Differential screw

A differential screw is a mechanism used for making small, precise adjustments to the spacing between two objects (such as in focusing a microscope,[2] moving the anvils of a micrometer,[3][4] or positioning optics[5]).

Flamsteed’s Preface to the Historia Coelestis Britannica: "Richard Towneley ... carried forward and completed his instrument (the micrometer) and made it perform with one screw, what on Gascoigne’s instrument had required two.” [9] A drawing by Robert Hooke in 1667 clearly shows Towneley’s Micrometer with the single screw with two different pitch threads on it.

With this differential screw, one thread was half the pitch of the other, Towneley was able to keep the micrometer's indicating pointers centered in the field of view as they opened and closed.

Another arrangement holds the two "nuts" co-axially in a single fixture and has two separate screws with slightly different pitches (distance from the crest of one thread to the next) entering from opposite ends.

[1] For single start threads, each turn changes the distance between the nuts by the effective pitch, Peff.

Rotating a bolt through two nuts with slightly different thread pitches for each changes the separation of the nuts by the difference between the threads.
Micrometer adjuster with differential threads. The threads 11 on rod 4 have one pitch (e.g. 25 tpi, blue ), while the threads 10 in the barrel 1 have another (e.g. 20 tpi, orange ). A full turn of the thimble 12 rotates the nut sleeve 13 and its two threads ( 20 tpi outside and 25 tpi inside ) to move the rod 1 / 20 - 1 / 25 = 0.01 in (0.25 mm) relative to the barrel.
Differential screw illustration from an 1817 machine design handbook. ab & ef have one thread pitch while cd has a different one. One turn of AB moves the whole spindle one ab thread distance; simultaneously, M moves one cd thread distance and the amount that AB moved. M's overall movement is thus the difference between ab and cd. [ 1 ]
Differential screw leveling feet, drawing by Joshua Rose , 1887.