That tractor will run without a battery. The charging syt. starting with the dynamo, it's what the radiator fan is mounted too, find the 2 blue wires going to the dynamo and unplug the bullet conectores, start the engine and run it at full throttle, conect a volt meter to the blue wires from the dynamo, VOLT METER ON AC VOLTS, you should have about 40 AC volts.
The only thing I have seen go bad with these dynamo's is the bearings go bad and stop turning. If you have around 40 AC volts then reconect the blue wires and unplug the conector at the voltage regulator, (I call it a rectifier, kubota calls it a regulator) It's about 3"x3" with cooling fin's. I can't remember if it's under the insterment panel or in front of the panel under the hood.
Do the same test again at the reg plug, 2 blue wires at the plug should have around 40 AC volts. If you have 40AC volts at the plug then most likely the reg. is bad. I think the red wire goes down to the big terminal on the starter to charge the bat.
Paul
June 2009