Trajectory scaling techniques adapt online the robot timing law to preserve the desired geometric path when the desired motion does not respect the robot limits. State-of-the-art non-predictive methods typically provide far-from-optimal solutions, while high computational burdens are the main bottleneck for the implementation of receding horizon strategies. This paper proposes a predictive approach to trajectory scaling subject to joint velocity, acceleration , and torque limitations. Computational complexity is dramatically reduced by means of the parametrization of inputs and outputs and the iterative linearization of the optimal control problem around the previous output prediction. This allows the online implementation of the method for sampling periods in the order of one millisecond. Numerical and experimental results on a six-degree-of-freedom robot show the effectiveness of the method.