广义Waterbomb折纸管的刚性折叠运动特性

Rigid Folding of Generalized Waterbomb Origami Tubes

对折叠模式的精确描述是折纸结构工程应用的前提,但现有的理论和方法无法全面地分析大多数折纸结构的刚性折叠过程。以广义Waterbomb折纸管为研究对象,基于球面机构运动学理论系统地分析了其折叠行为与运动协调条件,推导了折叠管刚性收缩和扭转运动的两套解析运动学方程。研究了各种几何设计参数对Waterbomb折纸管刚性折叠行为的影响,并讨论了该折纸结构折叠过程中的分岔行为与可能的物理干涉,及其引起的刚性折叠与结构形变的转化。此工作为基于广义Waterbomb折纸管的可编程超材料、可变形结构和机器人的设计与控制奠定了理论基础和设计依据,同时为复杂折纸结构的运动学分析提供了有效的手段。

The accurate theoretical description of the folding motion of origami structures is the foundation for their design and precise control in engineering applications.However,the folding behavior of most general origami structures is very difficult to analyze because of the lack of theoretical model and analysis methodology for the complex mobile assemblies of spherical linkages.This paper focuses on the widely-used Waterbomb origami tubes.Based on the kinematics and compatibility of spherical linkages,the rigid folding behavior of generalized Waterbomb tubes was systematically analyzed with analytical kinematics equations to describe their rigid contract and twist motion.The effect of various geometrical parameters on the rigid folding behaviour,bifurcation property as well as physical blockages of the Waterbomb origami tube was studied.This work lays a theoretical foundation for the design and control of programmable metamaterials,deformable structures,and robots based on Waterbomb origami tubes,while such kinematic model can be readily applied to other origami patterns.