In-Plane Small-Deformation Equivalent Method for Kinematic Analysis of Tubular Miura-Ori

The tubular Miura-ori (TMO) structure has attracted much attention due to its excellent folding capability and rich application diversity. However, the existing theoretical research on origami structure is overly complex, and kinematic analysis rarely involves bending motion. In the present work, based on geometric kinematics, “equivalent deformation mechanism” is proposed to study the axial and bending motions of TMO under small in-plane deformations. Firstly, the geometric design is studied using the vector expression of creases. To simplify the kinematic analysis of axial motion, TMO deformation is equated to a change in angle. The proposed method is also applicable to bending motion, because both bending and axial motions can be described using similar deformation mechanisms. In addition, the accuracy of the proposed method is validated through numerical analysis, and the error between analytical and numerical solutions is sufficiently small for the folding angle \(\gamma \in \left[ {25^\circ , 65^\circ } \right]\). Finally, the numerical simulation is validated with mechanical experiments. Results show the effectiveness of the proposed method in describing the kinematic law of TMO structures in a simple way. This research sheds light on the kinematic analysis of other origami structures and establishes a theoretical framework for their applications in aerospace engineering, origami-based metamaterials, and robotics.