an automatic motion or position control dc servomotor system in which a load - driving axis driven by a dc motor to be controlled in one rotary mechanism is rotated synchronously with , or following the rotation of , a reference axis manually operated or driven by another dc motor . the system comprises a position signal generator producing first sine - and cosine - wave signals corresponding to an angle of rotation of the controlled load - driving axis ; a command signal generator producing second sine - and cosine - wave signals corresponding to an angle of rotation of the reference axis ; an arithmetic unit processing the first and second sine - and cosine - wave signals and providing a sine - wave feedback voltage output signal ; and a driver circuit amplifying the feedback voltage signal and providing a thus amplified signal to the dc motor driving the load - driving axis . when the reference axis is driven by another dc motor , the command signal generator may be a second position signal generator . the command signal and position signal generators each consists of a combination which preferably comprises a sine - cosine potentiometer . the dc servomotor system is suitably applicable to a sewing machine in such manner that the rotating hook shaft is driven by a first dc motor and the arm shaft by a second dc motor , the first dc motor being controlled synchronously with the second one under closed - loop feedback control as stated above .