These plastic pieces come with lampshades and are used to support the shade in it's box (I seem to recall). If you know somebody or someplace that sells lamp shades you can probably get them in bunches from the store, maybe at the dumpster. The round plastic top is what "scratches" your back. It's simpler and safer than some of the tools with "fingers and finger nails" made on them. The dowel handle could be improved with something rubbery (comfortable feeling) maybe?
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For a couple of months my itching back has been driving my husband and I crazy. Plastic back scratchers are easily broken. I needed something long and strong enough for frequent use.
When your back really itches and there is no one to scratch it and no way to reach it, try rubbing the itch up and down on a corner of an open doorway. Isn't that much better? I know! It works!