The invention concerns a control apparatus for machines designed to operate on a workpiece. The apparatus comprises a programming element consisting of a disc which has concentric tracks of varying transparency or reflectance; an optical scanner comprising an emitter unit emitting light beams to the programming element and a receptor unit for the light beams which have been transmitted or reflected; drive means for rotating the disc by the relative displacement of a tool and the workpiece; and an electric circuit connected to the receptor unit and to a motor for controlling the speed of rotation of the motor as a function of the intensity of the signal given by the receptor unit. The apparatus is applicable in particular to machines for working on plates, pieces of glass or plastics material, for example window panes, plate glass or lenses.