Numerical control system with hierarchical interpolation functions

A process and device are provided for numerical control, in particular, of machine tools or robots having a plurality of axes. The process and device use base interpolations performed on a block-by-block basis and, in addition, one or more gear interpolations that convert a controlling guiding motion into a follower motion. Each gear interpolation is assigned parallel to one or more base interpolations and functions independently of block limits of a base interpolation in its own gear interpolation segments. The coupling characteristic of a gear interpolation ensues from a coupling factor, from a control curve stored in tabular form, or from a control curve stored as a mathematical functional equation. The gear interpolations can be obtained from so-called gear interpolation units and can be cascaded. Moreover, they can be fed back directly or indirectly and can be variably interconnected, as needed, with any existing sources and actuators. Besides generating geometric reference signals, gear interpolations can also be used for process control and process monitoring.