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what exactly are you trying to do??/
need a better picture in my head...
dimensions would be nice...
 

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Across the width, or down the length? Size of the dowel and of the mortise, or the tennon.

Either way, you can cut two 45 degree strips in a 2x4, leaving you with a V groove into which you would clamp the dowel. This would be the basic setup whether you wanted to make a tennon on the end or a mortise in the middle somewhere. How you cut the tennon can vary, from using a Japanese pull saw to using a dado stack. Either way, the V groove and a clamp will stabilize the dowel as you make the cuts.

The simple illustration is the essence. If you're cutting a tennon on the end, let the dowel hang over one edge, put the 2x against your miter gauge and use the TS blade to flatten the tennon, flip the dowel over (measure carefully!) and cut the other side. You'll probably have to do some chisel work to shape from round to square for appearance sake.

If you're cutting a mortise, on a drill press, make sure the cut is made where the 2x supports the dowel.

Clamping could just be a strip of wood across the dowel and a couple of bolts sticking up from the edges of the 2x, through the strip of wood, with butterfly nuts to tighten the wood down. I'm probably use a hardwood for the V piece so it's less likely the wood will split. Pre drill a hole for the bolt and maybe use a fender washer underneath, countersunk a little bit, to spread the force of the tightened bolt across the 2x while keeping the bottom flat. Simple, cheap, make it from scrap.
 

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bore out the end and dowel it if it's large enough...
 
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couple of ways to bore out a dowel end...

V notch the end of a 2x...
install a drill bit the same dia as the dowel in your DP...
slide the V notched 2x up to the bit and clamp the 2x to the table...
change the bit to the desired 2nd bore size...
inset the dowel to be drilled into the V notch and clamp that in place...
the dowel will be auto centered to the bit...
bore the hole...

install a drill bit the same dia as the dowel in your DP...
bore/drill a hole in your 2x near the end... edge drill for longer dowels, face side for shorter dowels..
saw of the end of the 2x cutting through the bored hole leaving 60~70% of the hole...
set the 2x back on the DP w/ the bit you drilled the hole w/ set in the drilled hole and clamp the 2x in place...
change the bit to the desired 2nd bore size...
inset the dowel to be drilled into the open sided hole and clamp that in place...
the dowel will be auto centered to the bit...
bore the hole...

either works w/ a 4x4...
a 4x will give you better stability..
 

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yikes!!!
 
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plug cutter.. dowel piece insert...
plug cutter will be the easiest w/ a clamping set like I described..

cut on the RT...
whichever is easiest for you..
 

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Larry I don't normally correct spelling but you want a tenon and not a tendon. The only reason I'm doing it here is that if you tried a websearch using that spelling you won't get anything like what you are searching for.

Papasombre uses a method similar to Paul's but using a table saw instead of router in a router table. Both will work and the result is guaranteed to be dead center, at least if the starting dowel or rod is round and not eccentric.
 

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I have a 5/8" Dowel and I want a 3/8" tendon cut on the End.
Larry if you have a router table, the set up that I posted should work for you. You just need to raise your router bit 1/8 inch and rotate your dowel. Set the fence of your table to adjust the length of your tenon. If you want a rounded instead of sharp edge use a bowl (tray) bit.
 

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Charles, thanks for noting the difference - isn't it possible for you (or any mod) to correct the title of the thread?
Done. I don't often edit the titles unless the spelling makes the poster's intent confusing because as Stick said "most of us speak typonese here". And are guilty of some too. Especially when I use that accursed little phone keyboard. But I begin to digress.
 
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