3 Phase and Motors - a brief explanation

Lieblad said:
I see two sinewaves... A 'single phase' should display a single sinewave.
Is this actually measuring two AC voltages what are 180° out of phase ?

That phrase "two hots" is sorta redundant. In measuring any voltage AC or DC both conductors of the measured source are energised if one views it that way.

Now if you meant to write "two hots measured to a central point", (aka, neutral) ? What would require at least 3 connections to the measuring instrument.
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If referenced to the (max) negative value instead of the center tap it would graph as a single sine wave with twice the positive amplitude. You are confusing two phase with center tap reference. Easy to do (and theoretically no different if limited reference frame) with center tap and 180 deg.

A 240v single phase motor uses two wires (two "hots" in ref to gnd) just as a 120 single phase uses two wires (hot and "neutral"). Both are single phase referenced to one of the wires; Peak to peak voltage, 60 Hz.
 
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The power utility can deliver 3 phase in any number of ways; 240v delta (240v between each leg) - think triangle, 240v delta with center tap (2 legs 120v to gnd, one "wild" 208v to gnd)- think triangle with line off center of bottom, 208v Y (center ref to gnd, each leg 120 to gnd, 208v leg to leg) - think Y with line to gnd off center point. And of course 240v Y, 480v, etc... Although all based on a 3 phase system.

Residential gets 240v with center tapped (single phase). This comes off the secondary of a transformer, not simply off two legs of the 3 phase (which is likely much higher voltage). They center tap and ref to gnd for 120v to prevent high voltage accidents. Industrial historically got 240v delta 3 phase, center tapped if running the 120v off the same drop. 3 phase Y initially was for business to satisfy the high 120v (lighting) demand. Currently the power company prefers to drop 3 phase as Y, as it is way easier to balance than delta.
 
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A (240v) 3 phase induction motor can run on (240v) single phase power as an idler (not really under any appreciable load). However it can not self start on single phase, an external rotation or capacitor would be needed to induce phase imbalance in windings ("slip"). Essentially this is what a static "phase converter" does.

Once rotating, an idler can produce 3 phase from it's windings. Essentially this is what a rotary phase converter does.

Typically a rotary converter will want appropriately sized caps to smooth the voltage delivery between phases. If using a an idler motor as a converter you will want the load to be no more than half to 2/3 the idler rated HP.
 
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In keeping with the title as brief:

Residential typically gets 240v center tapped single phase. 3 phase equipment cannot run on single phase alone. static phase converter (not recommended), rotary phase converter, VFD, or digital phase converter are needed. Rotary can run multiple machines but not welders. VFDs can usually only run one machine (at a time).

3 phase drops in 480, 240, 208, etc are available, but expensive.
 
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