A variable transmission ratio apparatus comprising: a differential gear mechanism that adds rotation resulting from motor drive to rotation from an input shaft resulting from a steering operation and transmits the added rotation to an output shaft; a housing accommodating the differential gear mechanism and a motor, which is a drive source, the housing being fixed to a non-rotating portion; and a lock device that locks the housing and a rotation shaft of the motor in a manner prohibiting relative rotation therebetween; wherein the differential gear mechanism is formed by a strain wave gear mechanism including: a pair of circular splines (11, 12) arranged next to each other in a concentric manner; a tubular flexible spline arranged at an inner side of the circular splines (11, 12) in a manner concentric with the circular splines (11, 12) so as to be partially mated with each of the circular splines (11, 12); and a wave generator that rotates a mated portion of the flexible spline when driven by the motor; with one of the circular splines (11, 12) that is connected to the output shaft having a greater number of teeth than the other one of the circular splines (11, 12) that is connected to the input shaft, wherein the motor comprises a stator fixed to the housing arranged outside a rotor fixed to the rotation shaft of the motor. a differential gear mechanism that adds rotation resulting from motor drive to rotation from an input shaft resulting from a steering operation and transmits the added rotation to an output shaft; a housing accommodating the differential gear mechanism and a motor, which is a drive source, the housing being fixed to a non-rotating portion; and a lock device that locks the housing and a rotation shaft of the motor in a manner prohibiting relative rotation therebetween; wherein the differential gear mechanism is formed by a strain wave gear mechanism including: a pair of circular splines (11, 12) arranged next to each other in a concentric manner; a tubular flexible spline arranged at an inner side of the circular splines (11, 12) in a manner concentric with the circular splines (11, 12) so as to be partially mated with each of the circular splines (11, 12); and a wave generator that rotates a mated portion of the flexible spline when driven by the motor; with one of the circular splines (11, 12) that is connected to the output shaft having a greater number of teeth than the other one of the circular splines (11, 12) that is connected to the input shaft, a pair of circular splines (11, 12) arranged next to each other in a concentric manner; a tubular flexible spline arranged at an inner side of the circular splines (11, 12) in a manner concentric with the circular splines (11, 12) so as to be partially mated with each of the circular splines (11, 12); and a wave generator that rotates a mated portion of the flexible spline when driven by the motor; with one of the circular splines (11, 12) that is connected to the output shaft having a greater number of teeth than the other one of the circular splines (11, 12) that is connected to the input shaft, wherein the motor comprises a stator fixed to the housing arranged outside a rotor fixed to the rotation shaft of the motor.