ZHUANG Yan-shuai，ZHANG Fan，CUI Guo-hua.Foldability Analysis of Three-Vertex Rigid Origami Based on Screw Theory[J].Journal of Chongqing Technology and Business University(Natural Science Edition）,2021,38(4):15-22

Foldability Analysis of Three-Vertex Rigid Origami Based on Screw Theory

DOI：

 作者 单位 庄彦帅，张帆，崔国华 上海工程技术大学 机械与汽车工程学院，上海 201620

多顶点刚性折纸机构是可实现折叠和展开运动的一种空间机构，三顶点刚性折纸机构为多顶点中的一种形式，针对三顶点刚性折纸机构可折叠性问题，提出了运动学中基于旋量理论分析此类型机构可折叠性的方法；将三顶点刚性折纸机构运动学等效为双支链闭环的6R机构，建立该闭环机构的速度方程，对运动副的运动旋量之间的线性相关性进行判断，确定运动等效机构的可动性；基于Grassmann线几何原理，确定不同类型刚性折纸机构的维数，验证该类型刚性折纸机构运动旋量的线性关系；三顶点刚性折纸机构运动学等效与分析机构运动旋量线性相关性的综合方法，能够实现从运动学分析角度判断三顶点刚性折纸机构的可折叠性，并可拓展到其他多顶点刚性折纸机构的研究。

The multi-vertex rigid origami mechanism is a spatial mechanism that can be folded and expanded. The three-vertex rigid origami mechanism is a form of multi-vertex. Aiming at the foldability of the three-vertex rigid origami mechanism， a method based on screw theory in kinematics is proposed to analyze the foldability of this type of mechanism. The kinematics of the three-vertex rigid origami mechanism is equivalent to a double-branched closed-loop 6R mechanism， and the velocity equation of the closed-loop mechanism is established. The linear correlation between the motion screws of the kinematic pairs is judged to determine the movability of the motion equivalent mechanism. Based on the Grassmann line geometry principle， the dimensions of different types of rigid origami mechanisms were determined， and the linear relation of motion screws of the rigid origami mechanism was verified. The synthetical method of kinematic equivalence and linear correlation analysis of motion screws of three-vertex rigid origami mechanism can realize the judgment of foldability of the three-vertex rigid origami mechanism from the perspective of kinematic analysis， and can be extended to the research of other multi-vertex rigid origami mechanism.