A medical or dental handpiece has a grip. The grip includes first to third rotation shafts. The first and second shafts are connected through a first gear mechanism and the second and third shafts are connected through a second gear mechanism so that a rotation is transmitted from the first shaft through the first gear mechanism to the second shaft and then from the second shaft through the second gear mechanism to the third shaft. The first or second gear mechanism has an internal gear secured on one shaft and an external gear secured on the other shaft, the internal and the external gears being engaged with each other. The external gear is substantially enclosed within a cylindrical plane extending along a peripheral edge of the internal gear.
