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Researchers: Changwoo Ha , Jiook Chung,
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Collaborators: Prof. Glaucio H. Paulino (Princeton University)
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Themes: Lightweight and deployable structures
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Multi-degree-of-freedom origami patterns exhibit rich kinematics but are challenging to analyze because many distinct folding motions coexist near a given configuration. In this work, we introduce an eigenfolding framework that separates geometric feasibility from energetic accessibility. We first formulate exact rigid-foldability using quaternion loop-closure constraints, and compute the instantaneous null space of admissible infinitesimal motions. We then endow each crease with a torsional spring and pose a generalized eigenvalue problem restricted to this null space. The resulting eigenfoldings“ form a canonical, orthonormal basis of admissible motions ordered by ”eigenstiffness'', i.e., effective resistance to folding. Applied to one-orbit hexagonal Resch patterns, we discover that their eigenfoldings cluster into four interpretable families ($s$, $p$, $d$, and $f$), whose spatial symmetries resemble atomic orbitals. Configuration-space maps show how eigenstiffnesses evolve with the folding states of the Resch patterns. Quasi-static compression experiments on physical prototypes confirm the predicted dominance of the least-stiff $s$-folding and the stiffness-based ordering of the prototypes tested. Overall, the eigenfolding analysis provides a simple, physically grounded coordinate system for understanding and designing multi-DOF origami structures.
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