Current position data is determined of a first machining tool in a machining space having a second machining tool, the second tool having known position data with regard to the position data of the first tool which are to be determined, the first tool and the second tool being movable toward and away from one another, the first tool to be determined in its position comes into contact with a machining surface, known in its position, of the second machining tool, the rotary speed of a drive motor for the second tool being set to a starting rotary speed which is so low that the rotary speed of the second tool is measurably reduced when the tool comes into contact.