The machine consists of a rotationally driven work holder (2) and a rotationally driven tool holder (6) which is fitted with a fly cutter (7) for the undercuts (8) and with a fly cutter (9), axially and radially offset from the fly cutter (7), for the pockets (10) and which can be offset with its rotation axis (D2) with regard to the rotation axis (D1) of the work holder (2). In this arrangement, the rotational movements of work holder (2) and tool holder (6) can be matched to one another in such a way that, when the fly cutter (7) for the undercuts (8) is in the working position, the fly cutter (7) describes an open hypocycloidal path and, when the fly cutter (9) for the pockets (10) is in the working position, the fly cutter describes a closed hypocycloid. IMAGE
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