An apparatus is disclosed for determining the position of a moveable element in a three-dimensional workspace near a mounting surface. A sound source is provided in the moveable element. A plurality of at least three housing units are adapted to be secured to said mounting surface in spaced relationship to one another. A sound sensor is mounted on each of the units, and a sound source is mounted on at least some of the units. The positions of the sound sensor and the sound source of said at least some of the units can be adjusted. Means are provided which are responsive to the sound from the sound source of at least one of the units and received at the sound sensor of another of the units, for computing the distance between the sound source of said one of the units and the sound sensor of said another of said units. Also, means which are responsive to the initiation of sound from the sound source of the moveable element and to sound received at the sound sensors of the units, are provided for determining the three-dimensional position of the moveable element. In the preferred embodiment, the plurality of units comprises four units, and each of the units has a sound source mounted thereon. Also in this embodiment, means are provided for determining the distance between the sound source of any one of the units and the sound sensor of any other one of the units as a function of sound emitted by the sound source of said any one of the units and received by the sound sensor of said any other one of the units. Each of the units also includes means for adjusting the position of the sound source and the sound sensor in two substantially orthogonal directions.