In order to access the cord on the Miele S183 upright, you'll need to first remove the handle from the vacuum cleaner. There is a large screw that holds the handle in place that is located under neath of the lower cord wrap hook. Simply remove this screw, and slide the off the vacuum by pushing the handle towards the back of the machine.
Once you have the handle removed, now ope the bag door as if you were going to replace the vacuum bag. You'll see two screws directly above where the bag fits inside of the machine. These two screws will open up the switch and cord housing and give you access to the electrical cord.
You'll see that there are two screws that secure the cord as it comes into the vacuum from the back. Remove both of these screws so that the cord is no longer secured. I think the easiest way to replace this cord is to simply cut the cord (MAKE SURE THE VACUUM IS UNPLUGGED) so that there is about 4-5 inches of the cord jacket (rubber coating around the cord) remaining. You may now just pull this cord jacket off of the cord, along with the paper insulation so you have two bare wires of the old cord. Now take your new cord and push it into the back of the vacuum so that it comes through the switch housing. Instead of having to re-secure the cord with the two screws, I've found that if you tie a small knot in the cord, this works just as well at preventing the cord from pulling through the back of the vacuum.
Simply strip the wires that are left from the old cord, and simply wire nut the new cord after tying a knot (or re-securing it with the two screws), and reassemble the vacuum cleaner. Test the vacuum only after putting the switch housing cover back into place.
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Here's a link to a blown up parts diagram to help you visualize how the vacuum comes apart. http://lib.store.yahoo.net/lib/vacuumcleanerbacgs/miele-s183-upright-parts-diagram.gif
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