An algorithm for high-performance path tracking for robot manipulators in the presence of model uncertainties and actuator constraints is presented. The path to be tracked is assumed given, and the nominal trajectories are computed using, for example, well-known algorithms for time-optimal path tracking. For online path tracking, the nominal, feedforward trajectories are combined with feedback in a control architecture with a secondary controller, such that robustness to uncertainties in model or environment is achieved. The control law is based on existing path-velocity control (PVC), or so called online time scaling, but in addition to speed adaptation along the tangent of the path, the algorithm also comprises an explicit formulation and approach, with several attractive properties, for handling the deviations along the transversal directions of the path. For achieving fast convergence along the normal and binormal directions of the path in 3D motion, the strategy proposed has inherent exponential convergence properties. The result is a complete architecture for path-tracking velocity control (PTVC). The method is evaluated in extensive simulations with manipulators of different complexity, and PTVC exhibits superior performance compared to PVC.