Foldable piecewise linear origami that approximates curved tile origami

Research output: Contribution to journalArticlepeer-review

Abstract

Curved origami featuring curved tiles can store elastic energy and bias the structure toward a desired shape when subjected to appropriate constraints. Without constraints, however, a curved origami structure generally has infinitely many degrees of freedom. For engineering applications in which a particular folding motion is desired, a great many constraints have to be introduced. One natural strategy to reduce degrees of freedom is to discretize curved origami into piecewise linear origami while closely approximating the desired curved folding motion. Then, as we show, the degrees of freedom are vastly reduced (typically to one DoF in cases where the folding angle at the crease is not trivial, and excluding overall rigid body motions). In this paper we present a Lagrangian approach for constructing curved origami structures which is complementary to our approach in Liu and James (2024). Then, we generalize this approach to allow quite general curved creases. We outline a way to discretize curved crease patterns and present two optimization methods to refine these patterns. Our approach ensures that the deformed piecewise linear origami closely matches the folding angles and crease configurations of the curved origami. Piecewise linear origami structures that approximate curved origami offer promising potential for architectural and robotic design applications. They also give an efficient way to design desired smooth structures by optimizing finite-dimensional piecewise linear structures.

Original languageEnglish (US)
Article number105962
JournalJournal of the Mechanics and Physics of Solids
Volume195
DOIs
StatePublished - Feb 2025
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2024

Keywords

  • Architecture
  • Curved origami design
  • Discrete approximation
  • Kirchhoff's plate theory
  • Morphing structures
  • Origami design
  • Structural mechanics

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