Here are a couple of quick studies using Grasshopper, a kind of Visual Programming Language which works with Rhino3D.

Boxes rotated by a Laplacian field (as I wrote more about earlier):

And some Kinematics:

Download the .GHX grasshopper definition and associated Rhino file here

This ties in with some of my earlier work on deployable structures

Most deployable structures research has been limited to dealing with planar mechanisms – where although the overall structures have 3D spatial forms, the essential linkages from which they are built up are restricted to certain planes (the pantographic domes of Pinero and Hoberman fall into this category).

One reason for this is focus is that the geometric complications of dealing with truly spatial linkages are of considerable mathematical difficulty (when using traditional methods).

In fact most non-planar arrangements of hinges conflict with each other and are completely rigid, giving no mechanism at all.

However there is one wonderful spatial linkage found by Bennett in 1903 which I first encountered through the work of Zhong You, and particularly this thesis of his student Yan Chen.

It is a deceptively simple arrangement of four hinges which moves in a single degree of freedom through a beautiful swooping motion.

I started by modeling the linkage in Rhino using some complex arrangements of angled intersecting circles, but this was a rather slow and painstaking way to explore variations of angle and length.

Building a parametrically variable model allowed me to quickly get a better feel for the movement. I first did this in Generative Components, and just recently in Grasshopper.