I don't know if you have looked it up but Singer bought up another sewing machine company Wheeler and Wilson in 1905. The production at the factory was kept up until 1914 and I think it's mostly W&W No. 9 and 12 that was sold under the Singer name. I think yours are a variant on No 9. I haver never seen either of them in real life, but rumor has it that No 9. was even smoother than Singer's model 66, it's closest competition an the time. It's probably very simplified since there were a few producers with individual develompents in those years.