Continuing the theme of my previous post, this shows how several of these linkages can be joined to form larger deployable structures.

It works by defining an octahedron, based on 4 user positioned points and certain geometric conditions, which allow it to join to copies of itself along 4 of its edges.
The slider then controls the single degree of freedom of the resulting over-constrained structural mechanism.

At the moment all units are identical and the structure deploys to a flat plane, but I’m looking at ways of letting it curve and take on more interesting shapes. This is fairly simple to do for curvature in a single direction, to form vaults etc. But finding the necessary geometric conditions for doubly curved structures (such as domes) from networks of Bennett linkages is currently an open problem.
GH feels like it might be the right tool to solve it though.

Again this is based on the work of Y.Chen and Z.You which I linked to earlier. There’s also a shorter paper here, and a nice overview of motion structures here.

Will post the ghx as soon as I’ve cleaned it up a little.

Last year I was designing some shelters based on this stuff. I was looking at ways of bracing it with tape springs or bi-stable struts (a fascinating subject in its own right, which deserves its own post). The joint still needs work – the version shown below adds unwanted degrees of freedom.