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Fold Mapping: Parametric Design of Origami Surfaces with Periodic Tessellations

Authors:
  • Ars Electronica Futurelab

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We present a design method that prioritises in-context design for origami surfaces with periodic tessellations in a parametric CAD workflow using Grasshopper 3D. The key design criteria are: target geometry surface, user-defined folding patterns as periodic tessellations, and fold resolution. Using an error minimisation solver, we generate developable crease patterns from non-developable meshes. We evaluate our method through a study of a target geometry , Fold Mapped with various fold molecules at variable resolutions, and present a visual analysis as proof of form-fit to the target. This method affords rapid development of origami surfaces, bypassing significant trial and error in by-hand design processes.
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... An origami structure is built by a tessellation that is a repetition of a unit cell covering the entire sheet. Different unit cells generate different tessellations, with specific properties related to motion, configuration, and actuation [11]. One of the challenges of the origami design is to deal with the large number of variables and degrees of freedom (DoFs) associated with such complex structures. ...
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... The Flasher model is not directly related to buckling. However, the Flasher model and the Kresling model, both have tilted flaps (Fig. 2H-J) and it is possible that both models can be created by applying similar twist forces on basic curvilinear geometrical shapes (cylinder for the Kresling model and hemisphere for the Flasher model) [18]. Therefore, we tested whether a thin hemisphere that twist buckles is similar to the TRiC protein (and the analog Kresling based origami model). ...
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... The survey paper [Demaine et al. 2015b] reviews masterpieces of curved-crease folding and the corresponding design methods. The parametric design of origami surfaces with periodic tessellations is the topic of [Gardiner et al. 2018]. Analysis together with design has been done by Demaine et al. [2015a; for 'lens' crease patterns, and crease patterns formed by conics. ...
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Oricreate: Modeling Framework for Design and Manufacturing of Folded Plate Structures
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References [Chudoba et al. 15] R Chudoba, JD Van der Woerd, and J Hegger. "Oricreate: Modeling Framework for Design and Manufacturing of Folded Plate Structures." Origami 6 (2015), 523-536.
A Brief History of Oribotics
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Matthew Gardiner. "A Brief History of Oribotics." In Origami 4, edited by Robert J. Lang, pp. 51-60. AK Peters, 2009.
Folding and Unfolding a Million Times over
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Matthew Gardiner. "Folding and Unfolding a Million Times over:
Robotics and Biomimetics as Material Thinking in Oribotics
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Longevity, Origami, Robotics and Biomimetics as Material Thinking in Oribotics." Symmetrion 26:2 (2015), 189-202.