Research Papers

Kinetogami: A Reconfigurable, Combinatorial, and Printable Sheet Folding

[+] Author and Article Information
Wei Gao

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: gao51@purdue.edu

Karthik Ramani

School of Mechanical Engineering,
School of Electrical and Computer
Engineering (by courtesy),
Purdue University,
West Lafayette, IN 47907
e-mail: ramani@purdue.edu

Raymond J. Cipra

e-mail: cipra@purdue.edu

Thomas Siegmund

e-mail: siegmund@ecn.purdue.edu
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 1, 2013; final manuscript received September 4, 2013; published online October 8, 2013. Assoc. Editor: Alexander Slocum.

J. Mech. Des 135(11), 111009 (Oct 08, 2013) (10 pages) Paper No: MD-13-1050; doi: 10.1115/1.4025506 History: Received February 01, 2013; Revised September 04, 2013

As an ancient paper craft originating from Japan, origami has been naturally embedded and contextualized in a variety of applications in the fields of mathematics, engineering, food packaging, and biological design. The computational and manufacturing capabilities today urge us to develop significantly new forms of folding as well as different materials for folding. In this paper, by allowing line cuts with crease patterns and creating folded hinges across basic structural units (BSU), typically not done in origami, we achieve a new multiprimitive folding framework such as using tetrahedral, cuboidal, prismatic, and pyramidal components, called “Kinetogami.” “Kinetogami” enables one to fold up closed-loop(s) polyhedral mechanisms (linkages) with multi-degree-of-freedom and self-deployable characteristics in a single build. This paper discusses a set of mathematical and design theories to enable design of 3D structures and mechanisms all folded from preplanned printed sheet materials. We present prototypical exploration of folding polyhedral mechanisms in a hierarchical manner as well as their transformations through reconfiguration that reorients the material and structure. The explicit 2D fabrication layout and construction rules are visually parameterized for geometric properties to ensure a continuous folding motion free of intersection. As a demonstration artifact, a multimaterial sheet is 3D printed with elastomeric flexure hinges connecting the rigid plastic facets.

Copyright © 2013 by ASME
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Arkin, E. M., Bender, M. A., Demaine, E. D., Demaine, M. L., Mitchell, J. S., Sethia, S., and Skiena, S. S., 2004, “When Can You Fold a Map?,” Comput. Geom., 29(1), pp. 23–46. [CrossRef]
Demaine, E., Demaine, M., and Mitchell, J. S., 2000, “Folding Flat Silhouettes and Wrapping Polyhedral packages: New Results in Computational Origami,” Comput. Geom., 16, pp. 3–21. [CrossRef]
Lang, R. J., 1998, TreeMaker 4.0: A Program for Origami Design.
Demaine, E., and Tachi, T., 2010, “Origamizer: A Practical Algorithm for Folding Any Polyhedron,” Manuscript.
Miura, K., 2009, “The Science of Miura-Ori: A Review,” 4th International Meeting of Origami Science, Mathematics, and Education, R. J.Lang, ed., A K Peters, Natick, MA, pp. 87–100.
Hoffman, R., 2001, “Airbag Folding: Origami Design Application to an Engineering Problem,” 3rd International Meeting of Origami Science, Mathematics, and Education.
You, Z., and Kuribayashi, K., 2003, “A Novel Origami Stent,” Proceedings of Summer Bioengineering Conference.
Fischer, S., Drechsler, K., Kilchert, S., and Johnson, A., 2009, “Mechanical Tests for Foldcore Base Material Properties,” Composites, Part A, 40, pp. 1941–1952. [CrossRef]
Mullineux, G., Feldman, J., and Matthews, J., 2010, “Using Constraints at the Conceptual Stage of the Design of Carton Erection,” Mech. Mach. Theory, 45(12), pp. 1897–1908. [CrossRef]
Gurkewitz, R., and Arnstein, B., 2003, Multimodular Origami Polyhedra: Archimedeans, Buckyballs, and Duality, Dover, New York.
Hart, G., 2007, “Modular Kirigami,” Proceedings of Bridges Donostia.
Griffith, S., 2004, “Growing Machines,” Ph.D. thesis, MIT, MA.
Cheung, K., Demaine, E., Bachrach, J., and Griffith, S., 2011, “Programmable Assembly With Universally Foldable Strings (Moteins),” IEEE Trans. Rob. Autom., 27(4), pp. 718–729. [CrossRef]
Demaine, E., Demaine, M., Lindy, J., and Souvaine, D., 2005, “Hinged Dissection of Polypolyhedra,” Lect. Notes Comput. Sci., 3608, pp. 205–217. [CrossRef]
Demaine, E., Demaine, M., Eppstein, D., Frederickson, G., and Friedman, E., 2005, “Hinged Dissection of Polyominoes and Polyforms,” Comput. Geom.: Theory Appl., 31(3), pp. 237–262. [CrossRef]
Goldberg, M., 1942, “Polyhedral Linkages,” Math. Mag., 16(7), pp. 323–332. [CrossRef]
Gilpin, K., Kotay, K., Rus, D., and Vasilescu, L., 2008, “Miche: Modular Shape Formation by Self-Disassembly,” Int. J. Robot. Res., 27(3), pp. 345–372. [CrossRef]
Ke, Y., Ong, L., Shih, W., and Yin, P., 2012, “Three-Dimensional Structures Self-Assembled From DNA Bricks,” Science, 338(6111), pp. 1177–1183. [CrossRef] [PubMed]
Schatz, P., 1998, Rhythmusforschung und Technik, Verlag Freies Geistesleben, Stuttgart.
Sehattsehneide, D., and Walker, W., 1977, M.C.Eseher Kalerdoeycels, BallantineBooks, NewYork.
Chen, Y., You, Z., and Tarnai, T., 2005, “Threefold-Symmetric Bricard Linkages for Deployable Structures,” Int. J. Solids Struct., 42(8), pp. 2287–2301. [CrossRef]
Baker, E., 1980, “An Analysis of Bricard Linkages,” Mech. Mach. Theory, 15, pp. 267–286. [CrossRef]
Chen, Y., and You, Z., 2012, “Spatial Overconstrained Linkages—The Lost Jade,” Hist. Mech. Mach. Sci., 15, pp. 535–550. [CrossRef]
Gao, W., Ramani, K., and Cipra, R. J., 2012, “Reconfigurable Foldable Spatial Mechanisms and Robotic Forms Inspired by Kinetogami,” Proceedings of the ASME 2012 IDETC/CIE.
Milgram, R., 1974, “Surgery With Coefficients,” Ann. Math., 100(2), pp. 194–248. [CrossRef]
Kang, B., Wen, J., Dagalakis, N., and Gorman, J., 2004, “Analysis and Design of Parallel Mechanisms With Flexure Joints,” Proceedings of IEEE International Conference on Robotics and Automation.
Zotov, S., Rivers, M., Trusov, A., and Shkel, A., 2010, “Chip-Scale IMU Using Folded-MEMS Approach,” IEEE Sens. J., pp. 1043–1046. [CrossRef]
Hawkes, E., An, B., Benbernou, N. M., Tanaka, H., Kim, S., Demaine, E. D., Rus, D., and Wood, R. J., 2010, “Programmable Matter by Folding,” Proc. Natl. Acad. Sci. U.S.A., 107(28), pp. 12441–12445. [CrossRef] [PubMed]


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Fig. 4

54 unique 2D crease patterns with attaching facets for a cuboidal unit (6 parent patterns with a corresponding child pattern are shown)

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Fig. 3

(a) Isosceles tetrahedral BSU; (b) skew tetrahedral BSU; (c) isos-equal tetrahedral BSU (red: overall cuts; black: folds; blue: the fold that functions as a common hinge; shaded area: attachments)

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Fig. 2

(a) 2D-3D formation of a single tetrahedral unit. (b) Self-overlapping on a unfolded tetrahedral BSU pattern.

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Fig. 5

Net patterns of cuboidal BSU using three different edges as hinges (red: overall cuts; black: folds; blue: the common hinge)

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Fig. 6

(a) Triangular prismatic BSU; (b) rectangular pyramidal BSU; and (c) pentagonal pyramidal BSU

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Fig. 7

Kinematical combinatorics of tetrahedral BSUs

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Fig. 8

Prototypical Kinetogamic derivatives from 4 BSUs: (a)–(h) constructs using tetrahedral BSUs. (i)–(o) constructs using cubic/cuboidal BSUs, (p) and (q) constructs using prismatic BSUs, (r) and (s) constructs using pyramidal BSUs

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Fig. 9

Geometric parameters for determining variation of configuration states

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Fig. 10

Prototypical demonstration of fully, limited reconfigurable, and rigid-body state: single ring (a) with 3 isosceles tetra-BSUs, (b) with 4 isosceles tetra-BSUs, and (c) with 5 isosceles tetra-BSUs

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Fig. 11

Thresholds of fully, limited reconfigurable, and rigid-body state

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Fig. 1

Four representative ((a): tetrahedral; (b): cuboidal; (c): prismatic; (d): pyramidal) BSUs folded from a single sheet.

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Fig. 12

(a) Elementary-single-loop with n basic-structural-units B1,B2,…,Bn, (b) multiloop

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Fig. 14

Fabrication and construction rules for building a hexagram-like mechanism

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Fig. 15

Fabrication and hinge selection for cubic derivatives

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Fig. 13

Eulerian cycle generation for a hexagram-like mechanism

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Fig. 18

Visions of (a) a multimaterial-printed table reconfigures into a chair (b) a hexapod robot with multiple gaits

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Fig. 16

Ameliorated processes for a compact 2D pattern layout

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Fig. 17

(a) 3D Printed multimaterial sheet, (b) compactly flat-folded configuration, (c) folded into 6 tetrahedral BSUs in a ring, (d) morphed among configurations, and (e) flexure hinge



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