Supplementary Information;Supplementary Movie;Supplementary Figures from Kinematics and dynamics of non-developable origami

Non-developable origami is a unique type of origami structures that cannot be unfolded into a flat sheet without stretching. In this work, we study the kinematics and dynamics of such origami, theoretically, numerically and experimentally, considering rigid panels and stretchable creases. Unlike developable origami, we find that non-developable origami exhibits distinct folding angle relationships, leading to several separate branches in its kinematic configuration space with snap-through and locking behaviours. By modelling the creases as stretchable torsional springs, we derive a dynamic model to analyse the deployment of non-developable origami structures, from single-vertex origami to origami chains. Our dynamic model unveils the snap-through behaviour between the two kinematics branches of the single-vertex non-developable origami structure, which further validated by experiments with excellent agreement. We believe that our kinematic and dynamic framework of non-developable origami will greatly expand the current design space of origami structures and guide the design of novel origami actuators.

不可展折纸（non-developable origami）是一类独特的折纸结构，无法在不产生拉伸变形的前提下展开为平面薄板。本研究从理论、数值与实验三个维度，针对采用刚性面板与可拉伸折痕的不可展折纸结构，开展运动学与动力学分析。与可展折纸（developable origami）不同，我们发现不可展折纸呈现出独特的折叠角关系，其运动构型空间中存在多个独立分支，并伴随突跳（snap-through）与自锁行为。我们将折痕建模为可拉伸扭转弹簧，推导得到动力学模型，用以分析从单顶点折纸到折纸链的各类不可展折纸结构的展开过程。该动力学模型揭示了单顶点不可展折纸结构的两个运动学分支间的突跳行为，并通过实验验证，二者吻合度极佳。我们认为，本研究提出的不可展折纸运动学与动力学框架，将极大拓展现有折纸结构的设计空间，并为新型折纸驱动器的设计提供指导。