The present invention relates to a method and a device for the machining of an object using a tool, in which the tool (2) or the object (18) is guided using a handling apparatus, which has multiple movement axes for the coarse positioning of the tool (2) or object (18), which form a kinematic chain. In the method, an additional actuator (3), which has a higher positioning precision in at least one dimension or axis than the other movement axes, is inserted between a terminal link (1) of the kinematic chain and the tool (2) or object (18). A relative movement of the tool (2) or terminal link (1) of the kinematic chain to the object (18) is detected using at least one sensor (5) and a deviation from a target movement path is compensated for using the additional actuator (3). The method and the associated device allow the use of robots or other handling apparatuses having lower path precision for applications which require a high precision during the guiding of the tool.