Abstract: A method for the precision machining of flanks of gear-wheel-shaped workpieces, in particular those with convex teeth, using an internally toothed tool with crossed axes, in which simultaneous relative movements take place not only in three mutually perpendicular axes but also around an axis perpendicular to the cross-axes angle such that not only the tooth flanks of the tool and the workpiece have tangential contact with one another but also the base body of the tool and of the workpiece touch one another at a point of contact IV of which the position changes continuously, and a straight line g orthogonally penetrating the base body of the tool and the base body of the workpiece at the point of contact not only intersects the axis C1 of the workpiece or of its base body and the axis C2 of the tool or its base body (points III, II), but also passes through the center I of an ideal sphere K1 which adapts itself to the base body of the workpiece at the point of contact IV.

Abstract: A method for the precision machining of flanks of gear-wheel-shaped workpieces, in particular those with convex teeth, using an internally toothed tool with crossed axes, in which simultaneous relative movements take place not only in three mutually perpendicular axes but also around an axis perpendicular to the cross-axes angle such that not only the tooth flanks of the tool and the workpiece have tangential contact with one another but also the base body of the tool and of the workpiece touch one another at a point of contact IV of which the position changes continuously, and a straight line g orthogonally penetrating the base body of the tool and the base body of the workpiece at the point of contact not only intersects the axis C.sub.1 of the workpiece or of its base body and the axis C.sub.2 of the tool or its base body (points III, II), but also passes through the center I of an ideal sphere K.sub.1 which adapts itself to the base body of the workpiece at the point of contact IV.

Abstract: A method for the precision working of the tooth flanks of gear-shaped workpieces with an abrasive internally toothed tool wherein the tool, after each workpiece or after several workpieces, is dressed in the same mounting with a dressing wheel, the tooth system of which corresponds with the one of the gear-shaped workpiece and the tooth flanks of which are covered with extremely hard grinding granules. To improve the tool geometry the dressing of the internally toothed tool is done with a one-flank or a two-flank contact between the dressing wheel and the internally toothed tool and with an electronic forced guiding of the rolling and relative movements between the dressing wheel and the internally toothed tool, and, the precision working in the free or in the torque guided two-flank engagement between the internally toothed tool and the workpiece.

Abstract: A method for the precision machining of flanks of gear-wheel-shaped workpieces, in particular those with convex teeth, using an internally toothed tool with crossed axes, in which simultaneous relative movements take place not only in three mutually perpendicular axes but also around an axis perpendicular to the cross-axes angle such that not only the tooth flanks of the tool and the workpiece have tangential contact with one another but also the base body of the tool and of the workpiece touch one another at a point of contact IV of which the position changes continuously, and a straight line g orthogonally penetrating the base body of the tool and the base body of the workpiece at the point of contact not only intersects the axis C.sub.1 of the workpiece or of its base body and the axis C.sub.2 of the tool or its base body (points III, II), but also passes through the center I of an ideal sphere K.sub.1 which adapts itself to the base body of the workpiece at the point of contact IV.

Abstract: A shaving cutter, honing cutter or the like serving as a tool (T) matingly meshing at a crossed-axes angle (.delta.) with the toothed workpiece (W) during a precision working of crowned and/or conical tooth systems guided during a feed movement (V) at an angle (.epsilon.) inclined with respect to the workpiece axis and along same. The feed movement (V) is thereby superposed by an additional movement directed perpendicularly thereto and these two movements are coordinated in such a manner with one another that the working zones of the tool (T) are guided on a curve (55) which lies on a theoretical envelope (50) of the workpiece (W) defining the crown dimensions from one face of the workpiece (W) to the other. The working zones of the tool (T) have thereby at each contact point (K) a tangential contact with the workpiece tooth flanks (2, 3) to be machined.