J.E. Lloyd, V. Hayward A method has been devised for controlling the trajectories defined in Cartesian coordinates near or through the kinematic singularities of robot manipulators admitting a closed form kinematic solution. Our work considers a global approach based on ``path energy functions'' which in the regions of singularities reduce the path velocity in such a way that both joint velocities and accelerations remains bounded without incurring any deviation from the desired path. The existence proof of such path velocity schedules has been established for a large class of manipulators and desired trajectories. An algorithm has been found to construct these velocity schedules in the discrete case.