If you want to polish a pretty rock or a rusty old piece of metal, you have a couple of options. You can spend hours rubbing them with sandpaper until your fingertips bleed, or you can throw them in a rock tumbler. Rock tumblers use rough sand and small pebbles spinning in a drum to beat objects smooth, like accelerated erosion. This video from Mr Innovative will walk you through how to build your own rock tumbler polishing machine.
Simple rock tumblers aren't expensive, but this DIY machine has advanced features and is still quite affordable to build. Using the touchscreen interface, you can set the rotation speed and a timer. A polishing job can take several hours, so the timer is a great feature. But keep in mind that this is a rotary tumbler and not a vibratory tumbler, so you can plan accordingly.
Mr Innovative constructed his machine using CNC-cut plastic, 3D-printed plastic, and plywood cut on a table saw. But you can make all of the parts on a 3D printer if you don't have access to the other tools. An electric motor spins two axles with rubber wheels, which the barrel (a glass jar) sits upon. An Arduino Nano controls that motor through a special shield that Mr Innovative designed, though it would be easy to connect the Arduino directly to an H-bridge motor driver. The final part is a Nextion touchscreen LCD running a custom GUI. It's a simple machine, both mechanically and electronically, and would make a great weekend project for makers interested in polishing stones.