Various estimation schemes were proposed in [Li and Slotine, 1987] to identify the unknown parameters of the loads or links of robot manipulators. It was also suggested that these schemes could be used to generate new adaptation laws by combining them with the earlier adaptive controller of [Slotine and Li, 1986]. This new perspective of driving parameter estimation by both the tracking errors of the joint motion and the prediction errors of the joint torque is detailed in this paper. Global asymptotic tracking convergence is shown for a class of new adaptive controllers based on this approach, regardless of the excitation of the desired trajectories. Further, the adaptive controller which uses the modified exponentially forgetting least square estimation scheme is shown to guarantee global exponential convergence of the tracking and parameter errors if the excitation of the desired trajectories is strong enough. The superior performance of the new adaptive controllers is demonstrated in computer simulations.