Very rare - the writer knows of only one examples badged in this way - the plain-turning American Acme Power Equipment lathe was identical to that marketed by the Allen Electric & Equipment Co. of Detrioit and Kalamazoo, Michigan (a second Allen lathe has now been discovered). Probably intended as a simple machine for use in garages and repair workshops, the lathe had a centre height of around 4.5 inches and admitted something like 24 inches between centres. While it lacked backgear-driven low speeds it appears to have been sold complete with a neat, built-on countershaft consisting of a tall tube carrying, at the top, a cross shaft with a V-belt drive pulley overhung on one side to connect to the motor and, on the other, a 3-step flat-belt pulley to drive the lathe spindle. As flat belts work best when well spaced apart, this particular arrangement, though looking ungainly, is likely to have been effective in use.
With its flat top and V-edged ways the bed resembled those most often seen on small English lathes with a simple carriage carrying an apron-mounted "full nut" that could not be disengaged from the leadscrew; the result was that, without a quick-action rack-and-pinion drive, every movement up and down the bed required a furious twirling of the (un-graduated) tailstock-end handwheel. Unfortunately, instead of a proper compounded slide rest, or a single swivelling tool slide, only a single non-swivelling type was fitted -  this arrangement severely limiting the lathe's versatility.
Most unusually, instead of changewheels taking a drive from headstock spindle to leadscrew, the "Power Equipment" employed a vertical shaft with worm-and-wheel gearing at each end - an exposed view of what this looked like can be seen here on the British Flexispeed lathe. Although the gear-holding tube appears to have been fixed permanently in position -and hence the gears constantly in mesh - to disengage the drive a handwheel was fitted to the left-hand end of the leadscrew, this operating either cone-friction clutch, or possibly a positive-action dog clutch of some sort.
The tailstock could be set over for the turning of slight tapers and appears to have been fitted with a No. 2 Morse taper spindle.
If you have a Acme Power Equipment lathe (or other machine tool by the Company, the writer would be interested to hear from you.