You probably won't find it under the name, "dial and sew". The one Liz mentions has 3 dials on the front, your's only has 2 dials and one knob.
Generally speaking, many sewing machines that were manufactured in Japan were sold in the States under several different names depending on the retailer.
I would suggest you go to some of the major manual sites and look at the drawings on the front of the manual. It might say it's a certain brand or it might just have a model number on the manual. I have a manual I bought at an Estate Sale that just says "model 521", with no brand name.
Someone might recognize it and point you to a manual. Otherwise, you'll just have to go through the manuals until you find a matching drawing.
bkay