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Maths help please: Approximating a Flat Iteratively

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awemawson:
I want to cut spanner flats on round stock in my CNC lathe. I can position the chuck in 1 degree increments and approach the stock with an axially mounted end mill.

I envision positioning the chuck, feeding the end mill a certain X feed, withdrawing it, rotating the chuck to the next angular position and feeding the end mill in a calculated but different X feed then repeating the process.

Now this will make approximations to  flats which are actually a series of scallops with size of scallop depending on end mill diameter and the fine or coarseness of the increments of chuck rotation.

Note: the lathe only can move the cutter in Z (ie towards the chuck) and X (ie towards the axis of rotation) there is no Y movement which would make life so much simpler !

But I can't get my head around the maths of developing a 'general case' that will allow me to write an algorithm with parameters to define the variables. As I see it the parameters are:

a/ Cutter diameter
b/ Angular increment of chuck position
c/ Distance of flat from axis of rotation
d/ Length of flat

My brain hurts, can anyone help?

Sea.dog:
Is there anything you can use here, Andrew?

http://www.cnctrainingcentre.com/news/driven-tools-live-tooling-cnc-lathe/

awemawson:
That's a very interesting link Seadog, but the two case they show one has a Y axis and the other has a continuously rotatable C axis allowing milling while, unlike mine that the chuck can be rotated to position and locked for milling at that angular place.

Sea.dog:
Knowing nothing about G code I had no idea if there was anything of use there.

Thinking on, I'm wondering about how to generate a cam profile for a specific path, from a radiused follower. My gut intinct is, that for a point, it would travel as an inverse of the diametric portion bounded by the chord (i.e. one of the flats).

That's as far as my brain has let me go, so far. This link is relevant to the problem I believe.

https://www.cs.cmu.edu/~rapidproto/mechanisms/chpt6.html

efrench:
I suspect you can use the Pathagorean theorem.  a = distance from the center of the rod to the midpoint of the flat plus the radius of the cutter. b = distance from the midpoint of the the flat to the center of the cutter.  c = distance from the center of the rod to the center of the cutter.  Rotation angle for each cut can be determined from the above. 

For example: If the length of the flat is 10mm, then for the first cut at the edge of the flat, b = 5mm.

I'd post a diagram, but Photobucket says I can only have 250 images and I need to delete 400  :(

p.s. There are quite a few sites for determining cusp height.

p.s.p.s The a,b, and c in my post are not the same as the a,b, and c in the first post   :palm:

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