分叉
雅可比矩阵与行列式
运动学
数学
奇点
鞍结分岔
几何学
拓扑(电路)
数学分析
经典力学
物理
非线性系统
应用数学
量子力学
组合数学
作者
Jianguo Cai,Qiuyue Zhong,Xiaohui Zhang,Kexin Wang,Qian Zhang,Jian Feng Ma
出处
期刊:Journal of Mechanisms and Robotics
[ASME International]
日期:2023-01-23
卷期号:15 (6)
摘要
Abstract Bifurcation behavior analysis is the key part of mobility in the application of origami-inspired deployable structures because it opens up more allosteric possibilities but leads to control difficulties. A novel tracking method for bifurcation paths is proposed based on the Jacobian matrix equations of the constraint system and its Taylor expansion equations. A Jacobian matrix equation is built based on the length, boundary, rigid plate conditions, and rotational symmetry conditions of the origami plate structures to determine the degrees-of-freedom and bifurcation points of structural motion. The high-order expansion form of the length constraint conditions is introduced to calculate the bifurcation directions. The two kinds of single-vertex four-crease patterns are adopted to verify the proposed method first. And then, the motion bifurcations of three wrapping folds are investigated and compared. The results demonstrate the rich kinematic properties of the wrap folding pattern, corresponding to different assignments of mountain and valley creases. The findings provide a numerical discrimination approach for the singularity of rigid origami structure motion trajectories, which may be used for a wide range of complicated origami plate structures.
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