A rotary catheter for opening partially and totally obstructed bodily vessels of varying diameter (e.g., blood vessel) which comprises a motor-driven flexible hollow shaft rotatably disposed in a flexible tube, an aspiration channel defined between the flexible tube and the hollow shaft, a tip affixed to a distal end of the hollow shaft having a rounded distal end being rotatable and slideable over the guidewire, the tip having sides, a base and a crown that is offset away from a longitudinal axis of the hollow shaft further than the base and a distance between the sides being smaller than a distance between the crown and the base leaving open passages along the tip, the guidewire can be withdrawn proximally to allow the rotating crown to displace the distal end of the tip away from said wall of said vessel to tunnel through a total obstruction.
