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Regarding quad-mesh rigid origami, the flat-foldable pattern exhibits a widely acknowledged geometrical property—a non-trivial state guarantees a continuous motion. This article provides a sufficient condition for this motion-guarantee property in the generalized setting. Our method is a detailed algebraic analysis on the coupled two-vertex systems constituting the quad-mesh patterns. The result is expected to be a useful tool for inverse design applications.

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When Will the Existence of a Non-trivial State Guarantee a Continuous Motion for a Quad-Mesh Rigid Origami?

  • 会议论文

  • 发表日期：

    2026年

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  • Zeyuan He,
  • Kentaro Hayakawa,
  • Makoto Ohsaki

摘要

Regarding quad-mesh rigid origami, the flat-foldable pattern exhibits a widely acknowledged geometrical property—a non-trivial state guarantees a continuous motion. This article provides a sufficient condition for this motion-guarantee property in the generalized setting. Our method is a detailed algebraic analysis on the coupled two-vertex systems constituting the quad-mesh patterns. The result is expected to be a useful tool for inverse design applications.