Tangent Distance

RJay

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Jul 9, 2019
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Hi Kindly help to solve.
How to find the distance from center of vertical object to tangential point?
Please help me derive a formula.

12819
 

Dr.Peterson

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Please explain in words what you are given and what you want to find. The picture doesn't communicate fully. At the least, it would seem that you would need to know the radius of the arcs, assuming they are circles.
 

RJay

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Hi Dr. Peterson. Thank you for the reply.
First, I have an Elbow(object with an arc) and I have a vertical object in rectangular shape.
The center of the rectangular shape is aligned with center of the Elbow.
The distance from the end of the Elbow to the edge of the vertical object is 20mm with 75mm width
The diameter of the Elbow is 60mm.

I wanted to know the distance from the center of the vertical object to the intersection point (the one I encircled).
Basically I want to know the formula on how to get the distance with "???"
Please let me know if you need more information.

By the way, the distance from the edge of Elbow to its center is 76mm
 

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Dr.Peterson

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You still haven't mentioned the radius of the arcs -- the inside and outside radius of the bend itself. Or is one of those the 76 mm measurement?

It appears that the 75 mm measurement doesn't matter.

Here is a picture that shows all the pieces you need:

FMH116979.png

You have AB = 60 mm; DF = CE = 20 mm; and radius AC. You want to find FG.

One way would be to make a coordinate system and write the equation of the circle through A. Another is to use the Pythagorean Theorem on right triangle CEG (where you know radius CG and length CE) to find EG; then subtract EF (= CD) from that.
 

LCKurtz

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May 3, 2019
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It looks like Dr. Peterson and I were working at the same time. Here's what I got:
elbow.jpg
I get \(\displaystyle x=\sqrt{(106^2 - 20^2)}\) and \(\displaystyle d = x-76 = 28.096109 \).
 

RJay

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Jul 9, 2019
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Cool! :)
Thank you Dr. Peterson for the explanation.
I feel like I've been banging my head against a wall trying to understand this equation but you've explained it well!

Mr. LCKurtz, thank you so much for the illustration. It did help me understand even more.
One more thing, my question may sound basic but how did you get the 46 value? I honestly don't know the radius but based on the illustration radius is 106.
 

RJay

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I got it now! Thank you so much for the help.
 

Dr.Peterson

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I believe the 46 comes from guessing that the 76 you gave for "the distance from the edge of Elbow to its center" means the radius of the centerline of the elbow. If you don't know any radii for the arcs, then you just can't solve the problem!
 

LCKurtz

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That's right. The dotted lines in my figure represent center lines.
 

RJay

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Jul 9, 2019
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Can you please help me find the formula for the second scenario?
I want to find the distance from the center of vertical member to the intersection point which is marked with X.
The center of vertical object is also aligned with the center of the elbow.
 

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RJay

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It looks like this on bird view/ISO view
 

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