The problems of coordinated rate control and position control of multidegree-of-freedom arms are treated together in this paper. A mathematical formulation is presented which allows real time computer-assisted rate control under a variety of external coordinate systems. A new solution to the endpoint position control problem is given, allowing the arm to be driven to a final position specified in meaningful external coordinates without the corresponding final joint angles being known. Attention is given to redundant arms, to the possibility of singularities, and to the relation between this work and dynamic control of arms.