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I also use sewing machine oil.
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Sewing machine oil. Perfect for the job, and readily available. But it should ONLY be used after the parts being oiled have been completely cleaned...
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So I took off the shell and looked at the innards and tried to figure out what was going on a little more. I didn't find anything to be fixed, but I did notice
1) Definite resistance on the carriage rails, perhaps the bearings are stuck or dirty
2) There's a spring underneath that does expand when the carriage actually advances, and doesn't when stuck. But this seems like a symptom, not the problem.
3) Gravity helps! When I tipped it on its left side, the carriage advanced more often than when it's resting horizontally. So is the main spring weak?
4) The carriage often catches when all the way to the left and I push it over to start a new line. I have to jiggle it before it will slide on the rails, and then I notice problem 1 again.
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For any interested party, I took it to my "local" repairman, who discovered after much tinkering that the issue was with the spacing mechanism. He adjusted it and now it works great!