O.K. this post is going to get a bit technical (and hopefully no mistakes)
Firstly this is how a single phase 2 pole motor operates :-
Each pole consists of a pair of opposing coils, one pole pair is the "running wind" and the other pole pair the "starting wind".
The running wind is connected to power directly but the starting wind is connected via a capacitor.
The capacitor causes a 90° electrical shift in the A.C. waveform = so from the diagram above (top left) the start winding will reach max current 90° after the run winding causing the magnetic field vector between the two sets of coils to rotate - thus dragging the rotor around with it.
Note: Direction of rotation is changed by reversing the connection of the run wind (as above) but can also be accomplished by reversing the connection of the start windings (No way of determining which from the information thus far).
The terms L & N are nominally "Live" and "Neutral"
(At this point we are ignoring such things as a booster cap or centrifugal cut out switch as these are not present in
Yellow-cad's machine - I'm also stating rpm's without "slip".)
Next a four pole motor :-
This is effectively double what was described above.
So there are two run and two start windings since this now requires 2 electrical cycles to vector a single revolution, this motor will now only turn at half synchronous speed i.e. 1800rpm for 60Hz.
By bringing most of the coil terminals out of the motor we can arrange switchgear to "wire it up" as a 2 or a 4 pole motor by connecting adjacent coil pairs in parallel or series thus making them vector as singles to change the 4 pole wind to an effective 2 poles in operation - hey presto a dual speed motor.
Now we come to Yellow-cad's motor and what I infer from the plate (there are other possibilities) but the manufacturers have indulged in some creative license here.
This is effectively what was described above but I have added in what I can infer from Yellow-cad's motor plate by adding in the terminal numbers.
There is no way to actually "rewire" this via switchgear to a 2 pole configuration - hence my comment on "creative license".
What I think they do is this :-
They turn off one of the start windings (0)
The start winding V2-Z is off so the two run windings V1-Z and X1-Z effectively vector out to the plane of the inoperative start winding V2-Z at right angles to the start winding.
So now the motor runs at 3600rpm but only using 3/4 of its coils - which I think lines up with the motor rating plate of 1 HP or 3/4 HP.
This may also require (or recommended) that you start the motor in "low" (ie 4 pole) range and switch to "high" (pseudo 2 pole configuration) as the starting torque might otherwise be rather poor.
So you need to create a series of switches / relays / contactors to develop the switching as shown.
Before doing that try setting up the various circuit configuration using jumper leads - use a heavy electrical heater (say 1.5kW) as a ballast in case of accidental shorts to minimize the scope of sparks and smoke.
Anyone got any other suggestions ?
You might consider rewinding your motor to three phase and run it off an inverter - you can get more power and much more speed range with full variability. Might be less hassle.
See my thread on uprating my lathe :-
Single Phase To Three Phase Rewind - Lathe Uprate
Regards, Ken