Dynamical models of articulatory gestures relate the velocity of a vocal tract variable to its position via a function with one or more control parameters. In this paper we propose a minimal dynamical model of gestures. The model is empirically motivated by observations of the timecourse of the ratio of velocity to position in bilabial constriction movements by English and Mandarin speakers. We discovered that this ratio tends to follow an exponential growth curve over the course of a movement. A dynamical formalization of this empirical discovery, in combination with an assumption of point attractor dynamics, constitutes the core of our model. The model has only two parameters, T and r. T corresponds to the target position of the vocal tract variable and r corresponds to rapidity. Simulations from the model capture key elements of gesture kinematics, performing much better than the damped mass-spring model. Our model achieves these improvements despite having fewer control parameters. Future work will extend our model to other kinds of gestures besides bilabial consonant constrictions.