A reader asked for a photo of the bobbin case position on a 328. Fortunately I still have one of these machines and was able to photograph the bobbin case for her.
It occurred to me that a little photo tutorial on how to remove the bobbin case of these types of machines might be helpful. The 401, 403 and 404 all work the same way, basically. So does the 337 and I imagine the 338. I don't have a lot of experience but I think most of the newer top loading class 66 machines might work this way. Not the 201. That bobbin case is totally different and if you want to learn more about it go to The Vintage Singer Sewing Machine Blog http://vssmb.blogspot.com/2011/07/how-to-remove-201-bobbin-case.html
First remove the needle plate. It merely lifts off.
Raise the feed dogs to the highest position and lift the position bracket up and to the right.
When replacing the bobbin case be sure it is sitting just so and don't forget to move the position bracket back into place.
If the bobbin case is loose in the hook, it is possible to adjust the position bracket so that the bobbin case sits more snugly. I loosened both screws a quarter of a turn and gently moved the bracket toward the bobbin case until it felt snug. Then I tightened the screws.
This bobbin case has a bit of a rasp to it somewhere in its cycle. I don't think it is because I tightened the bobbin case. It was pretty raspy before I did that. The machine turns smoothly when the case is out. But when it is in place, it whispers. If there isn't any oil on the thing it grinds. The whole machine does need servicing and I suppose that will be on the agenda for tomorrow. The forecast is for rain, so I won't have to weed the perennial bed. Oh darn.