期刊
JOURNAL OF MECHANISMS AND ROBOTICS-TRANSACTIONS OF THE ASME
卷 15, 期 6, 页码 -出版社
ASME
DOI: 10.1115/1.4056576
关键词
bifurcation behavior; mobility analysis; origami plate structures; high-order constraint
This article introduces a novel tracking method for bifurcation paths in origami-inspired deployable structures. By establishing Jacobian matrix equations and using high-order expansion forms of length constraint conditions, the degrees-of-freedom and bifurcation points of structural motion are determined, revealing the rich kinematic properties of the wrap folding pattern.
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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