Abstract: A process and device are disclosed for positioning devices for temporarily fixing a workpiece in any desired angular position in a three-dimensional working space of which the coordinates are known, in particular when the workpiece requires a multidimensional support A computer-controlled machine with a tool movable in the direction of all co-ordinates is used for that purpose, together with a freely movable, vertically adjustable device or supporting column mounted on a base plate and upon which the supporting device for the multidimensional support of the workpiece is positioned. Based on the tool geometry or a C.A.D. programme, a coupling or an appropriately designed measurement head of a measurement machine is fixed on the tool with respect to a calculated plane of reference for the tool and to an axis inclined in relation thereto which cuts the plane of reference.