Relations between tangential velocity and trajectory curvature are analyzed for tongue movements during speech production in the framework of the 1/3 power law, discovered by Viviani and colleagues for arm movements. In 2004, Tasko and Westbury found for American English that the power function provides a good account of speech kinematics, but with an exponent that varies across articulators. The present work aims at broadening Tasko and Westbury's study (1) by analyzing speed-curvature relations for various languages (French, German, Mandarin) and for a biomechanical tongue model simulating speech gestures at various speaking rates, and (2) by providing for each speaker or each simulated speaking rate a comparison of results found for the complete set of movements with those found for each movement separately. It is found that the 1/3 power law offers a fair description of the global speed-curvature relations for all speakers and all languages, when articulatory speech data are considered in their whole. This is observed also in the simulations, while the motor control model does not specify any kinematic property of the articulatory paths. However, the refined analysis for individual movements reveals numerous exceptions to this law: the velocity always decreases when curvature increases, but the variation of the slope in the log-log representation is variable. It is concluded that the speed-curvature relation is not controlled in speech movements, and that it only accounts for general properties of the articulatory movements, which could arise from vocal tract dynamics or/and from stochastic characteristics of the measured signals.