A How to calculate twist rate for a cycloid on a cylinder

[Rdyno]

Hi all this is my first post.

Okay I can have a rifle cut into a barrel at any twist rate I want, so I want to see if a cycloid can work for what I want. Now most twist rates are static so as an example one barrel may be 1 turn in 12 inches for 26 inches an example of what is called a gain twist or as I refer to it as a progressive twist rate the barrel might start or breech at 1 turn in 20 inches and finish at 1 turn in 8 inches at the the end or muzzle. Now I was trying tho think how would I calculate a cycloid along say a 30 inch barrel? So If I want one the barrel maker will want the parameters to input into the CNC lathe I just don't know how to calculate such a parameter.

Also the barrel will be 7.62mm by 762mm long so 30 inch by .30 inch.

I would be grateful for any assistance. The barrel design is for competition use I'm trying to see if a cycloid will be too aggressive on the bullet.

Thanks.
Shane.

Edit I think I put this in the wrong section sorry.

 

[Nidum]

It's a helix not a cycloid .

Think of your rifling groove as being the same as one start of a multi start screw thread but with a very long pitch relative to diameter and only one or a small number of turns .

Cutting such a coarse pitch groove in a small bore and over a long length may not be possible on a standard CNC lathe even with special tooling .

Generally this type of groove is cut by broaching . There are CNC broaching machines which could do this task quite easily .

Modern CAM suites can generate the tool paths to cut a variable pitch groove on a suitable machine from just a few basic dimensions - there is no need to input any complex formulae .

 

[Rdyno]

I understand what you are saying. What I was wanting to know say if you lay a progressive twist rate flat on a 2d surface it's going to make a curve. what I want to know is if you have a cycloid lying flat on a 2d surface how do you twist it into a helix and then get the start twis rate of the cylinder and the finish twist rate?