方捻折纸纹样的刚性折叠性与山谷折痕的消除
Rigid Foldability and Mountain-Valley Crease Assignments of Square-Twist Origami Pattern
摘要：
刚性可折叠性允许折纸图案围绕折痕线折叠而不扭曲或拉伸组件面板。它能够折叠刚性材料，便于设计可折叠结构。最近的研究表明，刚性可折叠性是由山-谷折痕（M-V）的折纸图案分配的影响。本文采用基于运动传递路径的运动学方法研究了具有不同M-V分配的正方形扭转折纸图案的刚性可折叠性，分析了四种正方形扭转折纸图案，发现其中两种是刚性可折叠的，而另外两种是刚性不可折叠的。基于刚性折纸模型与球面4 R机构闭环网络的运动学等价性，推导了刚性情况下的显式运动学方程。我们还提出了一个折痕添加方法来转换刚性的非刚性模式的可折叠性。对修改后的图形进行了运动协调条件检验，验证了修改后图形的刚性可折叠性。运动学分析揭示了修改模式的分叉行为。这不仅有助于加深我们对折纸图案的刚性可折叠性及其与M-V赋值的关系的理解，而且为我们从非刚性折纸图案创造出更刚性可折叠的折纸图案提供了一种有效的方法。
英文摘要：
Rigid foldability allows an origami pattern to fold about crease lines without twisting or stretching component panels. It enables folding of rigid materials, facilitating the design of foldable structures. Recent study shows that rigid foldability is affected by the mountain-valley crease (M-V) assignment of an origami pattern. In this paper, we investigate the rigid foldability of the square-twist origami pattern with diverse M-V assignments by a kinematic method based on the motion transmission path. Four types of square-twist origami patterns are analyzed, among which two are found rigidly foldable, while the other two are not. The explicit kinematic equations of the rigid cases are derived based on the kinematic equivalence between the rigid origami pattern and the closed-loop network of spherical 4R linkages. We also propose a crease-addition method to convert the rigid foldability of the non-rigid patterns. The motion compatibility conditions of the modified patterns are checked, which verify the rigid foldability of the modified patterns. The kinematic analysis reveals the bifurcation behaviour of the modified patterns. This work not only helps to deepen our understanding on the rigid foldability of origami patterns and its relationship with the M-V assignments, but also provides us an effective way to create more rigidly foldable origami patterns from non rigid ones.
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