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These are fairly easy to rewind. Remove the bolts that hold the recoil housing onto the engine. This is as far as you need to disassemble it. Turn it over and you should see the knot from the old rope get some needle nose pliers if necessary and pull the old rope out by the knot. This is by far the hardest part. Once all the old rope is gone begin to prewind your pulley by turning it in the same direction as if you were pulling out the rope to start it. Wind it up as far as you can until it stops. Now turn it back until the hole in the pulley and the hole in the housing line up. Insert your new rope through the housing hole and straight through he hole in the pulley and tie a knot. Holding onto the rope, allow the spring tension to pull the rope into the housing. Reinstall on your engine.
Where can I purchase new rope?
Any small engine shop will be able to sell you a length of rope. Stay away form the cheap prepackaged replacement ropes that Home depot or other big hardware stores sell. Most of these are cotton rope which will just rot and break again.
You want to stick with a good nylon rope