Guy (etc) - You seem to be getting a bit hung up on this.
I don't know if you have a machine yet or not, or are just fishing around.
Basically any machine you buy for the "hobby" type market will have a single phase motor - at whatever voltage is standard in your country. To have speed control of an Alternating Current motor, you must have a three phase motor - so you will have to change it.
To control the power to the motor you need a single to three phase inverter (forget rotary converters and all that ****). These are a simple electronic plug in unit, with no moving parts, that take in single phase from your mains and put out three phase to your motor. They come in several sizes to suit what motor you wish to power.The three phase is electronically controlled at different frequencies to give you speed control of your motor. The more modern inverters have a simple push button control panel to control speed manually, but also have the ability to be controlled from a computer (which is what we want).
On my Warco lathe I had a 1HP single phase motor running at 250 volts (UK standard). I changed this for a three phase 1 3/4HP motor. I took one off and put the other one on - as easy as that. The inverter was a second-hand Omron inverter which I plug into my 13 amp socket (UK standard) and this is wired via a 4 wire lead to the motor (three phases and earth).The motor is about twice as much output as the original to give better torque when running slowly.
The motor will turn freely at any speed from 10 hz (600 rpm) to 50 hz (UK standard) (3000rpm). I have a set of pulleys available to alter the final drive output on my lathe, but I have not had to use them.
My Omron inverter is quite old, and does not couple directly to the computer - however I have been able to link it (via relays) to turn on in either direction and stop - as per m3 m4 and m5 commands in the program. I set the speed manually via a push button control panel on the front of the inverter (which is next to the computer anyway), and I have recently rigged up a reflective sensor on the spindle (thanks to info from Dr Stein on this forum) which reads into Mach3 - to check the speed.
You can fix a potentiometer on the Omron inverter to control the speed by turning the pot, so I am trying to think up some way of connecting a servo to this - to be controlled by Mach3.
I have spent some £200 ($400) on the lathe, given in a good overhaul in the process and I am highly delighted with the result, and Mach3. I have just turned off my first batch of handrail stancions for a miniature railway locomotive - something I could never have done by hand. I must admit the look very good - my wife says so anyway - but then again - she would.