Abstract A method is presented for approximating a curved surface by a developable rigid origami; a polyhedral shape which can be developed to a plane without deformation of its facets. Form generation starts from a triangulated surface, and an optimization problem is solved to obtain a polyhedron which satisfies the geometric conditions for developability. The degrees of freedom of a rigid origami mechanism with only triangular facets are often too large for the engineering application, and therefore, it is sequentially reduced by fixing (removing) some crease lines, along which the rigid facets rotate. However, the crease line that is not fixed often becomes unable to rotate in the process of fixing the crease lines; consequently, the polyhedron cannot be developed to a plane. To avoid such an unfavorable locking situation, selection criteria of the crease line to be fixed are proposed. They are defined based on the eigenvalues and their derivatives of the stiffness matrix of the frame model, which is the numerical model for form generation and mechanism analysis of rigid origami. The performance of the proposed criteria is demonstrated through the examples of surfaces with some patterns of crease lines.

中文翻译：

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基于部分刚性框架力学特性的曲面近似刚性折纸形式生成

摘要 提出了一种用可展刚性折纸逼近曲面的方法；一种多面体形状，可以发展成一个平面，而其小平面不会变形。形状生成从三角化曲面开始，并解决优化问题以获得满足可展开性几何条件的多面体。仅具有三角形刻面的刚性折纸机构的自由度对于工程应用而言通常太大，因此，通过固定（去除）一些折线来依次减小刚性刻面旋转的折痕线。但是，没有固定的折线在固定折线的过程中往往会变得无法转动；因此，多面体不能发展为平面。为了避免这种不利的锁定情况，提出了要固定的折痕线的选择标准。它们是基于框架模型刚度矩阵的特征值及其导数定义的，框架模型是刚性折纸的形状生成和机构分析的数值模型。建议标准的性能通过具有一些折线图案的表面示例来证明。