Welcome, Mrs Martin. You actually have what is called a 15-clone, probably made in Japan post WWII.
Sometimes these machines will have a JA or JC and then a number, which is cast or stamped in the bottom of the machine. There is a thread here on QB
Will the Real 15 clone please stand up It is a very long thread and has lots of pictures of differently named machines. The 15-clones have the needle tension on the nose and a round stitch length assembly. The 15-clones are a tad different than Singer 15 machines of that era, as they thread differently and usually have a drop feed knob on the bed.
A manual can be found at
http://ismacs.net/singer_sewing_mach...ion-manual.pdf
It looks like you have the needle clamp that is on the spool pin on the bed. It may need a thread guide. I would suggest putting an adhesive felt pad on the bottom of the hold down that is screwed to the base and a hole that goes over the bed of the machine
Janey - Neat people never make the exciting discoveries I do.
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