When using programmed machine tools many steps of a shaft are machined in one operation. Many shafts are not rigid enough and for the purpose of achieving high accuracy and productivity it is necessary to use an automatic follow rest and dimension control. The problem is complicated by necessity of an automatic reset in an operation from one step of a shaft to the other. The new scheme of a device is proposed in the paper that enables simultaneously to support the shaft being machined and control its dimensions. The work principle of a device is that the shaft is supported in a radial direction by a movable slider. Diameter of the shaft neck is measured by two levers turning round their axes driven by the movable slider with patterns. The main idea is that at motion of the slider equal to change of the shaft neck diameter measuring surfaces of levers are constantly tangent to diametrical surface of the workpiece while the slider is supporting the workpiece in radial direction, opposite to the cutting force. Dimension of a shaft neck is evaluated as a sum of motion value of a slider and deviation from tangent of lever measuring surfaces. Theoretical background of principle schemes and the work scheme of a device are presented in the paper.