TX Jim, has your answer. I too have clay soil and if its dry its way to hard to work. I usually try and work it when it has moisture in it, otherwise it's almost impossible to turn over.
Pre Kubota days for me, I used an old JD disc and some of the cutters were missing. I was able to keep some of the dirt out of the disk by hanging a log chain at just the right length to keep the dirt from accumulating. Depending on how damp the soil was it worked pretty well. I will have to say that I got the chain stuck in there a few times and it was a pain in the butt to get out.
Good luck....