Ball and Chain

George W. Hart

Ball and chain are the form and substance of this very cool sculpture, which I call Ball and Chain.  It is a 6-inch diameter ball made of chain mail, and quite amazing, if I do say so myself.  The material is nylon, robotically fabricated on a rapid prototyping machine by selective laser sintering.

Individual rings and links are polyhedral tori that are free to move, as you can see from this close-up rendering of the design.

In this close-up photo, you can see the chain mesh came out well, though near the limits of what this SLS machine can accurately produce.  Also notice one ring near the center has only five links while all the others have six. Twelve such 5-fold rings are distributed around the ball on the 5-fold axes.

If all the rings and links were free to move, it would collapse like an empty sack.  So I fused together some rings and links, shown in blue above, arranged like the edges of a dodecahedron.  Their solidity determines the overall form.  This leaves twelve circular regions, shown in red, arranged like the faces of a dodecahedron, where the links are free to move. There is one 5-fold link in the center of each red region.

You can see how gravity pulls down the free sections in the top hemisphere, while the rigid portions maintain the overall form. As you slowly rotate it, whichever circles are on top will hang inwards to be concave, while the bottom ones will hang outwards to be convex. So the top always looks dimpled and the bottom always looks spherical, no matter how you turn it.

All together, there are 920 rings with six links and 12 special rings with five links.  Plus there are 2790 links which each connect two rings. The detailed pattern is chiral, based on the (7,4) Goldberg polyhedron. Here is a high res image to show more detail.

Copyright 2009, George W. Hart