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Interesting. How close to final dimension does the rough stock need to be?, and can you use square blanks from the band saw?

I cut my rough stock on the table saw at 3/8" square. But my input hole on the die was 3/8" . Keep in mind that from corner across on a 45° to other corner will be 3/8 (.375) x 1.4142 = 0.530 (17/32). But it had to fit into a .375 input hole. That meant I needed to shave off .078" off each corner with my hand plane before chucking up into my drill and running into the 3/8" input. I did this in a matter of minutes.
Next time I will cut 5/16 (.312) rough stock. Across its diagonal it will only be .441. This minus .375 means I would only have to shave off .031 (1/32) from the corners. Basically a pass or two on each corner with my hand plane. 
Yes you can use square blanks from your bandsaw. You can cut them to 5/16" or 3/8" square. The corners will have to be knocked off to fit into your round input hole Either way will work. 
Hope this helps. 
Cheers.
Rick

That's pretty cool Rick, your follow up info in the comments is helpful too.

Slick setup. Nicely done.

Maybe this is rhe execution I'm waiting for. Simply because the results are exceptional compared to all other results. Moreover, the jig is quite easy to make.

Thanks for showing us all the test results.

Glad you like it Steve. Hope you give it a try. Cheers! Rick

Thanks Ryan!!

It was easy to make but accuracy in the making is very important. The results were very good and repeatable. I'm thinking now about making one for 3/8" dowel and will see if results are as good and repeatable as the 1/4".

You're welcome Dutchy. Thanks for looking and commenting. 

Looks great Rick!
Requires precision with the jig construction but once perfected, ready for use whenever needed.
Is your router bit a straight flute or spiral?

Thinking I could just cut the "U" relief for the bit with a core box bit of the same diameter. Easier for me to sneak up to the correct depth by raising the core box bit in the router table vs moving the fence.

Maybe that is how you cut your groove?

When I can make some spare time, I’m trying this.
I’ve been using my lathe to make spindles.
It’s good practice for pen making.

Thanks SplinterGroup... originally I was going to use an Onsrud spiral up bit but then decided it would be better to use my laminate flush trim bit. 
I wanted to make sure the hole for the bit was as perfect to the input output tangent point as possible so I marked up and drilled it. Then sawed out and perfected with a chisel. I didn't think about using a core box bit. Sounds like a good option for sure. 

Gary.... go for it! You'll love it. 

Great job Rick! It seems like it might be difficult to match up the router bit hole with the dowel holes to get that perfect diameter. Would you mind sharing your process? 

Thanks Fotodog..... I thought what I provided here would be enough. Now.. I'm not sure what kind of process you're after. Are you looking for a step by step?