This paper presents studies of the coordination f voluntary human arm movements. A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multi-joint arm movements. Coordination is modelled mathematically by defining an objective function, a measure of performance for any possible movement. The unique trajectory which yields the best performance is determined using dynamic optimization theory. In the work presented here the objective function is the square of the magnitude of jerk (rate of change of acceleration) of the hand integrated over the entire movement. This is equivalent to assuming that a major goal of motor coordination is the production of the smoothest possible movement of the hand. The theoretical analysis is based solely on the kinematics of movement independent of the dynamics of the musculoskeletal system, and is successful only when formulated in terms of the motion of the hand in extracorporal space. The implications with respect to movement organization are discussed.