# Design and Analysis of Yoshimura Tubular Origami Mechanisms
## 1 Introduction  
Origami mechanisms, with their unique properties, such as reconfigurability, negative Poisson's ratio, and high deployable ratio [1, 2, 3, 4, 5], have been widely applied in various fields, including aerospace [6, 7], biomedical engineering [8, 9], origami robotics [10, 11, 12, 13, 14, 15], architectural and civil engineering [16, 17], and spatially deployable mechanisms [6, 18]. The ongoing advancement of mathematical fields, such as computer science, graph theory, and computational geometry, has further bridged the art and science of origami through mathematical principles. For example, foldable space structures based on origami principles enable the creation of lightweight, compact, and expandable designs that can be efficiently deployed in space applications. These structures leverage origami's compactness and reconfigurability to improve deployment efficiency while reducing spatial constraints during launches. Additionally, integrating soft materials with origami structures has enhanced mobility and introduced novel movement patterns. [PERSON] [19] developed an amphibious origami robot with multimodal locomotion and body sensing capabilities, allowing for seamless transitions between land and water. This innovation holds promise for applications in environmental monitoring, search and rescue, and exploration. [PERSON] [20] proposed an origami-inspired soft actuator that integrates stimulus perception and crawling capabilities, enabling robots to sense environmental changes and respond dynamically, demonstrating potential for adaptive, untethered applications in exploration and environmental monitoring. An origami-based soft robotic gripper was also introduced, utilizing a water-bomb design with silicone and latex materials. This gripper achievesversatile, gentle handling of fragile objects through negative pressure actuation, making it suitable for a variety of applications [21]. Inspired by the rhombic dodecahedron (RDD) origami model, [PERSON] [22] introduces a 3D-printed soft multicellular robot with multi-modal locomotion, including crawling, turning, and climbing. Its reconfigurable design enables diverse patterns and functions without reshaping. [PERSON] [23] introduced a Miura-derived origami tube with programmable stiffness for a modular continuous robot. This robot, driven by steel wires, exhibits flexibility, scalability, and kinematic adaptability, as demonstrated in prototype experiments. Kirigami [24], a related art form that combines cutting and folding, has also been employed to design mechanisms with broader motion and transformation capabilities, expanding the versatility of origami-based engineering solutions. By precisely controlling the folding and unfolding of origami units, engineers can dynamically adjust mechanical properties such as stiffness and damping [25]. Researchers have also explored origami mechanisms with negative Poisson's ratios for applications in morphing structures, energy absorption, and deployable systems. Recent studies have optimized these structures to enhance their elasticity and deformation behavior [26]. Among various origami mechanisms, Yoshimura tubular origami stands out as one of the most popular. The three-dimensional Yoshimura tubular origami mechanism is typically centrally symmetric. Most research has focused on such symmetric Yoshimura tubes, often achieving specific functions through crease optimization [27], structural modification [28], and the integration of new materials [29; 30]. For example, [PERSON] [31] and colleagues developed an origami-based mobile robot structure utilizing a Yoshimura mechanism for axial crawling and obstacle navigation. [PERSON] [32] introduced a manufacturing method for a soft pneumatic actuator using elastomers embedded with non-expandable thin-walled or fiber structures, enabling anisotropic movements under pneumatic input.