Abstract: Disclosed is a machine tool for machining a workpiece which includes a machining cell with a machining device for machining the workpiece and a transfer point for transferring a workpiece to be machined to the machining device or for outputting a finish-machined workpiece from the machining device. In order permit a high flexibility in such a machine when used in a production line, the machine tool includes a conveying device which transports a workpiece transferred to it between at least two take-over positions, while bypassing the machining device.

Abstract: A grinding tool adapted to be mounted on an end of an arbor and rotated thereby about an axis in contact with a workpiece is unitarily formed with a head and a foot. The head has a frustoconical front end face centered on the axis, turned away from the arbor, and tapering away from the arbor. It also has a frustoconical back face centered on the axis, turned toward the arbor, meeting the front face at an outer circular edge centered on the axis, tapering toward the arbor, and forming with the front face an acute angle. The foot has a frustoconical outer surface centered on the axis, meeting the back face at a front inner circular edge centered on the axis, tapering toward the front edge, and forming a right angle with the back face. The front and back faces of the head meet at the outer edge at an angle of about 45.degree..