Geometric and Kinematic Analyses and Novel Characteristics of Origami-Inspired Structures
Abstract
:1. Introduction
2. Design Method of a Crease Pattern
2.1. Mathematical Theory for Origami Design
- (a)
- Given two points of P1 and P2, we can make a crease over P1 and P2;
- (b)
- Given two points of P1 and P2, we can fold P1 onto P2 along a crease to make the two points coincide;
- (c)
- Given two straight lines L1 and L2, we can fold line L1 onto L2 along a crease to make the two lines coincide;
- (d)
- Given a point P1 and a line L1, we can fold line L1 onto itself along a crease passing through point P1;
- (e)
- Given two points P1 and P2 and a line L1, we can fold point P1 onto line L1 along a crease passing through point P2;
- (f)
- Given two points P1 and P2 and two lines L1 and L2, we can fold P1 and P2 onto L1 and L2, respectively, along a crease; and
- (g)
- Given a point P and two lines L1 and L2, we can fold point P onto line L1 along a crease perpendicular to L2.
2.2. Common Crease Patterns
2.3. Design of Crease Patterns
3. Kinematic Analysis of Origami-Inspired Structures
3.1. Rigid Folding of Origami
3.2. Large Deformations of Origami Structures
3.3. Kinematic Singularity and Potential Bifurcation of Origami Structures
- (a)
- Set the initial iteration step size to , as the ideal structure moves along the unique motion path before singularity. is the maximum size of the members. Set the initial value of to , and denotes the entry of the r-th row and r-th column in the singular matrix .
- (b)
- In each iteration, the generalized displacement compatibility matrix J of the structure can be obtained according to the geometric configuration of the iteration step , and the corresponding minimum nonzero singular value can be obtained.
- (c)
- The size of iteration step is determined by . When , the minimum nonzero singular value decreases and approaches zero; take to avoid crossing singularities. is the maximum number of iteration steps. When , it moves away from singularities, take to accelerate the solution process.
- (d)
- After determining the size of , the motion path can be tracked and the configuration can be updated according to the nonlinear prediction-correction method.
- (e)
- When t is greater than the maximum number of iteration steps , the configuration is singular and the iteration ends.
4. Novel Characteristics of Origami Structures
Recongifurable Stiffness and Configuration
5. Discussion
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Chen, Y.; Yan, J.; Feng, J. Geometric and Kinematic Analyses and Novel Characteristics of Origami-Inspired Structures. Symmetry 2019, 11, 1101. https://doi.org/10.3390/sym11091101
Chen Y, Yan J, Feng J. Geometric and Kinematic Analyses and Novel Characteristics of Origami-Inspired Structures. Symmetry. 2019; 11(9):1101. https://doi.org/10.3390/sym11091101
Chicago/Turabian StyleChen, Yao, Jiayi Yan, and Jian Feng. 2019. "Geometric and Kinematic Analyses and Novel Characteristics of Origami-Inspired Structures" Symmetry 11, no. 9: 1101. https://doi.org/10.3390/sym11091101
APA StyleChen, Y., Yan, J., & Feng, J. (2019). Geometric and Kinematic Analyses and Novel Characteristics of Origami-Inspired Structures. Symmetry, 11(9), 1101. https://doi.org/10.3390/sym11091101