Open your umbrella, and lay it down. Remove the crank from the umbrella pole. Unscrew all the screws to remove the plastic housing, and use the socket wrench to remove the crank from the other end. Pull the string connected to the crank out of the umbrella pole.
Unscrew the pulley from the top of the umbrella. Push the top off of the umbrella, and bend the tilt.
Burn the end of the new rope to prevent unraveling, and push the rope into the tilt of the umbrella toward the top of the umbrella until the rope goes through the top end.
Tie the rope to the pulley at the top of the umbrella, and place it through the pulley's hole. Place the pulley back into the umbrella's pole. Screw the pulley back in place.
Thread the rope into the bottom side of the umbrella pole from the tilt area until it reaches the crank. Close and open the umbrella with the rope to see how long you need the rope to be. Cut off the excess rope, and burn the end of it. Push the rope through the right hole, and run it into the crank. Make a knot at the end of the rope.
Push the knotted end of the rope into the pole, and place the crank into the hole. Pull the string from the top to tighten it. Use the socket wrench to tighten the crank to the pole, and screw the housing unit over it. Turn the crank to open the umbrella all the way.