Adaptable Hypars

 

An exploration of the simplest Hyperbolic Paraboloidic ‘saddle’ form has lead to the development of a modular system that combines the principles of the hypar (Hyperbolic Paraboloid) and elastic potential energy.

A hyperbolic paraboloid is an infinite doubly ruled surface in three dimensions with hyperbolic and parabolic cross-sections. It can be parametrized using the following equations:

Mathematical:   z = x2 – yor  x = y z

Parametric:   x(u,v)=u   y(u,v)=v   z(u,v)=uv

The physical manifestation of the above equations can be achieved by constructing a square and forcing the surface area to minimalise by introducing cross bracing that has shorter lengths than the  square edges.

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A particular square hypar defined by b = n * √2 (b=boundary, n=initial geometry or ‘cross bracing’) thus constricting the four points to the corners of a cube leads to interesting tessellations in three dimensions.

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Using a simple elastic lashing system to construct a hypar module binds all intersections together whilst allowing rotational movement. The rotational movement at any given intersection is proportionally distributed to all others. This combined with the elasticity of the joints means that the module has elastic potential energy (spring-like properties) therefore an array of many modules can adopt the same elastic properties.

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The system can be scaled, shaped, locked and adapted to suit programmatic requirements.

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25/04/13 Tutorials

We are back from a month long break. Great tutorial last Thursday. Students are developping their temples which range from a temple to infinity all the way to aa temple for bees. Here are couple pictures of the work. Beautiful!

William Garforth Bless' ceramics tests for his temple for Water
William Garforth Bless’ ceramics tests for his temple for Water
Andrei Jippa's Temple to infinity VB.net script to intersect meshes.
Andrei Jippa’s Temple to infinity VB.net script to intersect meshes.
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Marilu Valente is creating a temple to the bio-economy using a mix of potato starch based bio-plastic and plaster.
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Marilu finding new ways to use her bio-plastic in a wall component.
Mike's new reciprocal structure prototype, here is aa small paper model of it.
Mike’s new reciprocal structure prototype, here is aa small paper model of it.
Jessica Beagleman's Selfridges pop-up roof structure made of tied plywood components.
Jessica Beagleman’s Selfridges pop-up roof structure made of tied plywood components.