In recent times, origami-inspired deployable structures have received significant interest from the research community as a major area of research in the fields of science and technology. This paper deals with the geometry and the deformation behavior of deployable cones based on the four-fold line origami concept. First, a novel geometric design algorithm is presented to develop axially foldable conical structures based on generalized Miura-ori pattern, which is then utilized to investigate the influence of four design parameters on folding geometry. The foldability of thus obtained origami patterns is verified with the help of physical models. The geometric incompatibilities during the deployment are highlighted using a simple experiment, showing the unfolding sequence of a paper model. The deformations due to incompatibilities are analyzed by adopting the concept of pin-jointed truss modeling of the origami structures. A mathematical model of the deployment problem is formulated to capture the deployment deformations of the structure, on the basis of which an algorithm for deformation analyses is developed. One example is considered to characterize the deformation behavior of the conical origami structures as the design parameters of the folding pattern are varied. The analytical findings demonstrate that the fold line strains of the origami cone are very sensitive to the changes in three design parameters, number of origami units ($m$), fold angle (${\alpha }_0$), and angle ${\theta }_2$; except the length ratio ($l{r}_0$). The variation in design parameters may induce bi-stability in the deployment path of the conical structure. The findings of the analytical investigation are verified numerically, demonstrating that the strain responses obtained from the numerical analyses are completely consistent with the analytical results.

近年来，受折纸启发的可展开结构作为科学技术领域的主要研究领域已引起研究界的极大兴趣。本文基于四折线折纸概念处理可展开圆锥的几何形状和变形行为。首先，提出了一种新颖的几何设计算法，用于基于广义Miura-ori模式开发可轴向折叠的圆锥形结构，然后用于研究四个设计参数对折叠几何形状的影响。借助于物理模型验证了如此获得的折纸图案的可折叠性。使用简单的实验突出显示了部署期间的几何不兼容性，显示了纸模型的展开顺序。通过采用折纸结构的销钉连接桁架建模概念，分析了由于不兼容而引起的变形。建立了展开问题的数学模型以捕获结构的展开变形，在此基础上开发了用于变形分析的算法。考虑一个示例来表征随着折叠图案的设计参数的变化，圆锥形折纸结构的变形行为。分析结果表明，折纸锥的折线应变对三个设计参数（折纸单位数（在此基础上，开发了一种变形分析算法。考虑一个示例来表征随着折叠图案的设计参数的变化，圆锥形折纸结构的变形行为。分析结果表明，折纸锥的折线应变对三个设计参数（折纸单位数（在此基础上，开发了一种变形分析算法。考虑一个示例来表征随着折叠图案的设计参数的变化，圆锥形折纸结构的变形行为。分析结果表明，折纸锥的折线应变对三个设计参数（折纸单位数（$米$），折角（${\alpha }_0$）和角度 ${\theta }_2$; 除长宽比（$升{\mathrm{[R}}_0$）。设计参数的变化可能会在圆锥形结构的展开路径中引起双稳定性。对分析研究的结果进行了数值验证，表明从数值分析获得的应变响应与分析结果完全一致。