Ian
This is what was taught to me as the "concentric double reduction pulley drive" set-up. No idea if that is the correct name or even whether it has an official one. Really needs a picture :-
Consider the motor shaft to be set concetric to the spindle it drives with sufficient space between the ends to permit both shafts and pulleys to turn without interference. Let there be another, intermediate, shaft spinning freely in suitable bearings arranged parallel to the motor shaft and spindle but offset by a convenient distance. Take two large pulleys of the same diameter and two small pulleys, also the same diameter. Fix one small pulley to the motor shaft and one large to the spindle. Fix the other pair to the intermediate shaft arranged so that the small motor pulley drives the large one on the intermediate shaft whilst its small compatriot drives the large pulley on the spindle. Clearly the overall reduction ratio is the square of the individual ratios i.e. if the pulley sizes give 3 to 1 reduction the total from motor to spindle is 9 to 1.
Clearly this arrangement is geometrically the same as a conventional lathe back gear. Indeed I have seen it described as a back belt system. Theoretically you can use the same length belt for each stage of the drive and tension both simultaneously by adjusting the offset shaft. In practice it will probably be needful to adjust the motor position away from absolute concentricity to get both belt tensions the same.
Like all useful engineering techniques this sort of set-up is amenable to a multitude of variations depending on the exact application. There is no need for the pulley pairs to be identical or even for the motor shaft and spindle to be concentric. The concentric arrangement is merely the most compact layout and, probably the easiest version to remember.
Clive.
Edited By Clive Foster on 13/05/2015 23:13:16