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Not sure,.........But I believe what a Third Generations key is referring to is if you were to copy a factory cut key,
you would have a first generation copy.
Take that copy and copy it. Now you have a Second generation key.
Copy the second generation key and now you have a third generation key.
If it(the third generation key) Works to open the lock, your machine is set up as close to perfect as possible.
Just Guessing?

Harvey you are correct make copy of a copy of a copy and if the 3rd one still works you are as close as you will get. Takes practice with each machine how much pressure to apply when you copy the key. Equal pressure on both the sample key and the blank should be applied. Best to use a dial caliper to adjust your machine. Easy way to start to adjust it is use original Schlage C key blanks in both jaws rotate the cutter by hand while applying equal pressure on cartridge. Usually you will find the cutter has a high spot that is obvious when you rotate the cutter against the blank. Adjust it until it just seems the cutter is not touching the blank turn on the machine slowly raise the cartridge and listen to see if the cutter is scrapping against the blank if it is you will be cutting too deep. Get it to where if you push a little harder it barely scraps the blank and cut a key using the pressure you feel is how you will be using the machine and see if the key works smooth in factory pinned Schlage cylinder. Then use dial caliper to check if it is shallow or deep and readjust it again until it is as close as you can get it. After you try this method you will quickly understand how to adjust your particular machine using the pressure you like to use.I have always found it best to use original Schlage blanks instead of say Ilco blanks. After adjusted try cutting several makes of keys to see they all works as best as you can get them to. Such as American, Master, Kwikset, Schlage, Yale ect and you are good to go.

Richard

Some VERY good instructions from Richard on calibration.

And yeah, how much pressure you apply can make huge differences.

I know my old Foley Belsaw is VERY finicky. Took me a while to get use to it.
For my machine, I found the first cuts (toward the bow) takes a light touch.
As I reach the tip, the last couple cuts require a lot more pressure.
I've gotten really accurate. But it took some time & experimenting.

I have one of these machines too. Got it and a very old Ilco for $100 and eventually got both working. Went through everything the OP did but used an O ring for a belt. The Micrometric is pretty cool but it would be better if it had a brush.

Richard thanks for the tip. I should have asked you this before I was adjusting mine but I too realized pressure means a lot. I couldn't get it to be perfect but for cutting keys once in a WHILE I will do. I realized the pressure factor when the cutter wasn't touching the blank at all but after cutting a key the cuts were deeper than original. Adjusted accordingly and so far it works great for the WB and Master keys I cut. I am very sure for more secure locks like an American, I will need to re adjust it.

Steve, I had an idea to drill a hole in the shaft, tap it and install an arbor which I can put brushes on or a polish wheel and use it to polish stuff. Idea is good but too much extra work for me since I barely use it.

I had one and the local sweeper repair shop had belts that worked perfect.