This is probably a simple question for the large group of people with better Japanese than me, but I just can't figure it out: The 取り (tori) in 片手取り (katate tori) etc. comes from 取る (toru; grab, catch), right? Is this a verb form my books fail to mention or an abbreviation?
I only picked up Japanese from my surroundings, so I canīt give a proper grammar explanation, basically yes, this is the same word. If you use the "i" form, the verb sort of becomes a noun.