In the fiscal year 2008, in the website of Japan Science and Technology Agency(JST), the corner of introducing Japanese science and technology was open. There, Origami Engineering is introduced as being promoted in the research committee of Japan Society for Industrial and Applied Mathematics (JSIAM). After the committee was established, the author organized the session for Origami Engineering and the accomplishments are published in the book “Computational Mechanics for Origami and Its Industrial Application, JSIAM Series, 2012”, and handbook “Industrial and Applied Mathematics”. There are 2 kinds of ways for industrialization of Origami, one is by using the deployment and folding of Origami, while another is by using light and rigid function of it. In addition, the Origami 3D software is introduced as the new current technique.

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This study presents a new method for designing self-deploying origami using the geometrically misaligned creases. In this method, some facets are replaced by “holes” such that the systems become a 1-DOF mechanism. These perforated origami models can be folded and unfolded similar to rigidfoldable(without misalignment) models because of their DOF despite the existence of the misalignment. Focusing on the removed facets, the holes will deform according to the motion of the frame of the remaining parts. In the proposed method, these holes are filled with elastic parts and store elastic energy for self-deployment. First, a new extended rigid-folding simulation technique is proposed to estimate the deformation of the holes. Next by using the above technique, the proposed method is applied on arbitrary-size quadrilateral mesh origami. Finally, by using the finite-element method, the authors conduct numerical simulations and confirm the deployment capabilities of the models.

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Conformal maps are applied for designing foldable forms. This method is able to produce the complicated developed patterns for the geometrical forms such as cones, disks, and tori with different main curvatures from the simple developed patterns for cylinders that are already known, based on the similarity of the quadrilateral elements that determine regular fold lines.

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To promote Origami Engineering, the algorithm to implement systematically solid Origami on the basis of reverse engineering was newly developed, And it has been named as Ori3D. Ori3D generates 2D patterns from 3D object and folds each pattern to partial 3D structure like Origami and connects each structure, so its target is not only paper but also plastic and metal. Appearance and cost as well as function are important for industrialization of Origami. It is described that the key to the former is development of geometry which approximates to plural developable surfaces not based on mesh but from CAD data for 3D free surface, and concerning the latter, it is mentioned that the problem to provide 2D pattern which robot inferior to human in manual dexterity can fold concerning the latter.

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