Robotized assembly and manufacturing often require to modify the robot motion at runtime. When the primary constraint is to preserve the geometrical path as much as possible, it is convenient to scale the nominal trajectory in time to meet the robot constraints. Look-ahead techniques are computationally heavy, while non-look-ahead ones usually show poor performance in critical circumstances. This paper proposes a novel technique that can be embedded in non-look-ahead scaling algorithms to improve their performance. The proposed method takes into account the robot velocity, acceleration, and torque limits and modifies the velocity profile based on an approximated look-ahead criterion. To do this, it considers only the last point of a look-ahead window and, by linearizing the problem, it computes the maximum admissible robot velocity. The technique can be applied to existing trajectory scaling algorithms to confer look-ahead properties on them. Simulation and experimental results on a 6-degree-of-freedom manipulator show that the proposed method significantly reduces path-following errors.