Design of three-dimensional origami structures based on a vertex approach

作者：Zhou, Xiang^*; Wang, Hai; You, Zhong

来源：Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2015, 471(2181): 20150407.

DOI：10.1098/rspa.2015.0407

• vertex method
• origami structure
• geometric design
• unfolding simulation

Origami geometric design is fundamental to many engineering applications of origami structures. This paper presents a new method for the design of three-dimensional (3D) origami structures suitable for engineering use. Using input point sets specified, respectively, in the x-z and y-z planes of a Cartesian coordinate system, the proposed method generates the coordinates of the vertices of a folded origami structure, whose fold lines are then defined by straight line segments each connecting two adjacent vertices. It is mathematically guaranteed that the origami structures obtained by this method are developable. Moreover, an algorithm to simulate the unfolding process from designed 3D configurations to planar crease patterns is provided. The validity and versatility of the proposed method are demonstrated through several numerical examples ranging from Miura-Ori to cylinder and curved-crease designs. Furthermore, it is shown that the proposed method can be used to design origami structures to support two given surfaces.

• 出版日期2015-9-8
• 单位上海交通大学