The task-dynamic model of sensorimotor coordination [20][21][22][23] is reviewed, highlighting the issues of the coordinate systems involved (e.g., articulator vs. task coordinates), the mappings between these coordinate systems, and the dynamics defined within these coordinate systems. The empirical question of which sets of coordinates are the most appropriate candidates for the control of speech and other tasks is addressed through the introduction of the uncontrolled manifold method [24][25]. This method is introduced using the non-speech example of planar reaching using a 3-joint arm, and is generalized to speech production. In particular, it is shown how the method can be applied to skilled behaviors, such as speech production, in which there is no analytic formula that can be (easily) derived between the hypothesized coordinate systems underlying the skill, e.g., the forward kinematic mapping from articulator positions to acoustic/auditory coordinates.