The invention concerns a tool head with a housing (11), in which at least one thrusting wedge (31, 32, 33) is provided, able to move back and forth in the longitudinal direction (L) in a first toothed guide, which is coordinated with a support (21, 22, 23) in the housing (11), able to move in a second toothed guide in a transverse direction (R1, R2, R3) transversely to the longitudinal direction (L), and the thrusting wedge (31, 32, 33) and the coordinated support (21, 22, 23) are in sliding contact with each other via a slanted contact surface (51, 52, 53) and a movement of the thrusting wedge (31, 32, 33) in the longitudinal direction (L) brings about a transverse movement of the coordinated support (21, 22, 23) via the slanted contact surface (51, 52, 53) and a cutting tool (161, 162, 163) can be fastened on the support (21, 22, 23) and the support (21, 22, 23) has a support arm (101, 102, 103) extending in the transverse direction (R1, R2, R3).