It could well be that another company copied Singer's design; I don't know of Singer making machines under other names but there is a LOT I don't know! The cams for Singer 600's are the same as for the 400's & 500's too, so there are TONS of those cams available; you can probably find some pretty cheap and try them out.
But if you post pictures of the machine and/or the cams you might get better info. The people on this forum know a LOT and someone might even have the same machine with a different name and be able to tell you all sorts of good stuff about it.