Making round stock into octagon

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shocktower

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My son want's to make some ink pens ( he is doing 90% of the work), I got some Ti 9/16 round stock, and he wants to make the pens into Octagon, what is the formula for this, I have a Bible and cannot find it.
I told him I would just take some Aluminum stock and figure it out ( I am not good at Trig ) what say you guy's.

Thank you for your time
 
If you have a copy of the Machinery then look for an inscribed octagon to get the dimentions for the chords.
You will need a rotary table or a spin indexer to move the cylinder in the eight sided set up.
 
You will need some type of indexer to do that. Each flat will be 45deg.
 
I just did the little trig problem to solve the generalized case and it's way too late and I'm way to tired to show the proof but... The formula you want to determine how much to take off after touching-off the part is:

Radius - Radius x Cos (Angle) where Angle is 45/2 (=22.5) degrees and Radius is 1/2 the diameter of the stock. 45 is the base angle because 8 x 45 = 360. This will make an octagon of maximum size for that diameter shaft. Once you calculate that value, put the part in the mill, touch off and zero the bit and cut away the amount you calculated then, rotate the part 45 degrees and cut to that same depth again. For a 2" diameter piece, the amount you cut down into each side would be 0.076"

This formula will work for any arbitrary angle. If you want to make the largest triangle, the base angle is 120 degrees and half that is 60. Therefore, for a 2" diameter piece, the radius is one and you get: 1 - 1 x Cos(60) = 0.5" In that case, you'd setup the piece by touching the top, digging-in 0.5" and flatten one side then, rotate 120 degrees and take the next surface off.


Ray
 
Dia x .86603 = H

H - Dia total removal

TR / 2 = cord

.86603x1= .86603

.86603 - 1= .13397

.13397 / 2 = .066985 your cord
 
Hey thank you guy's, and yes I have a rotary table.

Thank you again

- - - Updated - - -

Hey thank you guy's, and yes I have a rotary table.

Thank you again
 
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