Form generation of rigid origami for approximation of a curved surface based on mechanical property of partially rigid frames
Form generation of rigid origami for approximation of a curved surface based on mechanical property of partially rigid frames
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DOI：
10.1016/j.ijsolstr.2020.12.007
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发表时间：
2020-12
影响因子：
3.6
通讯作者：
K. Hayakawa;M. Ohsaki
中科院分区：
文献类型：
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作者：
K. Hayakawa;M. Ohsaki
提出了一种用可展开的刚性折纸逼近曲面的方法，该折纸是一种多面体形状，它可以展开成一个平面，而不会使它的面片变形。形状生成从三角化曲面开始，通过求解优化问题得到满足可展性几何条件的多面体。对于工程应用来说，只有三角形面片的刚性折纸机构的自由度往往太大，因此，通过固定(去除)刚性面片沿其旋转的折痕线来顺序地减小自由度。然而，在固定折痕线的过程中，未固定的折痕线往往变得不能旋转，因此多面体不能展开为平面。为了避免这种不利的锁定情况，提出了待固定折痕线的选择准则。它们是基于框架模型的刚度矩阵的特征值及其导数来定义的，框架模型是用于刚性折纸的形状生成和机构分析的数值模型。通过具有某些折线图案的曲面的实例，验证了所提准则的有效性。
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.