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Flip the vacuum over and remove the bottom plate from your vacuum using a screwdriver. Once you take off the back plate, you should see the roller brush and the belt connecting to the motor. Keep your vacuum unplugged while replacing a belt so it doesn't run and catch your finger. If your vacuum has side suction, look for the belt on the side opposite of where the hose attaches. If you have a vacuum that has a central suction unit, the belt will be in the middle of the bottom plate. Unloop the belt from the metal spindle and from the roller brush to take it off. Some vacuum cleaners require you to remove the roller brush in order to replace the belt. Loop the new belt around the metal spindle connecting to the engine. Then stretch the belt taut so it loops around the roller brush. Check that the belt isn't scraping against the side or scratching anything. Replacement belts can be purchased online, or from vacuum repair shops. The belt you need may depend on the model of vacuum you're using, so make sure to search for belts made for the machine you have. Before you replace the bottom plate, spin the roller brush slowly by hand so the belt can rotate. Make sure the belt doesn't snag or pinch on anything inside your vacuum or else it might break again. Keep your vacuum upside-down as you plug it in and turn it on. Check the roller to see if the belt is making it spin. If it still does not work, there may be a problem with the motor and it will need to be checked by a technician.
Open the bottom of your vacuum cleaner with a screwdriver. Locate and remove the belt on the side or center of your vacuum base. Place the new belt on the spindle and roller. Turn the roller by hand to check for any pinches or snags. Try running your vacuum to see if it works again.