Re: the sphere of motion
Anecdotally... Kawahara shihan used to have almost no movement visible at times and people would fly. The time he biffed me about I think the movements were pretty small but it all happened so fast. He would instruct at other times to make a BIG circular motion. Others have remarked that the movements get smaller as you get better - I haven't found that, personally, but then perhaps I'm not getting "better"...