PURPOSE: To enable internal superfinishing with a drilling machine by a method wherein a cam groove is provided in the tool-fitting member of an attachment, an unmovable cam follower is engaged in the groove and thereby the vertical motion is given to the rotating tool-fitting member.

CONSTITUTION: When a tapered projection 11a of an attachment 10 is put in the bore 5a of the main shaft 5 of a drilling machine, a tool-fitting member 13 is rotated together with an attachment-fitting member 11 as the main shaft 5 rotates. On the occasion, since a cam follower 23 fitted to an unmovable surrounding member is engaged in the cam groove 14 of the tool-fitting member 13, a sliding part 13a of small diameter is moved slidably in the vertical direction inside a slide hole 12 under the forced guidance given by the form of the cam groove 14. Accordingly, a tool 29 fitted to the tip makes vertical motions along with the rotation. In this way, the number of vibrations and the amplitude thereof which are essential for superfinishing machining can be altered with ease by selecting the sliding part of small diameter and the cam groove, and thus the superfinishing machining becomes possible.