We study the control problem of an aerial vehicle moving in the 3D space and connected to an independently moving platform through a physical link (e.g., a cable, a chain or a rope). The link is attached to the moving platform by means of a passive winch. The latter differs from an active winch by producing only a constant uncontrollable torque. We solve the problem of exact tracking of the 3D position of the aerial vehicle, either absolute or with respect to the moving platform, while the platform is independently moving. We prove two intrinsic properties of the system, namely, the dynamic feedback linearizability and the differential flatness with respect to the output of interest. Exploiting this properties we design a nonlinear controller able to exponentially steer the position of the aerial robot along any sufficiently smooth time-varying trajectory. The proposed method is tested through numerical simulations in several non-ideal cases.