A sheath of a delivery system is retracted by winding in cords coupled to the sheath. More particularly, a helical reel is rotated to wind the cords into a helical cord groove and retract the sheath. Rotation of the helical reel simultaneously causes a cord feed ring to slide ensuring that that the cords are correctly fed into the helical cord groove through cord feedthrough apertures of the cord feed ring. Initially, due to a minimal diameter of the helical cord groove, the cords are retracted slowly and with a high amount of torque, e.g., a high mechanical advantage. After retraction of the sheath has begun, the speed of retraction of the sheath is increased with reduced torque as the cords are wound around the increasing diameter of the helical cord groove.
