This work introduces a time-adaptive strategy that uses a refinement estimator on the basis of the first Frenet curvature. In dynamics, a time-adaptive strategy is a mechanism that interactively proposes changes to the time step used in iterative methods of solution. These changes aim to improve the relation between quality of response and computational cost. The method here proposed is suitable for a variety of numerical time integration problems, for example, in the study of bodies subjected to dynamical loads. The motion equation in its space-discrete form is used as reference to derive the formulation presented in this paper. Our method is contrasted with other ones based on local error estimator and apparent frequencies. We check the performance of our proposal when employed with the central difference, the explicit generalized- α and the Chung-Lee integration methods. The proposed refinement estimator demands low computational resources, being easily applied to several direct integration methods. Copyright © 2012 John Wiley & Sons, Ltd.