Stitch length control knob broken on my Necchi Supernova Julia

Doing a google search for the brand plus model number for a user guide or YouTube videos might find what you are looking for. That it is a Necchi doesn't supply the model number and of course models differ. On a 537L model, the large knob on the right side about halfway between the top and bottom of the machine adjusts stitch length. The numbers may range from 0 to 5 with 0 meaning no length and 5 being the largest length. Tension, stitch length and stitch width are all controlled by small dials on the front of the Necchi machine. If your stitch length is set to 0, the sewing machine will not feed the fabric. Incorrect tension will cause poor stitch quality. You must consult you machine's user manual to know how to adjust the tension as the procedure differs among machines. Here is a general guide, however:

How to Adjust the Tension on Sewing Machine

https://www.youtube.com/watch?v=i-7bnb_6EBU Necchi

It is generally the large knob on the right side about halfway between the top and bottom of the machine. The numbers should range from zero to 4 or 5. Zero is zero stitch length, five would be the largest stitch length.

https://docs.google.com/document/d/1OBOahdPrL29joIvK-_sddWvVcUuOblCc50xn2Q8eZrs/edit

http://www.sewingpartsonline.com/instruction-manual-necchi-537-l.aspx

http://www.sewingmachinemanual.net/Sewing_Machine_Manuals/Necchi/Necchi_537-L_instruction_manual.htm

Gillian, try using 2 part epoxy to glue Knob back together, use masking tape to keep knob clamped together till dry.

Necchi BF is a straight stitch machine
Necchi BU is zig zag machine
Necchi BU Supernova had cams for additional stitches

you could try www.sewingpartsonline.com , they stock some Necchi parts.

Are you certain that the pattern selector is set for straight stitch and not buttonhole?

Turn the handwheel so that the needle is up and the take-up lever is in it's highest position. Then turn the pattern selector knob through all of the patterns back and forth a few times. Finally, select straight stitch and see if the length works. If not, need to take it to a repair person to determine the course of action.

I could not think of another way then free-motion sewing.
Drop the feed dogs, and put a spring loaded needle on.

Try the Necchi Yahoo Group. There are members who often sell parts and they also are very knowledgeable and helpful.. You should also try eBay. They have parts for lots of vintage machines. You may not find what you are looking for right away but look often as things show up everyday.
https://groups.yahoo.com/neo/groups/Necchi_Pfaff_Sewing_Machine_Collectors/conversations/messages?messageStartId=9&archiveSearch=true

It's just in the front panel, where the drawing of all the built in stitches are, it's the drawing number eleven from the left, you'll see a zig zag (red) and a straight stitch (black) Select A group of stitches (knob with the arrow) and then select the eleventh stitch (same knob but use the dial, look the manual) and then select zero on your stitch width dial. Hope that helps :)

Try ebay for a parted out machine.