折纸机构折叠过程不共点折痕的位置分析

针对多顶点折纸中不共点折痕这一种典型折痕分布在折叠过程中空间位置的复杂变化,以及对 折纸机构刚性折叠特性所产生的影响,提出了一种通过分解折痕运动确定折痕空间位置并判断折纸机构刚 性折叠特性的方法。 该方法首先通过构造原折痕的平行折痕把各不共点折痕汇交于同一顶点,根据共点折 痕的旋转运动确定平行折痕位置变化;然后根据中心多边形确定旋转后平行折痕的平移方向和距离;最后确 定不共点折痕变换后的空间位置,并根据折叠平面的变形确定折纸机构的刚性折叠特性。 通过具体参数对 三顶点折纸折痕空间位置变化进行验证分析,结果表明:这种分析方法不仅简化了多顶点折纸中不共点折痕 位置的计算过程,也为确定折纸机构不可折叠时折叠平面的变形形式做了铺垫。

Analysis of the Position of Non-intersect Creases During the Folding Process of the Origami Mechanism

Aiming at the complex changes in the spatial position of the typical crease distribution in the folding process of the non-intersect creases in multi-vertex origami and the influence on the rigid folding characteristics of the origami mechanism, a motion through the decomposition of creases is proposed, a method to determine the position of the crease space and determine the rigid folding characteristics of the origami mechanism. This method first converges the different creases at the same vertex by constructing the parallel creases of the original creases, and determines the position change of the parallel creases according to the rotational movement of the intersect creases, then determines the translation direction and distance of the parallel creases after rotation according to the central polygon, determines the spatial position of the non-intersect creases after transformation, and determines the rigid folding characteristics of the origami mechanism according to the deformation of the folding plane. Through specific parameters, the three-vertex origami crease space position change is verified and analyzed. The results show that this analysis method not only simplifies the calculation process of the non-intersect point crease position in multi-vertex origami, but also paves the way for determining the deformation form of the folding plane when the origami mechanism cannot be folded.