[Jeff_H]

3 mm (a litle more the a 1/16" I am rough guessing)is not extremely excessive. From the post it is not clear where the movement is coming from. Is the shaft sliding in and out of the coupling or is the coupling itself moving. If the coupling is moving it may be a worn transmission thrust bearing. If the shaft is moving it may be a wallowed out setscrew dimple. A hose clamp or zinc on the shaft is always a good idea as a safety measure should the shaft slip out of the coupling.

Jeff

Jeff