Research Papers

Origami Design by Topology Optimization

[+] Author and Article Information
Kazuko Fuchi

e-mail: fuchikaz@msu.edu

Alejandro R. Diaz

Fellow ASME

Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 4, 2013; final manuscript received August 8, 2013; published online September 24, 2013. Assoc. Editor: Shinji Nishiwaki.

J. Mech. Des 135(11), 111003 (Sep 24, 2013) (7 pages) Paper No: MD-13-1242; doi: 10.1115/1.4025384 History: Received June 04, 2013; Revised August 08, 2013

An origami design method based on topology optimization is introduced. The design of a folding pattern is cast as a problem of assigning presence and type of fold to lines in a “ground structure,” using folding angles as design variables. A ground structure for origami design has lines drawn on a two dimensional domain, showing all line segments that may appear as crease lines in the folded geometry. For a given ground structure and folding angles, the 3D geometry of the folded sheet can be computed using the mathematics of origami. A topology optimization method is then used to find an optimal combination of folding angles, which results in a folding pattern with desired, target geometric properties.

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Fig. 4

Flat and folded states of a single-vertex crease

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Fig. 2

Origami grid systems. There are no line overlaps: there is a vertex at every intersection of two or more lines.

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Fig. 1

Typical measures used in target geometric properties

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Fig. 3

Variations of ground structures. There are no line overlaps: there is a vertex at every intersection of two or more lines.

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Fig. 5

Single-vertex crease

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Fig. 6

Objective function f

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Fig. 7

Flowchart of foldline elimination algorithm

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Fig. 9

Candidates of fixed folding angles. There are no line overlaps: there is a vertex at every intersection of two or more lines.

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Fig. 10

Design 1, Example 1

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Fig. 11

Design 2, Example 1

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Fig. 13

Design 2, Example 2

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Fig. 12

Design 1, Example 2

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Fig. 14

Convergence plot for Design 2, Example 2



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