Abstract
Abstract. Origami that can form various shapes by setting simple creases on the paper and folding along these creases has a lot of applications from the fields of art to engineering. The inverse problem of origami that determines the distribution of creases based on the desired shape is very complicated. In this paper, we use theoretical kinematics to systematically analyse an inverse folding problem of a toy about how to fold a piece of paper into a disc through a smaller hole without breaking it. The results show that some four-crease and six-crease patterns can achieve the expected function, and they can be easily folded with 1 degree of freedom (DOF). It not only opens up a new way to solve the inverse folding problem but also helps students to understand mechanisms and machine theory.
Highlights
Origami, a kind of traditional art of paper folding originating in East Asia, has attracted much attention in the fields of science and engineering due to the property that it can generate a large number of 3D structures by setting creases on a piece of paper
The target of this paper is to systematically find proper kirigami patterns that can realize the function of allowing a round disc to pass through a smaller square hole in a piece of paper, namely to determine the distribution of creases
If d ≤ 2l cos α, the disc can pass through this hole by folding the four-crease pattern; otherwise, the disc could not
Summary
A kind of traditional art of paper folding originating in East Asia, has attracted much attention in the fields of science and engineering due to the property that it can generate a large number of 3D structures by setting creases on a piece of paper. An interesting toy of the paper-folding problem on how to get a round disc through a smaller square hole in a piece of paper (see Fig. 1) has attracted the attention of the authors. As Tadashi Tokieda explained, the 2D paper is transferred into a 3D structure when being folded up off the table by twisting the paper, and the disc can pass the smaller hole (Haran, 2021). The mechanism behind the problem such as creating creases by twisting the paper and the folding process has not been explained explicitly yet. The target of this paper is to systematically find proper kirigami patterns that can realize the function of allowing a round disc to pass through a smaller square hole in a piece of paper, namely to determine the distribution of creases.
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