Abstract
Rigidly foldable origami allows for motion where all deflection occurs at the crease lines and facilitates the application of origami in materials other than paper. In this paper, we use a recently discovered method for determining rigid foldability to identify existing flat-foldable rigidly foldable tessellations, which are also categorized. We introduce rigidly foldable origami gadgets which may be used to modify existing tessellations or to create new tessellations. Several modified and new rigidly foldable tessellations are presented.
Highlights
An important characteristic of origami structures is rigid foldability
An origami tessellation is rigidly foldable if all sectors remain rigid and deflection only occurs at the crease lines
We present gadgets that facilitate the creation of rigidly foldable tessellations and show some resulting tessellations
Summary
An important characteristic of origami structures is rigid foldability. An origami tessellation is rigidly foldable if all sectors remain rigid and deflection only occurs at the crease lines. Tachi developed conditions for partially folded quadrilateral surfaces [23] These methods resulted in systems of nonlinear equations, requiring optimization techniques to converge to solutions. A method for analysing the rigid foldability of origami patterns composed entirely from flatfoldable, degree-4 vertices has been developed previously by the authors [25]. We use this method to evaluate previously existing tessellations for rigid foldability. These tessellations are characterized and a comparison of these tessellations is presented. We develop several new origami gadgets, which are tools in the modification and creation of rigidly foldable tessellations. These gadgets are used in two different ways. The gadgets are tessellated to make new rigidly foldable patterns
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