折纸运动学综述

随着21世纪折纸工程学的发展,折纸不再仅仅是一项民间艺术,一方面数学家前期的大量工作随之浮出水面,另一方面工程应用对折纸结构折叠过程的描述与分析都提出了新的挑战.同时,折纸的对象也不再局限于简单的纸张,工程中存在大量的厚度不可忽略的平板结构,他们的折叠展开问题一直困扰着相关的工程应用.近几年超材料的发展给模块化折纸带来了一次从玩具到高科技的飞跃,然而如何协调地安排这些折纸模块使得整体结构展现出超常且可变化调控的性能是折纸领域的新热点.由此可见,折纸运动学在诸多应用与探索方面都起到了决定性的基础作用.本文重点介绍了已有的机构学理论与方法及其在各种折纸结构分析设计中的应用,旨在为折纸工程学的发展提供坚实的理论技术基础.

Review on origami kinematics

Origami is no longer a folk art with the development of origami engineering in this century, in which a lot of previous work of mathematicians has surfaced and the engineering applications present new challenges to describe the folding process of rigid origami. Meanwhile, origami is not limited to the thin sheet, the folding and unfolding of thick panels have always hindered their related engineering applications. Recently, the development of metamaterials has brought a leap from toys to high technology for modular origami. How to coordinately set up the origami modules to enable the entire structure with excellent and tunable performance is a new hotspot in modular origami. Hence, origami kinematics has played a decisive role in many applications and explorations. This review focuses on the developed mechanism theories and their applications in the analysis and design of origami structures, which hopefully could be able to provide the theoretical foundation for origami engineering.