The invention relates to a numerically controlled machine for milling cylindrical toothing with circular-arc directrix . According to the invention, the machine comprises a circular feed kinematic chain which simultaneously drives a piece (1) to be machined into rotation and translation movement, by means of a kinematic chain of longitudinal feed, the two kinematic chains being driven by the same numerically controlled electric motor (24), and having rigid kinematic connection with adjustable transmission ratio through a mechanism (B) with change wheels, forming together a rolling kinematic chain, whereto, by means of a numerically controlled discrete division kinematic chain, it provides the piece (1) with a supplementary translation division movement during each stage of return to the initial position of the piece (1), in order to machine a new gap of the toothing, the machining being performed by a tool (2) such as a face milling cutter with frontal teeth placed in circular arc, driven by a main shaft (3), using the principle of rolling of a piece (1) to be machined over the fixed rack.
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