Ribbing attachment under the Singer 555 name matches is standard-gauge knitting machine Singer 555 and very likely its clone, Silver SK103.

Judging by the simplicity of the connecting arm, it is very likely that the carriages of the main needle bed and the ribbing bed are moved one after another (not simultaneously as in late models). Vintage Brother machines (like KH551 and KH585) when in double-bed configuration (AKA, attached to the ribber) operate similarly. Watch my video shown that vintage Brother ribber operate to get an idea how this Singer 555 ribber will work.