Origami-Paper Folding and Its Generalization - Tomohiro Tachi, The University of Tokyo

Origami-Paper Folding and Its Generalization

Tomohiro Tachi, The University of Tokyo

1.Introduction

Origami,traditional art of folding a piece of paper into variety of three-dimensional figures, is a rapidly developing interdisciplinary research field, bridging mathematics, science, art, and engineering. Technical applications of origami involve lightweight and high-stiffness structures manufactured from self-foldingof sheet materials and reversely foldable deployable mechanisms that change their shape and volume. In order to enable such applications,studies on the geometry of origami and computational method to solve geometric problems of origami, i.e., computational origami,plays an important role.

1. Origami Design

Which form can we make from a sheet of paper only by folding without stretching or cutting? Surprisingly, the answer is "everything." From an arbitrarily given polyhedral surface, we can obtain the crease pattern that folds into the surface. In this talk, a computational method Origamizer converts polyhedron into a crease that universally solves this design problem and pattern. interactive design systems to extend origami-based manufacturing to freeform surfaces are reviewed.

1. Rigid Origami

Consider scaling up an origami pattern and substituting rigid thick panels and door hinges for facets and edges of the pattern. Such a mechanism is termed rigid origami. Designing a continuously transformable mechanism out of rigid origami turns out to be more difficult than achieving a mechanism with a sheet of paper, which can bend and stretch temporari ly. The talk covers the theoretical studies and the design methods of rigid origami and their possible applications.

Conclusion

In this talk, design methods and systems of static and kinematic origami is introduced. The generalization through mathematical origami can lead to micro-scale self-folding origami and large scale architectural origami.

References

[1] 60SME (6th International Meeting on Origami in Science, Mathematics and Education) origami.gr.jp/6osme/

[2] Tomohiro Tachi: "Origamizing Polyhedral Surfaces," IEEE Transactions on Visualization and Computer Graphics,16(2), pp. 298-311,2010.

[3] Tomohiro Tachi and Koryo Miura, "Rigid-Foldable Cylinders and Cells", Journal of the International Association for Shell and Spatial Structures (IASS), 53(4), pp.217--226, 2012.