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arXiv · 2206.12691

Explicit kinematic equations for degree-4 rigid origami vertices, Euclidean and non-Euclidean

Riccardo Foschi·Thomas C. Hull·Jason S. Ku
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Abstract

We derive new algebraic equations for the folding angle relationships in completely general degree-four rigid-foldable origami vertices, including both Euclidean (developable) and non-Euclidean cases. These equations in turn lead to novel, elegant equations for the general developable degree-four case. We compare our equations to previous results in the literature and provide two examples of how the equations can be used: In analyzing a family of square twist pouches with discrete configuration spaces, and for proving that a new folding table design made with hyperbolic vertices has a single folding mode.

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Riccardo Foschi, Thomas C. Hull, Jason S. Ku. 2022-06-25. Explicit kinematic equations for degree-4 rigid origami vertices, Euclidean and non-Euclidean. https://doi.org/10.1103/physreve.106.055001

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