The velocity curves of human arm and speech movements were examined as a function of amplitude and rate in both continuous and discrete movement tasks. Evidence for invariance under scalar transformation was assessed and a quantitative measure of the form of the curve was used to provide information on the implicit cost function in the production of voluntary movement. Arm, tongue and jaw movements were studied separately. The velocity curves of tongue and jaw movement were found to differ in form as a function of movement duration but were similar for movements of different amplitude. In contrast, the velocity curves for elbow movements were similar in form over differences in both amplitude and duration. Thus, the curves of arm movement, but not those of tongue or jaw movement, were geometrically equivalent in form. Measurements of the ratio of maximum to average velocity in arm movement were compared with the theoretical values calculated for a number of criterion functions. For continuous movements, the data corresponded best to values computed for the minimum energy criterion; for discrete movement, values were in the range of those predicted for the minimum jerk and best stiffness criteria. The source of a rate dependent asymmetry in the form of the velocity curve of speech movements was assessed in a control study in which subjects produced simple raising and lowering movements of the jaw without talking. The velocity curves of the non-speech control gesture were similar in form to those of jaw movement in speech. These data, in combination with similar findings for human jaw movement in mastication, suggest that the asymmetry is not a direct consequence of the requirements of the task. The biomechanics and neural control of the orofacial system may be possible sources of this effect.