Screwy Math For Super Fine Adjustments: Differential Screws

Apr 30, 2023

For any sort of precision machine, precision adjustability is required. For the hacker this usually involves an adjustment screw, where the accuracy is determined by the thread pitch. This was not good enough for [Mark Rehorst] who wanted adjustment down to 10 μm for his 3D printer's optical end-stop, so he made himself a differential adjustment screw.

Differential screws work by having two threads with a slightly different pitch on the same shaft. A nut on each section of thread is prevented from rotating in relation to the other, and when the screw is turned their relative position will change only as much as the difference between the two thread pitches.

The differential screw in this case started life as a normal M5 bolt with a 0.8 mm thread pitch. [Mark] machined and threaded section of the bolt down to a M4 x 0.7 mm thread. This means he can get 0.1 mm (100 μm) of adjustment per full rotation. By turning the bolt 1/10 rotation, the relative movement comes down to 10 μm.

This mechanism is not new, originating from at least 1817. If you need fine adjustments on a budget, it's a very elegant way to achieve it and you don't even need a lathe to make your own. You can partially drill and tap a coupling nut, or make a 3D printed adapter to connect two bolts.

Fabricating precision tools on a budget is challenging but not impossible. We’ve seen some interesting graphite air bearings, as well as a 3D printed microscope with a precision adjustable stage.