Origami building blocks: Generic and special four-vertices

S.R. Waitukaitis, M. Van Hecke, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 93 (2016).


Journal Article | Published | English
Author
Waitukaitis, Scott RIST Austria ; Van Hecke, Martin
Abstract
Four rigid panels connected by hinges that meet at a point form a four-vertex, the fundamental building block of origami metamaterials. Most materials designed so far are based on the same four-vertex geometry, and little is known regarding how different geometries affect folding behavior. Here we systematically categorize and analyze the geometries and resulting folding motions of Euclidean four-vertices. Comparing the relative sizes of sector angles, we identify three types of generic vertices and two accompanying subtypes. We determine which folds can fully close and the possible mountain-valley assignments. Next, we consider what occurs when sector angles or sums thereof are set equal, which results in 16 special vertex types. One of these, flat-foldable vertices, has been studied extensively, but we show that a wide variety of qualitatively different folding motions exist for the other 15 special and 3 generic types. Our work establishes a straightforward set of rules for understanding the folding motion of both generic and special four-vertices and serves as a roadmap for designing origami metamaterials.
Publishing Year
Date Published
2016-02-03
Journal Title
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Acknowledgement
This work is part of the research programme of the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organisation for Scientific Research (NWO).
Volume
93
Issue
2
Article Number
023003
IST-REx-ID
122

Cite this

Waitukaitis SR, Van Hecke M. Origami building blocks: Generic and special four-vertices. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2016;93(2). doi:10.1103/PhysRevE.93.023003
Waitukaitis, S. R., & Van Hecke, M. (2016). Origami building blocks: Generic and special four-vertices. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 93(2). https://doi.org/10.1103/PhysRevE.93.023003
Waitukaitis, Scott R, and Martin Van Hecke. “Origami Building Blocks: Generic and Special Four-Vertices.” Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 93, no. 2 (2016). https://doi.org/10.1103/PhysRevE.93.023003.
S. R. Waitukaitis and M. Van Hecke, “Origami building blocks: Generic and special four-vertices,” Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 93, no. 2, 2016.
Waitukaitis SR, Van Hecke M. 2016. Origami building blocks: Generic and special four-vertices. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 93(2), 023003.
Waitukaitis, Scott R., and Martin Van Hecke. “Origami Building Blocks: Generic and Special Four-Vertices.” Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 93, no. 2, 023003, American Physiological Society, 2016, doi:10.1103/PhysRevE.93.023003.
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