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On the basis of the classical computed torque control method, a composite nonlinear feedback (CNF) design method for robot manipulators with bounded torques is presented. The resulting controller consists of two loops. The inner loop is for the full compensation for manipulators nonlinear dynamics and the outer loop is the CNF for stabilisation and performance enhancement. Stability analysis is carried out with an estimate of the domain of attraction specified in the presence of actuator saturation. In addition to the guaranteed stability properties, the controller takes advantage of a varying damping ratio induced by the CNF control. The varying damping ratio allows fast transient response without overshoot and compensates the effect of the frictions. It also takes advantage of the high-gain action embedded in the outer loop to compensate the friction effect. Simulation results demonstrate the effectiveness of the proposed design.