Norb,
The Urethane belts are common in conveyor applications, as has been mentioned. I am not sure what a spin grinding fixture is, ie is this a high speed belt drive for a grinding spindle?
It is available in quite a few grades, the harder grades transmit more torque, but are stiffer (ie won't go round small pulleys) and the real strong grades have a non-stretch core.
But you would be looking at the softest grade probably.
Check your pulley diameters and compare them with the belting minimum diameter specs.
The joins are done with a welding kit. This is like a special set of pliers that holds the two ends square, and a teflon covered heating element (like a flattened soldering iron). When the ends are nicely melted, you squeeze the pliers together and lock them, leaving it to cool down. Carefully linish off the excess.
Can you weld them with a hot cardboard cutter knife, gas flame, cigarette lighter etc? Yes, but they will almost inevitably break soon after.
In fact, we don't even weld our own despite having the correct gear - there are still failures, we order them made to length - much the best option!
Generally the tension on the installed belt will be around 5-10%. Simple way is to wrap a long length to the setup, with just enough tension to remove the sag, mark the length with a felt pen, then deduct 5-10% of this length to give you the correct pre-tension.
Jim has mentioned Habasit - this should be top quality (Swiss!), there are several others too. Fenner is another brand.
I think the real secret is in ordering the belt pre-made.
Actually, urethane belting can be a frustrating product - generally because too much is expected of it. If you overload it, it will break, wear, jump off....
It seems very forgiving stuff, but even mis-aligned pulleys will wear it, because it is so 'grippy'. Having said that, you can use it for crossed drives, but don't let the belts touch where they cross.
Another thought, if this is a high speed grinding application, then you really will need a perfect join.