Hello,

Sorry for the vagueness, perhaps a picture will help. Both points are on the truncated cone and the tapered helix is following the cone surface. If there was some way to pull the helix to the red point since the pitch is not known, it's a bit of a chicken/egg issue. The pitch would change along the same axis as the helix while following the parameters set for the tapered helix. I don't think a 1D scale will work since that would then have the tapered helix deviate from the truncated cone surface.

Hi OSTexo, just want to make sure you didn't miss my second post above...

Your additional picture above there helps to explain what you're looking for a bit more, thanks. But yes I think that like I wrote above just being able to put in 2 points as the pitch will not help you at all for your particular case here, because the particular distance you are interested in is not at a full revolution from the start point.

But I'd think you could measure the distance in z between those 2 points, and also measure the angular deviation between the start point and your target point as viewed down the z axis, then scale up that distance by the angular deviation to get the actual pitch value. I think...

- Michael

Hello Michael,

Yes I did, thanks. The distance in Z between the green and red point is 2.4351833. The angle between the green and red point when viewed down the Z axis is 71.9037512 degrees. I tried fiddling with the numbers a few different ways but am missing something. My uneducated guess is I'm trying to solve this linearly when the helix looks like it involves some higher math other than arithmetic. I found this article, it looks like something relevant, but I can't make sense of it:

http://tex.stackexchange.com/questions/129860/helix-on-a-cylinder

Hi OSTexo, well a helix is a pretty linear progressing thing, generally I think linear reasoning should work with it.

The way I'd do it, is that you want to measure the angle that your red point has traveled along the helix, so you want to use the longer angle of 288.0962488 degrees, not just the smallest angle between them.

So at this angular travel station of 288.0962488 degrees, your point has traveled a distance in Z of 2.4351833 . To get the pitch you want the distance that will be traveled at a full 360 degrees, so the conversion factor is 360.0 / 288.0962488 - multiple the current distance of 2.4351833 by that conversion factor to get the pitch:


360 / 288.0962488 * 2.4351833 = 3.042962


Does that work to get you the proper pitch?

- Michael

Hello Michael,

Right on the money, thank you very much for your help, I don't think I would have figured that out despite passing the first grade.

You're welcome!

And you're probably all set now because you already know the height and top/bottom radius of your cone.

It should also be possible to calculate the bottom radius just given those 2 points as well, to do that you'd measure the radius at each of those points and get the change in radius, then multiply that by the same angular scale factor (360 / 288.0962488) and that should give you the change in radius for a full turn, so multiply that by how many turns you want and add that to the top radius to get the bottom radius.

- Michael