The head of a work piece (46) is allocated to a work piece holding device (82) on which a work piece (10) can be arranged in such a way that the tips of the teeth (18) of a cutting tooth (12) that is to be machined are located in a stationary reference axis (A). A tool spindle (52) that can be fitted with disc-shaped tools (100) is arranged in such a way that it can be driven around the axis of a spindle (C). The head of the tool (46) is supported in such a way that it can be displaced by a movable carriage (34) which can slide back and forth along a lift guide (32) in a diagonal direction in relation to the reference axis (A). A feed carriage (24) can be displaced along a feed guide (22) in a diagonal direction in relation to the lift guide (32) and a drag bearing (42) defines a swiveling axis (B) parallel to the lift guide (32). The head of the work tool (46) can pivot around said swiveling axis by means of a swivel drive (60) so that it can move from a normal position to machine the surfaces of the cutting teeth (12) lying parallel to the reference axis (A) to an inclined position to machine the inclined surfaces of the cutting teeth (12). The distance (x) of the active surface (106) of the work tool (100) from the swiveling axis (B) can be measured with a measuring device (108).