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High-speed path tracking with a kinematically redundant manipulator mounted on a flexible base is addressed. Thereby, possible vibrations of the base are to be suppressed. In general, the presence of kinematic redundancy allows these two subtasks to be performed simultaneously. In practice, however, this can be done only within very limited areas of workspace, separated by singularity loci that change dynamically while the end-effector tracks the desired path. To avoid controller performance degradation in the neighborhood of such dynamic singularities, and to allow transitions between the distinct workspace areas through singularity boundaries, we propose here a new method for reactionless motion generation within a specified neighborhood of the singularity. In contrast to previous works, this method makes use of a nonzero coupling momentum which is conserved upon entering the neighborhood.