Is the featherweight machine made out of metal or white plastic? If metal, it is a vintage featherweight (model 221 or 222). If white plastic, it is the newer featherweight.
The bobbin winder on the vintage featherweights has a rubber ring that fits over the metal wheel; is this the "plastic" piece that is broken? If so, you can easily buy a replacement ring. Just remove the old one and slip the new one on -- sort of like a rubber band. Here's a link to the type of rubber ring I am talking about
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http://compare.ebay.com/like/3901472..._324952&UA=%3F*I8&GUID=1ab5f8dd12a0a0e203f7f407ffdf76a0&itemid=390147270299&ff4=263602_324952