Working on the trigonometric relationship between them, the solution of the following Ordinary Differential Equation sets the z(t) values as a function of gamma and the input curve.Īs an ODE, I have generated a script for solving the ODE using a finite difference. Vector t will be always normal to the ruling, the following infinitesimal relation happens: We also need the variation of z(t) to define the transformation of the point along the curvature. ![]() The remaining part of the triangle can be set as v(t). We will have absolute axis and an axis evaluating the surface generated, being t the direction of the curve and W the component parallel to the ruling lines. In a flat state, Fgamma is described as a semi arbitrary curve that will belong to the osculating plane when folded. The following approach is based on the chapter Resilence of Sam Calisch Phd Thesis Folded functional foams. The angle will be measured between the osculating plane and the ruling lines. This plane, called osculating plane, generates a fold in a certain angle. Computational Design with Curved Creases ( ) The former means that any reflected shape can be foldable if when intersected by a plane, the line generated belongs to a plane at any angle of folding. Demaine et all.(2016) Reconstructing David Huffman’s Legacy in Curved-Crease Folding.Ĭurved creases are a specific branch of Origami that can be explained as a Shapes of Reflection or as an infinitesimal discretization of a hinge. In the next chapter we will dive in two different answers for this question and the mathematics of an specific type of folding.Į. The question is what is foldable and what is not foldable, and there are certainly not a unique answer for that. There are certainly active research on them as David Huffman work or Erik Demaine. If the mathematics behind origami are not fully understood, curved creased foldings are even less. ![]() All of them have a flat state, that means a huge potential to simplify its manufacturing, DOF can be easily tuned to generate desired motions, t heir capacity of changing the wet area, auxetic behaviors, etc.īut here we are talking an specific type of Origami Tessellations. If we think about an origami tessellation in engineering terms, they collect all those properties and also add many others. They main interest on this type of discrete structures is their capacity to fill volumes with lower density, their good structural behavior and their potential to be escalated in a easier way than a pure monolithic structure. Inside engineering, there are tessellations everywhere. Te workflow proposed by this project is the following:įirst of all, lets dive in a bit of a theoretical and engineering look at Origami tessellations. The goal of this project is to calculate mathematically the folding to be able to use it with design and simulation proposes. This final project aims to deeply understand, reproduce and try to extend the current state origami curved crease tessellations from a structural point of view.
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