linkage We’re perfectly used to seeing machines move on their own; so much so that we might forget to look at them very closely. Among the simplest of machines are linkages, and as well as being useful they hold considerable mathematical interest.We recently discovered Nguyen Duc Thang’s extraordinary YouTube channel, which contains well over a thousand short videos illustrating machine components at work. Here’s a simple example; they’re weirdly fascinating and addictive.

Thang’s collection feels like a cabinet of anatomical specimens from the sorts of devices we interact with every day — and those that make mass-produced objects on production lines, too.

There’s something cold and detatched about them, perhaps something Baudrillardian and dystopian. They may come from the great steam engines of the industrial revolution but tiny versions of them probably surround you at this very moment.

Something very different is going on with Theo Jansen’s “animals”, which are decidedly futuristic:

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Anyway, at the Fine Art Maths Centre we look for the mathematics in all things, and linkages contain plenty. They’re geometrical objects, and also geometrical tools: after all, the compass we use for drawing circles in Euclidean and perspective geometry is a very simple linkage. Their configuration spaces[Warning: scary maths] also offer intuitively appealing examples of higher-dimensional space — we’ll touch on this in our non-Euclidean Geometry course, which will run again in the Spring term.

Special mention goes to this site — sadly the Java appplets will no longer work for many people but it’s worth a try.