Design of a wedge-shaped folded structure

Zakirov, I. M.; Алексеев, К. А.

doi:10.3103/s105261881005002x

Cited by 6 publications

(2 citation statements)

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“…Among the current research on origami mathematics, a great majority is focused on the flat-and/or rigidfoldability problems [10][11][12][13][14][15][16][17], whereas origami geometric design that studies the folded configurations and/or folding mechanisms of origami structures and is fundamental to many engineering applications is still intractable. Deriving parametric equations that describe the folding kinematics of a certain crease pattern is the most commonly used approach in origami design [18][19][20]. But this approach suffers from vast complexity and lacking of flexibility, which is particularly the case for one who does not have much knowledge about origami.…”

Section: Introductionmentioning

confidence: 99%

Design of three-dimensional origami structures based on a vertex approach

2015

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Origami geometric design is fundamental to many engineering applications of origami structures. This paper presents a new method for the design of three-dimensional (3D) origami structures suitable for engineering use. Using input point sets specified, respectively, in the x−z and y−z planes of a Cartesian coordinate system, the proposed method generates the coordinates of the vertices of a folded origami structure, whose fold lines are then defined by straight line segments each connecting two adjacent vertices. It is mathematically guaranteed that the origami structures obtained by this method are developable. Moreover, an algorithm to simulate the unfolding process from designed 3D configurations to planar crease patterns is provided. The validity and versatility of the proposed method are demonstrated through several numerical examples ranging from Miura-Ori to cylinder and curved-crease designs. Furthermore, it is shown that the proposed method can be used to design origami structures to support two given surfaces.

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Section: Introductionmentioning

confidence: 99%

Design of three-dimensional origami structures based on a vertex approach

2015

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“…In this context, a fundamental yet challenging issue is origami geometric design, which addresses the problem of how to create a crease pattern that folds into the desired three-dimensional shape. Deriving parametric equations to describe the folding kinematics for a certain crease pattern is a commonly used approach by many researchers [12][13][14]. However, this approach suffers from vast mathematical complexity and often lacks flexibility and applicability in real circumstances.…”

Section: Introductionmentioning

confidence: 99%

Design of rigid-foldable doubly curved origami tessellations based on trapezoidal crease patterns

et al. 2017

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This paper presents a mathematical framework for the design of rigid-foldable doubly curved origami tessellations based on trapezoidal crease patterns that can simultaneously fit two target surfaces with rotational symmetry about a common axis. The geometric parameters of the crease pattern and the folding angles of the target folded state are determined through a set of combined geometric and constraint equations. An algorithm to simulate the folding motion of the designed crease pattern is provided. Furthermore, the conditions and procedures to design folded ring structures that are both developable and flat-foldable and stacked folded structures consisting of two layers that can fold independently or compatibly are discussed. The proposed framework has potential applications in designing engineering doubly curved structures such as deployable domes and folded cores for doubly curved sandwich structures on the aircraft.

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