Abstract: Apparatus for changing the rotation speed of a workpiece holder axle relative to the axle of a drive shaft, the tangential acceleration of this movement, and the pressure between the surface of workpieces and lapping tools. These changes are set cyclically, directly in the apparatus for finishing. The machines for the realization of such control of the finishing process are equipped with units which are capable of regulating the value of the complex eccentricity of holder rotation and have independent drive systems for adjusting the kinematic factors in the course of finishing. This ensures uniform abrasion over the entire working surface of the lapping tools.