Technology Craft
Treating manufacturing machines as mathematical objects, and exploring what they can do.
We usually model the physical world inside mathematics: we find an abstract structure that captures how something behaves and reason about it there. Technology Craft runs that the other way round. Manufacturing machines are already mathematical objects. A three-axis CNC router, moving a tool along its X, Y and Z axes, is a model of three-dimensional linear algebra with a basis. Add two rotational axes and the space of the machine becomes the unit tangent bundle of Euclidean space. The motion of the machine is then a path through that space.
Most Computer Aided Manufacturing software is written from the point of view of production: you describe the object you want and the software works out how to get there. That is exactly right for a factory and exactly wrong for asking what a machine can do. There is a long tradition in craft of spending time with a tool, listening to what it wants to do. Technology Craft asks what that listening looks like for a machine controlled not by hand but by a list of numbers, and what new mathematics and new making appear when you control the machine rather than its output.
This is a body of work rather than a single project. Its threads include:
- CAMel — the open-source software that makes controlling the machine, not the output, practical.
- Zip-Form — using the parallel-transport frame of a curve to make doubly-curved forms from flat-cut material, from sculpture to optimised concrete formwork.
- 5-axis waterjet cutting and cooperative 3D printing — pushing specific machines past their standard workflows.
- Misshapen Chaos — clay 3D printing where the toolpath itself carries the mathematics of the logistic map.
- Gradient of Grain — letting the geometry of the material set the path of the cut.
- An Invitation to Category Theory for Designers and Wiring Euclid for Manufacturing — the theoretical frame: machines and processes as objects and arrows, manufacturing as a kind of practical Euclid.
Coverage: University of Arkansas News — Honors College Showcases Math Craft
