A device for machining components, in particular of a vehicle body has a transport and positioning unit for the component and several machining stations, which are arranged around said unit and to which the component held by a component holder of the transport and positioning unit can be fed in a position ready for machining. To transport the component from one machining station to the other machining stations while taking up the smallest possible surface area, the transport and positioning unit includes a rotor and a pivoting arm that is mounted eccentrically on said rotor, driven in opposition to the latter and supports the component holder. The drives of the rotor and the pivoting arm are synchronized in such a way that the component holder is displaced along a closed curved path comprising spaces between the neighboring apexes of said path.