In this paper, we consider a particular mechanism, constituted by a pair of infinitely rigid mating gears subject to backlash, where only the position of the actuated gear is measured, so that the system is unobservable if the impacts between the teeth of the gears are ignored. Under the assumption that there is an infinite sequence of non-smooth impacts (which assumption is generally satisfied during a usual task, e.g., when the mechanism is actuated by a constant torque), it is possible to design an observer that asymptotically estimates also the position and the velocity of the non-actuated gear. Simulation results are included to verify the effectiveness of the proposed observer.