Fredrich Wilhelm Müller junior's patent of 1888 can readily be identified as the basis for the now famous Müller no.1. The specification features the lever-action drive (visible in fig.1) and the forward motion walking presser foot feed - best viewed in fig.2.
Included below is Müller's opening patent statement, which clearly identifies the machine's intended market :-

"My invention relates to improvements in sewing-machines, particularly in small toy or pocket sewing machines for the use of children, and the object of my invention is to provide a construction, which, by its great simplicity, may be readily used by any child without preparatory practice, and without the assistance of adults, while, with the toy or pocket sewing machines, hitherto in use, children, in general, are not able to sew by themselves; such little machines, instead of amusing the child and affording a useful occupation are only a source of annoyance. The improved machine of my construction offers, besides, the considerable advantage of being the cheapest of all which for toy machines, is an essential condition for securing success."