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I wanted to communicate how single phase 240 could be converted to 3 phase 240 using an RPC. What exactly is the function made on L3.

You will have to move the reference point around. If you do You can find single phase 120 VAC, 208 VAC, 240 VAC, and 3P 240 VAC.

First: What's an "RPC"? Second: L1,L2,L3 end up looking like normal 3 phase if you move the ground to the junction point of R1,R2,R3 although this is a super complicated way to get 3 phase! As shown it is something strange and not normal 3 phase.

An RPC stands for rotary phase converter. Its basically an idle 3 phase motor being driven by single phase. The third leg is then generated in phase with the other two. Its the most common way to generate 3 phase from single phase 240.

Once 3 phase 240 is generated it is fed into a step up transformer to make 3phase 480. Great for bench testing industrial equipment in a home shop.

Ok--I thought maybe RPC meant rotary phase converter but that didn't make sense with the diagram. The new diagram makes sense and I've met up with it often enough in the past.