1981 KZ1100 A1 Shaft: Have problems starting when cold

https://www.youtube.com/watch?v=sDYUGnso0lA

https://www.youtube.com/watch?v=PHuB1lyagKM

Sometimes a temp problem like that is the ignition coil.
Hope this helps.

If it has spark and fuel then it may be worn, causing low compression and too weak to start. .

http://www.docstoc.com/docs/167065310/Kawasaki-KZ1100-KZ-1100-1981-1982-1983-Service-Repair-Manual-PDF-Downloadpdf

Sounds like the clutch plates are sticking. Happens over time. what you need to do is disassemble, inspect and clean the plates. If the parts are in good repair, this resolves the sticking issue. I use carb cleaner or brake cleaner.

The identification plate on cycles is up on the steering bearing mount forward of the fuel tank.

I’m happy to assist further over the phone at https://www.6ya.com/expert/gregg_78ecbb34e27be215

It may be your ignition coil. After the engine has run awhile, the coil gets hot, and starts to break up. Have you isolated this miss to 1 cylinder or does it seem to affect all cylinders?

presuming the car is front wheel drive, it sounds like the drive shaft, sometimes its ok when cold because of the grease inside is still thick, but as it gets hotter is becomes thinner,grease has good way of silencing things,on the shaft there is a joint called a CONSTANT VELOCITY JOINT this allows the shaft to bend whilst rotating (as in cornering) it looks like a cup with a rubber concertina gator on it,check to see if the rubber is split,if so this usualy lets the grease escape and leads to the knocking problem, im afraid the only cure is to replace the entire shaft, if its worse when turning left its usualy the left side thats gone, same goes for the right.
hope this helps
regards .......dave

Sounds like you have cracked coils. If they are the original ones that came with the bike I would change them. They are a known problem with these bikes.