This paper develops a new adaptive control law for rigid robotic manipulators, which is computationally very fast and therefore suitable for real-time implementations. This globally convergent adaptive controller is a modified version of the original scheme presented earlier, but results in simpler design conditions in comparison with the previous work in this area. The convergence properties of the proposed scheme are established through a basic theorem, using the theory of passive dynamic systems. Other aspects of this paper, such as a new general lemma on passive systems, which is utilized in proof of the basic theorem, and a procedure for determining the design parameters, are also of interest. This algorithm is simulated on a digital computer and the results confirm theoretical studies.