Machining centre for timepiece components

A machining centre includes a base supporting several superposed stages. At least one stage is movable and can be position indexed relative to the base. Each stage includes distinct stations at a constant angular pitch including machining units or grippers. The combination of stations from adjacent stages defines a plurality of machining locations each combining a unit and a gripper. Each relative movement between two indexing positions of two stages changes the composition of the locations. Each gripper has at least one rotational degree of freedom relative to the stage that carries it. At least one station includes both at least one machining unit and at least one gripper.