A numerically controlled machine tool has at least one movement axis and is connected to a numerical controller which includes a parts program. Movements of each movement axis are limited by maximum permissible axis dynamics. The parts program has a sequence of instructions for machining a workpiece which specify different maximum desired speeds for the machining of the workpiece which change abruptly over time. The numerical controller approximates the different maximum desired speeds which change abruptly over time with a desired speed profile that is continuous over time and has a profile of the maximum desired speeds which is also continuous over time. The numerical controller uses the continuous desired speed profile to calculate the desired values of an actual movement profile of the movements for each movement axis.

A numerically controlled machine tool has at least one movement axis and is connected to a numerical controller which includes a parts program. Movements of each movement axis are limited by maximum permissible axis dynamics. The parts program has a sequence of instructions for machining a workpiece which specify different maximum desired speeds for the machining of the workpiece which change abruptly over time. The numerical controller approximates the different maximum desired speeds which change abruptly over time with a desired speed profile that is continuous over time and has a profile of the maximum desired speeds which is also continuous over time. The numerical controller uses the continuous desired speed profile to calculate the desired values of an actual movement profile of the movements for each movement axis.