Just cleaned the 3880. It wasn't grabbing paper...
My expert told me to use WD-40 and lots of paper towels. It was a matter of cleaning/renewing the grabber eccentric wheel on the right side of the paper feeder and with the printer off, carefully turning the wheel with my finger and a paper towel with WD-40.
After a few turns and rubbing the grabber with the paper towels, I cleaned up the feeder and wiped things down with dry paper towels. I stuck plain paper in the feed and with the control panel, fed several through and its working quite well!
As always, your results may vary and if you damage your printer, that's your fault ;-)