How Do You Calculate the Distance ACD with Six Variable Geometric Parameters?

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The discussion focuses on calculating the distance ACD using six variable geometric parameters: radius (r), wall thickness (wt), distance between A and B (abd), angle of the blue line (abl), length of the two purple lines (pll), and distance between the two purple lines (pld). The relationship between these variables is crucial for determining the distance ACD, particularly how the angle and wall thickness affect the positioning of the purple lines within a 1/2-circle. The conversation highlights the need for advanced mathematical techniques, including trigonometric calculations, to solve the problem effectively.

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SpaceLight
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See attachment, please.
Six variables that can change individually and hence altering all connected.
The goal is always to find the distance between A & C, "ACD" if you will.

ACD = ...
Given 6 flexible variables:
(Abbreviated to perhaps make things easier: r, abd, wt, abl, pll, pld. Use or not, up to you.)

> r = radius of 1/2-circle
> wt = wall thickness of 1/2-circle
> abd = distance between A & B
> abl = angle of blue line
> pll = length of the 2 purple lines
> pld = distance between the two purple lines

Constants:

* The purple line inside the 1/2-circle is in contact with the inner wall. (Blue line angle changes and along with it changes the position of purple lines, and inner purple line always meeting with inner wall, as shown.)

* The blue line always through center of the two purple lines, and the two lines always perpendicular to the blue line.

* Distance between the two purple lines, whatever it may be, will always be divided by 2, for finding point C.

* Point B always along 'A' line, zero degrees.

* 'abl' always through point B.

My simple notes so far, maybe helpful...:

* Position of inner purple line dictated by abl, wt, pll.

* Radius of 1/2-circle minus wall thickness, r - wt = ... That new radius, along the inside wall, where the inner purple line is in contact with.

* Calculating for sin of theta, maybe involved, I can do that, but that's about it for my resourcefulness, individually...; I have more notes, but they seem to cause more stress than clarity. Seems to be very advanced mathemetics, multi-dimensional sort of geometric thinking, I can't even figure out where to start.
It's improtant, though...
I hope you can help.

Ask questions. I'll revise up here if I should have included more points...

Thank you.
 

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I'm not interested in this problem, but here's a picture so people don't have to hunt for it.

https://www.physicsforums.com/attachment.php?attachmentid=68158&d=1396223228
 
Thanks :)
(my first post on a forum...*red face*)
 

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