This paper presents a novel family of modular flat-foldable rigid plate structures composed by assemblies of 4R-linkages. First, in the field of foldable plates, the proposed system is characterized by being not only foldable but also transformable: the slope of one module over the other is capable of changing not only magnitude but also sign. This transformable behavior extends the range of application of foldable plates from simply larger–smaller configurations to substantially different configurations and usages. The transformable curve is obtained by means of symmetry operations on the spherical length of links. For each module, three configurations can be designed. Various examples are illustrated.
Issue Section:
Design of Mechanisms and Robotic Systems
References
1.
Chen
, Y.
, Feng
, J.
, and Fan
, L.
, 2013
, “Mobility and Kinematic Simulations of Cyclically Symmetric Deployable Truss Structures
,” Proc. Inst. Mech. Eng., Part C
, 227
(10
), pp. 2218
–2227
.2.
Mitani
, J.
, 2009
, “A Design Method for 3D Origami Based on Rotational Sweep
,” Comput.-Aided Des. Appl.
, 6
(1
), pp. 69
–79
.3.
Kokotsakis
, A.
, 1933
, “Über Bewegliche Polyeder
,” Math. Ann.
, 107
(1
), pp. 627
–647
.4.
Izmestiev
, I.
, 2017
, “Classification of Flexible Kokotsakis Polyhedra With Quadrangular Base
,” Int. Math. Res. Not.
, 2017
(3), pp. 715
–808
.5.
Stachel
, H.
, 2010
, “A Kinematic Approach to Kokotsakis Meshes
,” Comput. Aided Geom. Des.
, 27
(6
), pp. 428
–437
.6.
Xie
, R.
, Chen
, Y.
, and Gattas
, J. M.
, 2015
, “Parametrisation and Application of Cube and Eggbox-Type Folded Geometries
,” Int. J. Space Struct.
, 30
(2
), pp. 99
–111
.7.
Schenk
, M.
, and Guest
, S. D.
, 2013
, “Geometry of Miura-Folded Metamaterials
,” Proc. Natl. Acad. Sci.
, 110
(9
), pp. 3276
–3281
.8.
Sareh
, P.
, and Guest
, S. D.
, 2015
, “Design of Isomorphic Symmetric Descendants of the Miura-ori
,” Smart Mater. Struct.
, 24
(8
), p. 085001
.9.
Watanabe
, N.
, and Kawaguchi
, K.
, 2009
, “The Method for Judging Rigid Foldability
,” Fourth International Conference on Origami in Science, Mathematics, and Education
(4OSME
), Pasadena, CA, Sept. 8–10.10.
Tachi
, T.
, 2009
, “Simulation of Rigid Origami
,” Fourth International Conference on Origami in Science, Mathematics, and Education
(4OSME
), Pasadena, CA, Sept. 8–10.11.
Tachi
, T.
, 2009
, “3D Origami Design Based on Tucking Molecule
,” Fourth International Conference on Origami in Science, Mathematics, and Education
(4OSME
), Pasadena, CA, Sept. 8–10.12.
Yasuda
, H.
, Chen
, Z.
, and Yang
, J.
, 2016
, “Multitransformable Leaf-Out Origami With Bistable Behavior
,” ASME J. Mech. Rob.
, 8
(3
), p. 031013
.13.
Resch, R. D.,
1973
, “The Topological Design of Sculptural and Architectural Systems
,” National Computer Conference and Exposition (AFIPS
), New York, June 4–8, pp. 643–650.14.
Guest
, S.
, and Pellegrino
, S.
, 1994
, “The Folding of Triangulated Cylinders—Part I: Geometric Considerations
,” ASME J. Appl. Mech.
, 61
(4
), pp. 773
–777
.15.
Evans
, T. A.
, Lang
, R.
, Magleby, S.P., and Howell, L. L., 2015
, “Rigidly Foldable Origami Gadgets and Tessellations
,” R. Soc. Open Sci.
, 2
(9
), p. 150067
.16.
Chiang
, C. H.
, 1988
, Kinematics of Spherical Mechanisms
, Cambridge University Press
, Cambridge, UK
.17.
Gosselin
, C. M.
, and Angeles
, J.
, 1990
, “Singularity Analysis of Closed-Loop Kinematic Chains
,” IEEE Trans. Rob. Autom.
, 6
(3
), pp. 281
–290
.18.
Huffman
, D. A.
, 1976
, “Curvature and Creases: A Primer on Paper
,” IEEE Trans. Comput.
, C-25
(10
), pp. 1010
–1019
.19.
Barreto
, P. T.
, 1997
, “Lines Meeting on a Surface: The Mars Paperfolding
,” Origami Science and Art: Second International Meeting of Origami Science and Scientific Origami
, OSME, Otsu, Japan, Nov. 29–Dec. 2, pp. 343–359.20.
Beatini
, V.
, 2015
, “Polar Method to Design Foldable Plate Structures
,” J. IASS
, 56
(2
), pp. 125
–136
.21.
Gioia
, F.
, Dureisseix
, D.
, Motro
, R.
, and Maurin
, B.
, 2012
, “Design and Analysis of a Foldable/Unfoldable Corrugated Architectural Curved Envelop
,” ASME J. Mech. Des.
, 134
(3
), p. 031003
.22.
Gattas
, J. M.
, Wu
, W.
, and You
, Z.
, 2015
, “Miura-Base Rigid Origami. Parameterizations of First-Level Derivative and Piecewise Geometries
,” ASME J. Mech. Des.
, 135
(11
), p. 111011
.23.
Beatini
, V.
, 2015
, “Translational Method for Designing Folded Plate Structures
,” Int. J. Space Struct.
, 30
(2
), pp. 85
–99
.24.
Zhang
, Y.
, Gao
, W.
, Paredes
, L.
, and Ramani
, K.
, 2016
, “CardBoardiZer. Creatively Customize, Articulate and Fold 3D Mesh Models
,” Conference on Human Factors in Computing Systems
(CHI
), Santa Clara, CA, May 7–12, pp. 897
–907
.25.
Hoberman
, C.
, 1991
, “Reversibly Expandable Structures
,” U.S. Patent No. 4981732 A
.26.
Beatini
, V.
, and Korkmaz
, K.
, 2014
, “Shapes of Miura Mesh Mechanism With Mobility One
,” Int. J. Space Struct.
, 28
(2
), pp. 101
–115
.27.
Chen
, Y.
, Feng
, J.
, and Liu
, Y.
, 2016
, “A Group-Theoretic Approach to the Mobility and Kinematic of Symmetric Over-Constrained Structures
,” Mech. Mach. Theory
, 105
, pp. 91
–107
.28.
Pellegrino
, S.
, and Calladine
, C. R.
, 1986
, “Matrix Analysis of Statically and Kinematically Indeterminate Frameworks
,” Int. J. Solids Struct.
, 22
(4
), pp. 409
–428
.29.
Chen
, Y.
, and Feng
, J.
, 2015
, “Mobility of Symmetric Deployable Structures Subjected to External Loads
,” Mech. Mach. Theory
, 93
, pp. 98
–111
.30.
Gao
, W.
, Ramani
, K.
, Cipra
, R. J.
, and Siegmund
, T.
, 2013
, “Kinetogami: A Reconfigurable and Printable Sheet Folding
,” ASME J. Mech. Des.
, 135
(11
), p. 111009
.31.
Kiper
, G.
, and Söylemez
, E.
, 2013
, “Polyhedral Linkages Obtained as Assemblies of Planar Link Groups
,” Front. Mech. Eng.
, 8
(1
), pp. 3
–9
.Copyright © 2017 by ASME
You do not currently have access to this content.
