A cutting tool mechanism 11 for providing a cutting, abrading or grinding action is disclosed. The mechanism 11 has an inner circular part 17 having teeth 19 extending radially outwardly, a surrounding circular part 25 having inner teeth 27 extending radially inwardly. The circular parts 17 and 25 co-operate by engagement their teeth 19 and 27. Rotation of one circular part causes the other to move constrained by the engagement of the teeth in an orbital, oscillatory or impact motion. An input coupling 81 is provided for transmission of rotary motion, and an output coupling 37 is provided to transmit said orbital, oscillatory or impact motion to a blade 13. In further embodiments, the surrounding circular part 25 can be provided with outwardly extending teeth and surrounded by a further outer circular part with inwardly extending teeth, to cooperate with the outwardly extending teeth, to provide more complex orbital, oscillatory or impact motion.