Of traditional American WW (Webster Whitcombe) design, the 50 mm centre height, 8 mm collet Zimmerman was stamped on the end of its bed: M.R. Zimmerman Mach. Wks. Holsopple, PA. U.S.A.
In the 100 years spanning from the middle of the 19th to the middle of the 20th centuries a very large number of watchmaker's lathes were produced, with many re-branded so as to appear by other than their real maker. Hence, although Zimmerman might have been the maker (and the stamping Machine Works would lend credence to this) there is no surviving evidence as to their manufacturing capabilities - nor indeed to any other horological tools they might have produced. Hence, it is just as likely that they were a supply company who commissioned a batch of lathes from one of the better-known makers.
If the finish is chrome - and it appears to be - the very rare Zimmerman would have been made post 1930. See also: http://www.lathes.co.uk/watchmaker
If you have a Zimmerman, or any literature concerning the Company's machines, the writer would be very interested to hear from you.