Relative movement between a tool and a workpiece for machining the workpiece with a machine tool is controlled by defining a machine coordinate system (MKS) relative to a machine base of the machine tool and a rotation coordinate system (RKS) relative to the MKS by defining the origin of the RKS in the MKS, defining the orientation of a selected coordinate axis of the RKS in the MKS, defining an axis of rotation around which the RKS rotates in the MKS, defining an angular velocity with which the RKS rotates around the axis of rotation, defining a tool path in the RKS, and controlling the relative movement according to the defined tool path. With this procedure, complex movements of a machine tool, in particular in connection with so-called interpolation turning, can be described or programmed in a relatively simple manner.

There is provided a method for determining a machining means in a hybrid ultraprecision machining device for manufacturing a micro-machined product from a workpiece, the machining device comprising: an electromagnetic-wave-machining means for roughly machining the workpiece; a precision-machining means for precisely machining the roughly machined workpiece; and a shape-measurement means for measuring a shape of the workpiece upon use of the electromagnetic-wave machining means and the precision-machining means, wherein a choice is made between the electromagnetic-wave-machining means and the precision-machining means in the determination of the machining means, on the basis of: information on a stereoscopic model of the micro-machined product; information on a removal volume to be removed from a volume of the workpiece in the manufacturing of the micro-machined product; and data on a removal process time of the electromagnetic-wave-machining means and data on a removal process time of the precision-machining means.