Work pieces, especially of rotational symmetry, are machined in a rotary broaching operation. The machine tool for this purpose has a tool carrier carrying a plurality of cutting edges arranged on a curved path in a radial work piece plane. In order to reduce down-time and to simplify the construction of the broaching apparatus, the insertion of a work piece blank into the apparatus and the removal of a finished work piece from the apparatus are preferably performed without interrupting the motions of a tool carrier. For this purpose the tool carrier is provided with a zone which is free of cutting tool edges. This tool free zone of the tool carrier is located downstream of the last cutting edge as viewed in the rotational direction of the tool carrier. This feature avoids the need for a return stroke of the tool carrier. Accordingly, respective return slides and return controls are also obviated. The apparatus is equipped with angular sensing devices for ascertaining the angular positions of the tool carrier at the beginning and at the end of a work cycle to provide respective control signals for the insertion and removal of a work piece in the zone without cutting edges and to start a new work cycle when a work piece blank is inserted into the machine tool.