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This paper presents the study of an adaptive control which tracks a desired time-based trajectory as closely as possible for all times over a wide range of manipulator motion and payloads both in joint-variable coordinates and Cartesian coordinates. The proposed adaptive control is based on the linearized perturbation equations in the vicinity of a nominal trajectory. The controlled system is characterized by feedforward and feedback components which can be computed separately and simultaneously. The feedforward component computes the nominal torques from the Newton-Euler equations of motion either using the resolved joint information or the joint information from the trajectory planning program. This computation can be completed in O(n) time. The feedback component consisting of recursive least square identification and one-step optimal control algorithms for the linearized system computes the variational torques in O(n3) time. Because of the parallel structure, the computations of the adaptive control may be implemented in low-cost microprocessors. A computer simulation study was conducted to evaluate the performance of the adaptive control in joint-variable coordinates for a three-joint robot arm. The feasibility of implementing the adaptive control in Cartesian coordinates using present day low-cost microprocessors is discussed.