EAPSI: Geometry and mechanics of origami surface structures

一种被称为折纸镶嵌的折纸结构是通过将小而简单的“瓷砖”折叠成设计图案而形成的。然后，这些图案可以折叠成表面结构，由于它们的平铺设计，这些表面结构表现出奇异的几何和机械行为。例如，Miura Ori图案是一个简单的镶嵌图案，当折叠成一个表面结构时，它只能变形成马鞍形状的表面。这种特殊的图案被用来将可展开的太阳能电池板送入太空。更复杂的图案可以变形成球体、马鞍或其他组合的形状。本研究将探讨由折纸褶皱设计的表面结构的几何和力学行为。这项研究将与日本东京大学的Yasushi Yamaguchi博士和Tomohiro Tachi博士合作完成。Yamaguchi博士领导着一个计算机图形实验室，正在进行计算折纸项目，Tachi博士是计算折纸和折纸镶嵌领域的领先研究员。本项目将着重于发展镶嵌折纸结构的运动学和力学的分析和计算模型。这些方法将用于模拟三维柔性和计算镶嵌结构的力学性能。此外，该项目将开发设计修改的镶嵌图案的技术，当折叠时，形成近似任意曲率表面的结构。该项目的最终目标是鼓励将这些结构应用于设计和架构、软机器人系统和可部署的空间有效载荷等问题。NSF EAPSI奖是与日本科学促进会合作资助的。

A class of origami structures called origami tessellations is formed by taking small, simple 'tiles' of folds and arranging these into design patterns. These patterns can then fold into surface structures which - thanks to their tiled design - exhibit exotic geometric and mechanical behaviors. For example, the Miura Ori pattern is a simple tessellation that, when folded into a surface structure, can only deform to surfaces shaped like saddles. This particular pattern was used to send a deployable solar panel into space. More complicated patterns can deform into surfaces shaped like spheres, saddles and other combinations. This research will investigate the geometric and mechanical behavior of surface structures designed by origami folds. This research will be done in collaboration with Dr. Yasushi Yamaguchi and Dr. Tomohiro Tachi at the University of Tokyo in Japan. Dr. Yamaguchi leads a computer graphics lab with on-going projects in computational origami and Dr. Tachi is a leading researcher in the field of computational origami and origami tessellations. This project will focus on developing analytic and computational models of the kinematics and mechanics of tessellated origami structures. These methods will be used to to simulate the 3D flexibility and to compute the mechanical properties of tessellated structures. Additionally, this project will develop techniques to design modified tessellated patterns that, when folded, form structures that approximate a surface with arbitrary curvature. The project's ultimate goal is to encourage the application of these structures to problems in design and architecture, soft robotic systems, and deployable space-bound payloads. This NSF EAPSI award is funded in collaboration with the Japan Society for the Promotion of Science.