A machine tool for cutting a profile in a rotating workpiece has a body centered having an elongated edge formed with an angularly extending row of seats each having a radially directed seat face and an axially directed seat face. Respective Z-shaped holders in the seats each have an outer part, an inner part parallel thereto, and a flexible middle part transversely connecting the inner and outer parts. Respective fasteners releasably fixing the inner parts to the body against relative movement. Respective cutting are fixed on the outer parts of the holders. An adjustment wedge between one of the seat faces and the respective holder face is displaceable to shift the outer part of the respective holder relative to the body and transversely of the respective one seat face.