You name it

[Northwoods]

What is the general name for the device that clamps into a carpenter's brace and then connects to sockets?

[turnnut]

just a rough guess, " BIT BRACE SOCKET ADAPTER"  ???

[Bill Houghton]

Lee Valley calls it a "brace driver."  I'm not sure what the generic term would be.

I don't know who else is making them these days; I do remember talking with an auto shop instructor once and wondering, idly, why no one was making tools to turn a brace into a mechanic's tool*.  He said something to the effect that they just weren't the right sort of tool for that purpose.  My later reading in old shop literature revealed that, in the late 19th/early 20th century, metal-bodied braces were used in just about all the mechanical trades...but the practice fell away, and later generations forgot.

*I could, of course, have purchased a speeder wrench instead, a tool that is functionally identical to a brace with a square male drive on the end to accept sockets.  I did, later, when I found them in yard sales.

[Northwoods]

What is the general name for the device that clamps into a carpenter's brace and then connects to sockets?

Well, of course, it doesn't connect to a socket.  It IS a socket.  Found its mate on Ebay.  It seems to be 5/8".  I wonder if the 19 32 is actually 19/32.  That is what mine looks like.
Hargrave with a circle H mark (as found on Craftsman tools) just above the name.
Fixed socket and modern speed wrenches crowded these out of existence.

[Bill Houghton]

No pictures?

And, I bet, the 19 32 does indeed mean 19/32.  There were a couple of sizes of 32nds that were once quite common on machinery.  Chevrolet was particularly fond of these sizes, I believe.

I've got a couple of sockets with short shanks and square tapers to fit a brace.

[Northwoods]

http://www.ebay.com/itm/Vintage-HARGRAVE-NUT-DRIVER-BIT-for-Brace-Drill-19-32-155-/282218931902?hash=item41b58f26be:g:6y4AAOSwPCVX~9vv

Should we assume that the H-Circle indicates New Britain as found on earlier Craftsman tools?

[lptools]

Ween't those simply called nut drivers? They were used by lineman for the square nuts, lag screws, etc.. I have a couple that are stamped Bell System. Regards, Lou

[turnnut]

 they came in square and hex.  also screwdriver bits.

[Chillylulu]

5/8" is a valid drive size.  I have both male and female adapters. One is a recent Brazil Tools (S-K) find.  I found all the  sockets, including 31/32". 

I think Snap-On had a 5/8" drive.  At least Snap-On and Plomb had 9/32" drive sizes.

I've spent too long pressing a 1/4" socket off of a 9/32" driver.

Chilly

[john k]

About using a brace for turning sockets, it all came down to money.  I have several square sockets, 1/2, 5/8 and 3/4, called wagon wrenches, for assembling wagon boxes back in the day.   First 20 years of the last century, money was darn tight, and working men didn't spend on any frivolous extras.  If one owned a brace, then why buy a speed wrench?   Except the manufacturers caught on quick, and started making socket wrenches, with fixed handles.   Then Snap-On came along and that changed.  Handles with interchangeable sockets, how innovative.   The early detachable sockets I have seen seem to be all hex drive, Mossberg  and others made sets.  So actually by the time interchangeable sockets came about, the speed handle was already here.