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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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Figures

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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. 2

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

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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. 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. 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. 12

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

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Fig. 13

Eulerian cycle generation for a hexagram-like mechanism

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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. 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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Fig. 18

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

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