JM, welcome back.
There were two Simplexes of Woonsocket. Simplex Tool Company had already been around for some time when they came to market in 1923 with the "Simplex Gray" bench vise. The claimed improvement was the all steel slide which would eliminate breakage. In 1931 the company was taken over by the similarly named Simplex Corporation who continued production of the vises.
The vise line (and maybe whole company) was later sold to Desmond-Stephen and eventually to Ridge, but I don't have any dates for those.
More below with reference info.
-Fred
SIMPLEX BENCH VISE A bench vise known as the "Simplex Gray" is made by the Simplex Tool Co., Woonsocket, R. I. The particular feature of this vise is the fact that it is provided with an all-steel slide for the purpose of eliminating breakage.
1923 Machinery - Volume 30 -- Page 485
The square thread screw is machine cut and is retained in place by a cap in front of the sliding jaw, which eliminates the necessity of coring the inside of the vise for a collar. The Simplex Gray, as it is called, is made in sizes of from 3 to 7 in.
1924 Motor Transport - Page 103
Vise Has All Steel Slide The Simplex Tool Co., Woonsocket, R- I- has placed on the market a vise having an all steel slide. The body of the vise is cast of special crucible metal and the jaws are made of fine grade steel hardened and ground.
1924 The Iron Trade Review - Volume 74 - Page 426
Simplex Corporation, Woonsocket, R. I., has taken over the Simplex Tool Co. The new company will specialize in the manufacture of the Simplex line of steel slide vises developed by the old company in 1924.
1931 Machinery - Volume 38 page 80