Hello and welcome. Until a current owner/ user comes along,
I Had a hunt round, I have a k5, but I'm not too familiar with the differences on the 636, 637, and 638.
I have a copy of the 636 manual, a bench top model, It looks similar to the other numbered P/T's
If similar, The cutterblock is driven from the motor, obviously, and the thicknesser drive is a 6mm wide belt, from the cutter block, to a wheel, then chain drive ti the feed rollers, the 636 is a 710mm x 6mm flat belt but the motor to cutter block looks to vary from model, to model.
Here's a link below for what I could find which may help, English page 9 onwards.
If you need another Flat belt, I bought some from a french dealer a while ago but I was advised to go to Redhill Bearings, and ask for Optimax HF T150, Then the belt length, not used them myself, but they came highly recommended
HTH Regards Rodders
file:///C:/Documents%20and%20Settings/Administrator/My%20Documents/Downloads/p4777283%20(5).pdf
As you can see, I'm having problems with either me or my computer, just found this,
https://ssli.ebayimg.com/00/s/NzY4WDEwM ... h/$_86.JPG
https://www.google.co.uk/search?q=kity+ ... W1wLM4M%3A