Arc Line

Completed in 2024, this kinetic sculpture has 20 steel rings that follow a smooth but seemingly unpredictable path. The upper part has a single electric motor but because of differing sprocket sizes the movement takes 27 minutes to repeat. It’s about 7′ wide and 10′ tall and is nearly silent.

Although the path appears unpredictable, it is not random, and can be calculated by the geometry of the upper mechanism and the relative rotational speeds of the blue levers that pull on the strings. Because I wanted each ring to trail the previous one by an equal amount of time (5/24 of a second, to be exact), the lengths of the wooden arcs had to be determined by the lever speeds.  This means that the path is hardwired into the geometry and that I had to choose one path out of an infinite number before I could begin construction.

To see what my options were I made an animation that iterated through thousands of paths.  Some were highly symmetric and predictable.  Others were more complex and would take a year to repeat.  Many of the paths looked like what I imagine an x-ray of steel wool to look like. Sometimes the steel wool was fresh out of the package and orderly.  Other times it had been pulled apart into a wild nest.  I found it impossible to pick a path that was objectively the best, but this path had a good balance of expected and unexpected turns, steep vertical dives and wide horizontal sweeps, and in an nod to pragmatism, could be made with off-the-shelf sprockets (with 20, 21, 27 and 35 teeth).

While each individual ring moves in a 2D plane, the path all the rings follow often seems to be 3D, winding its way back and forth through space.  I believe it appears like this because our minds interpret motion as having a minimum of curvature, and so assumes a third dimension if the 3D path would have less curvature than a 2D path.  This makes sense because in our experience 3D paths with gentle curves are more common than 2D paths with sharp curves.  I found it surprising how much variety results from just four axis driven by a single rotation.  It made me think about how the world could be both predictable and unpredictable, soothing and sudden, at the same time.

The video below shows one complete 27 minute cycle.