Automated Design of Tubular Origami with Anisotropic Stiffness

Abstract

Thin sheets can be assembled into tubular origami structures that combine deployability with pronounced anisotropic stiffness, enabling applications ranging from robotics to deployable systems. However, most existing tubular origami designs remain limited to degree-four vertex topologies and are characterized primarily in axial and radial loading modes, without a full assessment of anisotropic stiffness. Here, we present an automated design framework for tubular origami that jointly explores local vertex topology through generalized degree-$n$ vertices and global tube topology through the polygonal cross-section, for the systematic design and optimization of anisotropic stiffness. Using a calibrated bar-and-hinge model together with experimental validation, we quantify large-deformation stiffness responses in axial translation, in-plane translation, torsion about the tube axis, and rotation about in-plane axes, thereby characterizing the anisotropic stiffness of the tube across its compliant and constrained deformation modes. The resulting design-space exploration showed that the polygonal cross-sectional topology is the primary factor governing the anisotropic stiffness. We further show that increasing the local vertex degree can improve global structural performance, particularly for tubes with a small number of cross-sectional vertices, demonstrating that higher local kinematic freedom does not necessarily compromise stiffness at the structural scale. Compared with a benchmark design, the optimized architectures achieve more than 50 times higher constrained rotational stiffness. Together, these results highlight higher-degree vertices and polygonal cross-sectional topology as powerful design variables for tailoring anisotropic stiffness in tubular origami.