I want to know how to rewire a sewing machine foot controller (pedal) which has the plug and the controller on one cord, and how to know if the updated controller is safe for my vintage machine. If you need pictures, please let me know!

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Pictures are always helpful. The older machines used a foot switch controller that was a variable resistor of fairly high wattage. Current machines are computer controlled and use an entirely different control method. The two foot switches are probably not compatible.