摘要
折纸弹簧结构是一种简单的折纸结构,它由两条尺寸相同的长纸带相互折叠后粘接得到,因其具有多模式大变形能力而受到广泛关注.论文首先通过实验探究了折纸弹簧结构的多模式变形能力和力学特性,包括轴向拉扭耦合变形和各向弯曲变形,发现了两种弯曲模式,即对顶点弯曲和对侧边中点弯曲.实验结果表明,弯曲过程力-位移曲线呈现近似线性,但部分弯曲变形的力-位移曲线存在明显的跳跃现象,对应观察到折面的突弹跳变.为解释上述现象,我们在折面上引入了虚拟折痕.基于虚拟折痕山折和谷折的不同组合,单个折纸弹簧单元表现出四种几何不同的构型.根据单元间旋转和平移的堆叠方式,推导顶点坐标的齐次变换矩阵,进而得到了折纸弹簧结构刚性折叠的运动学模型,其可以描述折纸弹簧结构的所有变形模式.进一步在折痕上指定扭转刚度并基于最小势能原理,明确了不同变形模式下的势能本构和力-位移关系本构,定性验证了折纸弹簧的非线性轴向拉扭耦合变形特性及线性各向弯曲变形特性.论文的研究结果有助于设计和开发具有三维变形和运动能力的折纸机器人.
The origami spring structure is a simple origami structure,which is obtained by folding two long paper strips of the same size and gluing them to each other.Recently,it has received a lot of attention because of its multi-mode large deformation ability.In this paper,the multi-mode deformation capability and mechanical properties of the origami spring structure are studied experimentally,including the axial stretch-twist-coupling deformation and the bending deformation in all directions.Two bending modes,namely,vertex-to-vertex bending and side midpoint-to-side midpoint bending,are found.The results show that the force-displacement curves of the bending process are approximately linear,but there are obvious jumps in the force-displacement curves of some of the bending experiments,corresponding to the snapthrough transition of the bending facet.To explain these phenomena,virtual creases are introduced along the diagonal of each square facet.Based on different combinations of mountain and valley folds of virtual creases,a single origami spring cell could exhibit four different geometric configurations.A rigid folding kinematic model of the origami spring structure is obtained by deriving the displacement transformation matrix of the vertex coordinates based on the stacking of rotation and translation between cells.This model can describe all deformation modes,i.e.,axial stretch-twist-coupling and two bending modes,of the origami spring structure.The potential energy constitutive landscape and the constitutive profile of the force-displacement relation for different deformation modes are clarified by specifying the torsional stiffness at the crease based on the principle of minimum potential energy.The nonlinear axial stretch-twist-coupling deformation characteristics and linear bending deformation characteristics in all directions of the origami spring structure are also qualitatively verified.The findings of this paper uncover the mechanism of multi-mode deformation of origami spring structures and contribute to the design and development of origami robots with three-dimensional deformation and locomotion capability.
作者
张子安
刘作林
徐鉴
方虹斌
Zian Zhang;Zuolin Liu;Jian Xu;Hongbin Fang(Institute of AI and Robotics,Hehai University,Shanghai,200433)
出处
《固体力学学报》
CAS
CSCD
北大核心
2023年第4期497-511,共15页
Chinese Journal of Solid Mechanics
基金
国家重点研发计划项目(2020YFB1312900)
国家自然科学基金项目(12202104,12272096)
博士后科学基金项目(2021TQ0071,2021M700819)资助
关键词
折纸弹簧
多模式大变形
刚性可折叠模型
轴向拉扭耦合
各向弯曲
origami spring structure
multi-mode large deformation
rigid-folding model
stretchtwist-coupling
bending in all directions
