Currently most of control methods are of one degree of freedom (1-DOF) control structure for the robot systems which are affected by unmeasurable harmonic disturbances, at the same time in order to obtain perfect disturbance attenuation level, the controller gain must be increased. In practice, however, for robotic actuators, there are physical constraints that limit the amplitude of the available torques. This paper considers the problem of tracking control under input constraints for robot manipulators which are affected by unmeasurable harmonic disturbances. A new control scheme is proposed for the problem, which is composed of a parameter-dependent nonlinear observer and a tracking controller. The parameter-dependent nonlinear observer, designed based on the intal model principle, can achieve an estimation and compensation of a class of harmonic disturbances with unknown frequencies. The tracking controller, designed via adaptive control techniques, can make the systems asymptotically track the desired trajectories. In the control design, the continuous piecewise differentiable increasing function is used to limit control input amplitude, such that the control input saturation is avoided. The Lyapunov stability of closed loop systems is analyzed. To validate proposed control scheme, simulation results are provided for a two link horizontal robot manipulator. The simulation results show that the proposed control scheme ensures asymptotic tracking in presence of an uncertain extal disturbance acting on the system. An important feature of the methodology consists of the fact that the designed controller is of 2-DOF control structure, namely, it has the ability to overcome the conflict between controller gain and robustness against extal disturbances in the traditional 1-DOF control structure framework.