In a machine for the precision working of tooth flanks of a gear-shaped workpiece, the workpiece having a first axis of rotation, said machine having a tool head for supporting and rotatably driving an annular internally toothed tool for rotation about a second axis of rotation and for angular movement about a third axis oriented transversely with respect to said first axis of rotation, said machine also having first means for supporting the workpiece to be machined and second means for accomplishing relative feeding and working movements between the tool and the workpiece, wherein the improvement comprises:
- a machine bed on which is directly supported a first carriage movable along an X-direction oriented transversely with respect to the workpiece axis of rotation;
- a drivingly movable second carriage guidingly mounted on said first carriage and for movement along a Y-direction oriented perpendicularly with respect to the workpiece axis of rotation and to the X-direction, said tool head being mounted on said second carriage on a side thereof remote from said first carriage and for movement therewith;
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- wherein said first means includes a headstock and a tailstock movably supported on said machine bed and on opposite sides of said tool head and for movement along a Z-direction oriented perpendicularly with respect to the X-direction and to the Y-direction, the workpiece being supported by and between said headstock and said tailstock so that said first axis of rotation thereof extends in the Z-direction, and wherein said headstock is drivable along the Z-direction and the tailstock is suitably controlled to follow the headstock so as to facilitate a relative movement between the workpiece and the tool along the Z-direction.