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Research Papers

Folding Flat Crease Patterns With Thick Materials

[+] Author and Article Information
Jason S. Ku

Field Intelligence Laboratory,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: jasonku@mit.edu

Erik D. Demaine

Computer Science
and Artificial Intelligence Laboratory,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: edemaine@mit.edu

1Corresponding author.

Manuscript received June 27, 2015; final manuscript received October 8, 2015; published online March 7, 2016. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 8(3), 031003 (Mar 07, 2016) (6 pages) Paper No: JMR-15-1159; doi: 10.1115/1.4031954 History: Received June 27, 2015; Revised October 08, 2015

Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly applicable algorithm to transform certain flat-foldable crease patterns into new crease patterns with similar folded structure but with a facet-separated folded state. We provide conditions on input crease patterns for the algorithm to produce a thickened crease pattern avoiding local self-intersection, and provide bounds for the maximum thickness that the algorithm can produce for a given input. We demonstrate these results in parameterized numerical simulations and physical models.

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References

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Figures

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Fig. 1

Some existing thick folding techniques: (a) hinge shift, (b) volume trimming, (c) offset panel, and (d) offset crease

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Fig. 2

From left to right: (1) generic crease pattern Ξ0, (2) locally flat-foldable crease pattern Ξ with layer ordering graph Λ, (3) with reduced layer ordering graph Γ, and (4) flat folding fΞ(Ξ)

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Fig. 3

Polygon construction. A generic internal crease-pattern vertex showing relationship between offsets and angles.

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Fig. 4

A nonsimple vertex polygon and refinement by clipping crossings

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Fig. 5

Trimming intersecting region

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Fig. 6

Unbounded intersection for inside touching creases in input flat-folded state

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Fig. 7

Scale factor calculation showing relevant quantities

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Fig. 8

Construction process

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Fig. 9

Numerical folding simulation of two thickened crease patterns using Freeform Origami

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Fig. 10

Parameterized thick single-vertex construction in Mathematica

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Fig. 11

Foam core model of a thickened traditional bird base

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