This paper presents a mathematical model for sound localization in space using two-microphone devices that possess at least two degrees of freedom. It proves a series of theorems and lemmas that are based on time difference of arrival measurements and movements of the interaural axis, forming a powerful instrument for practical robot applications. For instance, it shows that a single determined rotation of the interaural axis is sufficient to exactly yield the azimuth or the elevation of an immobile sound source in the far field, independently of microphone spacing and the speed of sound and hence of the surrounding medium. It proves that at any moment the knowledge of one value determines the magnitude of the other, with the restriction that the sign of the second value is undefined, which means that, depending on the rotation, either the back-front or the up-down ambiguity is kept unsolved. This paper also shows that parallax motion unlocks essential information about the distance and the Cartesian coordinates of the sound source. Shifting the microphone system sideways fixes the distance and the coordinate on the interaural axis. Combining rotation and translation movements completely solves the localization problem. In order to illustrate the efficacy of the model, this paper presents experiments with a low cost robot developer kit during which the azimuth, the elevation, and the distance of continuous sound sources are determined at a precision of 10 degrees and 0.5 m, respectively. Achieving this performance with low power material demonstrates how easily the model can be implemented into any robotic system.