Simple Wood Lathe
When making phase plugs for speakers (see the article on phase plugs under Speakers page), some means of spinning the plug to machine it to shape is required.  Due to these plugs being very short objects, a standard wood lathe with 3' or more of bed length is a bit of overkill.  Also, because the plug components are usually made with a hole saw, they have a 1/4" hole in the centre which is used to clamp them together when gluing.  Therefore a chuck is a more convenient method of drive - something not standard on your basic wood lathe.  The first plug I made was done by clamping my electric drill in the bench vice, and machining with a rasp!  Due to how surprisingly well this method worked, I decided to make a more stable lathe using my drill as the drive element.

The frame and bed were made from 1" RHS steel, with 1/4" flat steel used for the drill mount and tailstock.  For my application, chuck-to-chuck mounting of the work was best, so I utilised a chuck from my old blown-up drill for the tailstock.  The creation is shown below.  It has an effective work length of 300mm and a swing of 120mm.
Closer views of the drill mounting clamps and the tailstock
The clamp on the tool rest mount allows for angle and bed position on the one adjustment.
In this view the workpiece as mounted on a 1/4" threaded rod secured by each chuck.  The tool rest is also in position.
The lathe in action.  For machining MDF, I find standard wood chisels seem to work fine.  Note that I only have one hand on the chisel in this photo as I was also pressing the camera button - both hands should be used.

If using a variable speed drill, such as mine is, don't be tempted to use this feature - the drill will overheat if run for a period of time on a slower speed.

All the the phase plugs shown in the speakers section were made on this "lathe".