Why won't my Elna SU model 62c feed fabric through?

It may depend on your particular model, but the Elna SP manual indicates there is a darning and button plate which means the feed dogs do not raise or lower.
Page 36:
ELNA SP Manual Page 23

Here are some tutorial videos that may be helpful:
Elna SU 62C Basics

At about minute 34 of the video, he puts the plate cover over the feed dogs so it is doubtful that your machine is any different.

Sounds like the upper thread is hanging up somewhere. Check that the thread is not looped around a thread guide or is catching on something, like the thread notch on the thread spool, etc. Usually, it is correctly by totally rethreading the machine. When threading the upper thread, be sure to ALWAYS raise the presser foot so the thread will seat completely in the tension disk. If the machine is threaded correctly and still has an issue, there could be a problem with the tension mechanics.

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Lift the pressue foot off the fabric. Hold the thread spool with one hand and lightly pull the thread hanging out the back of the needle. This should seat the tread into your top tension discs properly. Now try sewing again. If it still throws loops, you either do not have your machine threaded correctly or your tension on top is set to zero.

It is likely that your elna graph gear is broken.
remove thread from machine and open door to where you put cams in. Step on pedal and run at full speed. It the mechanism where the cams go spinning? If not the gear is broken.

thread looping on the underside is a symptom of no tension on the top thread so you need to look at the top threading path and the tension dial, is it set to 5? and is the thread pulled fully into the tension disc? Also always thread the top thread with the presser foot raised as this opens up the tension discs so the thread can bed in correctly. If you can see the feed dogs rising up and down above the needle plate during their cycle then they should be gripping and moving the fabric forward. Is there presser foot coming down firmly onto the fabric when you release the presser foot bar? This part does have a big spring inside which applies pressure downwards, maybe this is what the mechanic meant was broken. Was he a sewing machine technician? Maybe try to locate an old school Elna technician, start with www.elna.com and go to your country, then search for a local dealer.

Really you are very appreciated in your machine maintenance. If you wanted to Elna SU 62c machine bobbin case
please see the link :
http://www.ebay.com/bhp/elna-sewing-machine-bobbins .

It's most likely not the machine. It's the other things, ie needle, thread, etc. combination. For sewing knit, be sure to use a ball point needle. The needle eye size is important to so the thread is neither too small nor too large for the thread weight.

FWIW, it sounds like bird nesting. --the thread is not seated completely in the tension disk. Remove the top thread from the machine and ALWAYS RAISE the presser foot when rethreading!

Also, check that the tension is appropriate for the project. The two threads should meet in the middle of the fabric. If there is top thread showing on the underside of the fabric, the top tension is too loose. Tighten it until it until the top thread pulls the bobbin thread up into the fabric.

All About Needles SCHMETZ Needles

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you need to check that the top thread is corrctly into the tension device, this is the most common cause of looping on the underside of the fabric because the tensioner is not pulling the top thread back up to the fabric surface as the needle is raised during the stitch sequence. Check that the tension is set to the middle number, usually 4 or 5, and that the thread has gone into the tension device. Always thread with the presser foot up, as this opens up the tension device so that the thread can seat fully.

Also double check that the bobbin thread is also fully into the tension spring and that the bobbin is in the right way, the thread needs to come off the spool and make a "V" shape as it reverses direction through the tension spring. If your bobbin is the same top and bottom, (ie plastic clear ones) it is easy to drop it in in the wrong direction. Some models have a little image on the clear bobbin cover showing right direction of rotation. Usually, when you pull thread, the bobbin will rotate counter clockwise (this is for horizontal top loading bobbins such as the modern Elnas).

If you can't find your manual then try this link to download a new one.
http://safemanuals.com search on Elna, then you should see a list of models over on the right including the 6005, click on it, then you'll get the option of giving your opinion, or using the security code to download. Click on the security code, watch the four digits that come up, and enter them into the other window alongside. You'll then get the download box. Wait for the pdf to load, its a large file.

Goodluck with your Elna.

It sounds crazy but if you have loops on the underside of your fabric it means your upper thread is not properly threaded (and vice versa for loops on the top of your fabric). So re-thread your top thread, change to a new needle if you've been sewing with it for a months and you should be good to go. Let me know if you need any more help.

I have a 26 year old Elna and this is the only weakness it has. Before sewing, try this. Turn the wheel manually and watch the upper thread pick up the bobbin thread. Pull both back to the left. Make sure they are plenty long. This helps me prevent the tangling in the dogfeed. My Elna has a universal tension on the bottom and I haven't ever had a problem with it unless the top tension is too tight.