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This article addresses the problem of designing robust tracking controls for a class of robotic manipulators with flexible joints that use only position measurements. This class of flexible-joint robots is perturbed by time-varying parametric uncertainties and external disturbances. A reduced-order observer is constructed to estimate the velocity signals, and then an observer-based robust position feedback tracking controller without velocity measurements will be developed such that all the states and signals of the closed-loop system are bounded and the trajectory tracking errors can be made as small as possible. Consequently, the robust tracking control scheme developed here possesses the properties of computational simplicity and easy implementation. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control algorithms.