Method for ascertaining a rough trajectory from a specified contour

A method for controlling a machine tool having at least two mutually redundant drive devices for carrying out superimposed movements following a contour function, the method comprising:

• determining a specified contour for controlling the machine tool by the contour function defined in portions by contour nodal points (P0 to Pn+1) and respective contour portion functions (p0 to pn), wherein a respective contour portion function (pj) connects two adjacent contour nodal points (Pj, Pj+1);
• determining a rough trajectory by a rough trajectory function (Qj, qj) which is defined in portions by rough trajectory nodal points (Q0 to Qn+1) and respective rough trajectory portion functions (q0 to qn), wherein a respective rough trajectory portion function (qj) connects two adjacent rough trajectory nodal points (Qj, Qj+1);
• ascertaining, for each contour nodal point (Pj), a respective assigned rough trajectory nodal point (Qj) such that a difference in gradients of the two adjacent rough trajectory portion functions (qj−1, qj) which contain this rough trajectory nodal point (Qj) is minimal and that a distance of the contour nodal point (Pj) from the rough trajectory nodal point (Qj) satisfies a specified distance condition;
• and
• directing movement of one of the at least two mutually redundant drive devices based on the respective assigned rough trajectory nodal point (Qj).

A system for controlling a machine tool, the system comprising:

• the machine tool comprising at least two mutually redundant drive devices for carrying out superimposed movements following a contour curve;
• and
• a computer numerical control (CNC) device configured to:
• determine a specified contour for controlling the machine tool by the contour function defined in portions by contour nodal points (P0 to Pn+1) and respective contour portion functions (p0 to pn), wherein a respective contour portion function (pj) connects two adjacent contour nodal points (Pj, Pj+1),
• determine a rough trajectory by a rough trajectory function (Qj, qj) which is defined in portions by rough trajectory nodal points (Q0 to Qn+1) and respective rough trajectory portion functions (q0 to qn), wherein a respective rough trajectory portion function (qj) connects two adjacent rough trajectory nodal points (Qj, Qj+1),
• ascertain, for each contour nodal point (Pj), a respective assigned rough trajectory nodal point (Qj) such that a difference in gradients of the two adjacent rough trajectory portion functions (qj−1, qj) which contain this rough trajectory nodal point (Qj) is minimal and that a distance of the contour nodal point (Pj) from the rough trajectory nodal point (Qj) satisfies a specified distance condition, and
• direct movement of one of the at least two mutually redundant drive devices based on the respective assigned rough trajectory nodal point (Qj).