How many revolutions do the gears have to turn? Some computer hard drives use a steel band pinned in the center and looped around a drum on the head positioning stepper motor shaft. Then each end is pinned to circular portion of the pivoting arm that carries the read/write heads. Some floppy drives do this also to provide linear positioning of the heads. The band is held in tension. If the drums have no runout and the steel band does not stretch, the only theoretical error would be due to thermal expansion. If the drums are wide enough and the band were wound in a spiral so that it did not cross over itself, several turns of one and possibly both drums would be possible. Note however, that this arrangement is only good for a limited number of the revolutions.
Weston Bye - Author, The Mechatronist column, Digital Machinist magazine
~Practitioner of the Electromechanical Arts~
Theory & Practice-
Theory is when you know something but it doesn't work.
Practice is when something works but you don't know why.
It it dangerous to combine Theory & Practice;
nothing works and you don't know why.