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Wire-based tracking devices are an affordable alternative to costly tracking devices. They consist of a fixed base and a platform, attached to the moving object, connected by six wires whose tension is maintained along the tracked trajectory. One important shortcoming of these devices is that they are forced to operate in reduced workspaces so as to avoid singular configurations. Singularities can be eliminated by adding more wires, but this causes more wire interferences, and a higher force exerted on the moving object by the measuring device itself. This paper shows how, by introducing a rotating base, the number of wires can be reduced to three, and singularities can be avoided by using an active sensing strategy. This also permits reducing wire interference problems and the pulling force exerted by the device.