Trying to find this part.
It seems to be a 5/16" stub on the bearing end and 3/8" coupler on the lead screw end. I need to get one in 5/16 x 1/2" for a larger lead screw but I don’t know what to search for.
Not sure if langmuir had these made custom, worst case i’ll switch to a pillow block or find a guy with a lathe.
Essentially it is called a lead screw coupling sometimes the term coupler is used.
Langmuir refers to the servo motor end as a screw coupler and on the bearing end a lead screw adapter.
The servo motor side has common availability but you will have to make something up for the bearing end. one thought is turn that end of the lead screw down to 3/8" to fit the current adapter. I don’t recall the OD of the current adapter if it is greater than 1/2" you could turn that down to half and use a standard coupler over it but it maybe under size already from 1/2" I don’t recall. Again you will have to make up something on that end. depending on the scope of you project the pillow block would be the greatest amount of work.
There are several people on here with lathes that likely could turn something for you.
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Realistically it would be easier just to weld a flange on and use a pillow block if it isn’t readily available.
The motor side coupler I found a 1/2" to 1/4" one for $25.
Correction, after some measuring a pillow block isn’t ideally what I want.
It will work but I either have to make a whole new bracket for the end or make something that doesn’t look as clean on the table.
If anyone is interested in turning this for me at a fair price please let me know.
The problem I had with sourcing the part for my build is most companies have a minimum charge for a one off part. I took a shot at making my adaper on a mill. Didn’t turn out too bad.
The issues I had was drilling a straight hole thru the part and the material not being thick enough. I tried to make it out of 3/4" material but it didn’t leave enough material to drill and tap for set screws. My order of operations need to be refined. I was getting a lot of wondering when drilling a hole thru the part. Could be I was trying to drill a hole about 7 times deeper then the diameter of the bit in a not so rigid setup. A lathe would make this so much easier. I also wanted to use a 1/4-20 cap screw instead of the 10-32 cap screw to hold the adapter to the bearing but that was also too big for the part. Haven’t had time to get back out there and try to make another part.
I’m thinking the easiest option would be to turn down the 1/2" leadscrew to fit the existing adapter. I have a few ideas on how to accomplish this without a lathe and might give that a try before making another adapter.
First two attemps.
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I think as you suggested turning down the lead screw would be the best option.
I have a machinist I used for a couple projects who may do it for me for a couple bucks.
You really need a lathe to make that part dead center. I used to have one that I off course sold for space. Now occupied by the crossfire. Ironic isn’t it 
The other easy option is drilling the stock adapter from langmuir to 1/2" which leaves it with only a 1/16" wall. Not much to grip the set screw.
You’ve done well to make that with a mill. I’ve always said if there’s a will there’s a way.