Many robot controllers require not only joint position measurements but also joint velocity measurements; however, most robotic systems are only equipped with joint position measurement devices. In this paper, a new output feedback tracking control approach is developed for the robot manipulators with model uncertainty. The approach suggested herein does not require velocity measurements and employs the adaptive fuzzy logic. The adaptive fuzzy logic allows us to approximate uncertain and nonlinear robot dynamics. Only one fuzzy system is used to implement the observer-controller structure of the output feedback robot system. It is shown in a rigorous manner that all the signals in a closed loop composed of a robot, an observer, and a controller are uniformly ultimately bounded. Finally, computer simulation results on three-link robot manipulators are presented to show the results which indicate good position tracking performance and robustness against payload uncertainty and external disturbances.