Need help with some unconventional geometry... (need formula reversed)

[88keys]

This is a formula I came up with some years ago to determine a radius or (r) using a gage pin (D).

Basically, find the largest one that will fit in between the corner and the larger radius and perform that highlighted calculation, and you have measured your radius.

What I want to do now is find out how I could calculate the largest gage pin (D) that would fit if the radius (r) is known.

I tried to jog my memory as to how I came up with this, and I basically pretended that my gage pin diameter(D) was the side of a square, and calculated the diagonal, etc etc to determine 'r', but doing this in reverse isn't quite that easy or I'm just too tired right now.

To clarify, I have a formula to determine 'r' when 'D' is known. What I need is a formula to determine 'D' when 'r' is known.

Thanks in advance

 

[Elixer]

For homework assignments, I only charge AT members $100/hr. Deal?

 

[88keys]

Do you take monopoly money?

 

[Chaotic42]

Keep in mind that I have a fever, but I'm getting s = [(sqrt(2) * r - r] / (1+sqrt(2)) where s is the radius of your smaller circle. So in this case:

r = 195.25
s = [sqrt(2) * 195.25 - 195.25] / (1 + sqrt(2))
s = 80.875198 / 2.41421356
s = 33.5
D = 67

Edit: lost a parenthesis

 

[repoman0]

r = D * (1/sin(45) + 3/2)
D = r / (1/sin(45) + 3/2)

 

[Cappuccino]

You can find the answer on your scientific calculator. Do you know the formula? You should know it if you have given that question. Also D is no answer. It is infinite.

 

[Chaotic42]

You can find the answer on your scientific calculator. Do you know the formula? You should know it if you have given that question. Also D is no answer. It is infinite.

That's what he's asking for, the formula to find D given r. D is only infinite if r is also infinite or if you start straying from normal space. I assumed he wasn't on a Calabi-Yau manifold, but maybe.

 

[Cappuccino]

 

[Fenixgoon]

assuming the equation in your picture is correct, ultimately you just have R = xD, where x is a constant. D = R/x.

now if you wanted to prove it from scratch..i'm too goddamn lazy for that.

 

[Chaotic42]

Like I said, I've got a 100F+ fever and rising, so I might have misread your post. If I came across harsh, I apologize, that wasn't my intention.

assuming the equation in your picture is correct, ultimately you just have R = xD, where x is a constant. D = R/x.

now if you wanted to prove it from scratch..i'm too goddamn lazy for that.

As repoman said, it's just D = 0.3431457505076198 * r since the smaller circle scales with the larger circle.

 

[zinfamous]

Oh, I know the answer!

 

[Pulsar]

D = 2*r*sin(45) / (3 * sin(45) + 2)

Someone will need to check my algebra. Been a while.

 

[sdifox]

If you know the radius of the big circle (a), just find out the diagonal of the square through Pythagorean theorem, the radius of D is (diagonal of square - (radius of a*2))/4

 

[88keys]

Okay, so I went back in some of my other notes and figured this out.


Basically I'm working on Go/No Go Gaging to measure or check dimensions that would otherwise take alot more time using sophisticated measuring equipment.

If I have a radius up against a 45 degree angle, I want to know what is the largest diameter pin gage that would fit in between the radius and the angle.

So if I have a radius that nominally measures 195.25. I would apply the highlighted calculation below to determine the largest pin size that would fit through.

I was also about to slightly simplify my original calculation and, yest I just realized that I'm missing a parenthesis.