Developable & Ruled Surfaces

 

 

All experiments in this post are still under-construction

 

3

a form of ruled surface

 

keywords:

Developable surface, Origami, Folding, Ruled Surfaces

Helicoid, hyperbolic Paraboloid, Oloid

 

3

 

another form of double ruled surface

 

Forming Metal Plates

When I started this post, my aim was to understand the process of Folding metals and  forming with sheets and then reach the ability to create curved metal plates  using simple bending or even positive molds. I looked for keywords, which guided me to the origin of the topic; developable surfaces, and then back again to the Ruled surfaces.

 

oloidtry  Oloid02

 

 

 

just another experiment, nothing particular, just close to the Oloid

 

Developable Surfaces and Ruled Surfaces

In Brief, those curved surfaces which can be flattened into planar patches, without distortion. In other words, it’s the kind of surfaces can be created by single direction bending at a time, without the need for stretching the surface. In mathematics means; it’s a surface with zero Gaussian Curvature value at any point. It’s made usually out of one single sheet of material, materials such as metal, wood, and cardboard. Developable surfaces are a subclass of Ruled surfaces. Ruled surfaces are the surfaces which controlled by two sets of points, swept and connected by straight lines creating the shape, for example, a cone is a ruled surface, and also hyperbolic paraboloid is another example.

 

References:

http://www.mscsoftware.com/training_videos/patran/Reverb_help/index.html#page/Laminate%20Modeler/lam_tutorial.3.05.html

http://en.wikipedia.org/wiki/Developable_surface

http://en.wikipedia.org/wiki/Ruled_surface

http://www.geometrie.tuwien.ac.at/

http://www.geometrie.tuwien.ac.at/pottmann/2008/fold08/paper_docs/fold.pdf

http://members.home.nl/arie.brederode/olo3.html

 

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