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research-article

Rigidly Foldable Quadrilateral Meshes from Angle Arrays

[+] Author and Article Information
Robert J. Lang

Lang Origami, Alamo, California, USA
robert@langorigami.com

Larry L Howell

Department of Mechanical Engineering, Brigham Young University, Provo UT 84602
lhowell@byu.edu

1Corresponding author.

ASME doi:10.1115/1.4038972 History: Received September 18, 2017; Revised December 17, 2017

Abstract

We present a design technique for generating rigidly foldable quadrilateral meshes, taking as input four arrays of direction angles and fold angles for horizontal and vertical folds. By starting with angles, rather than vertex coordinates, and enforcing the fold-angle-multiplier condition at each vertex, it is possible to achieve arbitrarily large and complex panel arrays that flex from unfolded to flatly folded with a single degree of freedom. Furthermore, the design technique is computationally simple, reducing for some cases to a simple linear programming problem. The resulting mechanisms have applications in architectural facades, furniture design, and more.

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