Rotor position detection is indispensable for three-degree-of-freedom spherical motors. Since the numerical relationship between the electrical angle and the mechanical angle varies with the three rotation angles, making traditional single high-frequency signal injection methods unsuitable for sensorless detection in reluctance spherical motors. Therefore, this paper proposes a sensorless position detection method for reluctance spherical motors based on the induced electric potential generated by the dual-signal injection method. In this method, two detection signals of different frequencies are injected into the motor from two stator coils at the same time, and by performing a fast Fourier decomposition of the mutual inductance potential detected in the third coil, the induced potentials generated by the two frequencies are obtained. The position angles between the detection signal coil and the two injection signal coils are calculated from these two induced potentials, so as to obtain the position angle information of the rotor. In this paper, the frequency option dual-injected signals and location option of the injection, as well as the position test effect, are analyzed and verified by simulation.