Rexman lathes were made, in some numbers, in the immediate post-WW2 years in Melbourne, Australia. The Company was owned by Rex Osman (hence Rex-Man) who made his 4.5 inch centre height machine available in various bed lengths. The machine appears to have been very well built and finished and absolutely conventional in design and execution. Typical of the type made for amateurs in the period 1930 to the early 1950s, a flat-topped V-edged bed with a gap was used, the spindle bearings were in plain bronze, a slow-speed backgear was fitted on an eccentric engagement shaft and screwcutting was by changewheels. Drive to the spindle came from a robust countershaft bolted to the bench behind the headstock with final drive by a smooth-running flat-belt over a three-step cone pulley -  Useful fittings for this market included a proper compound slide rest (with the T-slotted cross slide equipped with a "step-out" bracket supporting the end of the feed screw and allowing an extra 1.5 or so inches of travel), tumble-reverse gearing to the leadscrew, a hollow tailstock spindle with a No. 2 Morse taper, an extension to the end of the leadscrew allowed a handle to be fitted and the thread-dial indicator was of a decent, easily-read size.
Mr. Osman was, apparently, amenable to supplying lathes to a customer's requirements and it is thought that a Norton-type quick change screwcutting and feeds gearbox may have been available as an extra.
A relative provides the following interesting information:
Rex Ronald Osman was my uncle - my mother's elder brother - and he was a bit of a rascal. The 'factory' was a shed at the rear of 98 Camberwell Road, Camberwell, next to the then brickworks, now the location of Swinburne College.
I believe that he had up to just three employees but, with the advent of cheaper imported lathes, production of Rexmans became uneconomical and he switched to buying machines from Taiwan (with a 20 thou tolerance) and upspec'd them before selling them on. His latter working years were with William Adams Company, who are large Caterpillar dealers, where he used his ingenuity to save mining companies a fortune.
Rather than transporting huge scrapers hundreds of kilometres, he designed and built a jig that could be fitted to the articulated joint for re-machining prior to new bearing fit.
Earlier, during WW2 and it's petrol rationing, he built a gas producer - possibly burning charcoal - and bolted it to the rear of his car.
He and my auntie had no children, so I was pleased to fit this role when we met, though this was only occasionally as I lived in South Australia, but when I moved closer, I had a lot more to do with him.
My son and I had to clean up his shed and yard in Ringwood when he died, and there were lathe beds laying everywhere. I kept a few Rexman bits as mementos. A Top Bloke.
If you have a Rexman lathe, or any more information about the Company and its products, the writer would be very interested to hear from you.