2010
, “
Freeform Rigid-Foldable Structure Using Bidirectionally Flat-Foldable Planar Quadrilateral Mesh
,”
Advances in Architectural Geometry 2010
,
Springer
,
Vienna, Austria
, pp.
87
102
.
8.
Tachi
,
T.
,
2009
, “
One-DOF Cylindrical Deployable Structures With Rigid Quadrilateral Panels
,”
IASS Symposium 2009
, Valencia, Spain, Sept. 28–Oct. 2, pp.
2295
2306
.
9.
Schenk
,
M.
, and
Guest
,
S. D.
,
2013
, “
Geometry of Miura-Folded Meta-Materials
,”
Proc. Natl. Acad. Sci.
,
110
(
9
), pp.
3276
3281
.
10.
Tachi
,
T.
, and
Miura
,
K.
,
2012
, “
Rigid-Foldable Cylinders and Cells
,”
J. Int. Assoc. Shell Spat. Struct.
,
53
(
4
), pp.
217
226
.
11.
Cheung
,
K.
,
Tachi
,
T.
,
Calisch
,
S.
, and
Miura
,
K.
,
2014
, “
Origami Interleaved Tube Cellular Materials
,”
Smart Mater. Struct.
,
23
(
9
), p.
094012
.
12.
Bricard
,
R.
,
1897
, “
Mémoire sur la théorie de l'octaèdre articulé
,”
J. Math. Pures Apple
,
5
(
3
), pp.
113
150
.
13.
Nelson
,
G. D.
,
2010
, “
Extending Bricard Octahedra
,” e-print
arXiv:1011.5193
.
14.
Lang
,
R. J.
,
Magleby
,
S.
, and
Howell
,
L.
,
2015
, “
Single-Degree-of-Freedom Rigidly Foldable Origami Flashers
,” ASME Paper No. DETC2015-46961.
15.
Tachi
,
T.
,
2011
, “
One-DOF Rigid Foldable Structures From Space Curves
,”
IABSE-IASS Symposium 2011
, London, Sept. 20–23.
16.
Connelly
,
R.
,
Sabitov
,
I.
, and
Walz
,
A.
,
1997
, “
The Bellows Conjecture
,”
Contrib. Algebra Geom.
,
38
(
1
), pp.
1
10
.
17.
Connelly
,
R.
,
1977
, “
A Counterexample to the Rigidity Conjecture for Polyhedra
,”
Publ. Math. Inst. Hautes Étud. Sci.
,
47
(
1
), pp.
333
338
.
18.
Schenk
,
M.
, and
Guest
,
S. D.
,
2010
, “
Origami Folding: A Structural Engineering Approach
,”
Origami5, 5th International Meeting on Origami in Science, Mathematics and Education
, Singapore, July 13–17, pp.
293
305
.
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