Help solve complex math problem... reward if found.

[John O]

resizing the screen till the ball measures 1" my measure tape shows 1 3/4 between lines

 

[rwm]

I hope this diagram helps:


We need to find the short side of that triangle. We were given the other side length.
.705/2=.3525 = cos30 x r (r is the radius of the hypothetical circle). Solving that for r=.4070
The short side then = sin30 x .4070 = .2035
So 1 -.2035 + .814 =1.6105

I think this is correct.

 

[WobblyHand]

Without doing this in CAD, from the picture just above, it is hard to tell if the ball is touching at the desired places. What is the significance of the 0.705", are these the desired contact points? The picture seems to indicate contact points at a smaller dimension, but that might be an illusion.

 

[Asm109]

.705 is a basic dimension where the .814 dimension must be in tolerance.

The ball is drawn in by the machinist. There is no assumption or guarantee that it touches the part at the .705 dimension. (it doesn't).

 

[rwm]

.705 is a basic dimension where the .814 dimension must be in tolerance.

The ball is drawn in by the machinist. There is no assumption or guarantee that it touches the part at the .705 dimension. (it doesn't).

You can't know this since the other diameters are not given. It could touch at the .705 dimension .

 

[eotrfish]

Just to confirm - Ischgl99 got it.

 

[rwm]

Just to confirm - Ischgl99 got it.

View attachment 459213

Not fair. You guys are using advanced knowledge of chambers. The .0500 dimension was not given. It was not specified that this was a gauge ball. still good work on solving it! Does this help the OP?

 

[WobblyHand]

My cad shows the ball always hits the ID first and never hits the flat. The ball is too small to hit the chamfer except at the ID.
But this is an under constrained problem - there are missing dimensions, which are essential to solving the problem.

 

[xr650rRider]

This assumes the dimensions give are correct. Problem is a 1" gauge ball is not going to be tangent at 0.705" unless maybe your chambering a .50 BMG.

 

[mickri]

I drew it in Sketchup. The distance is 1.6878" This assumes that the inner dimension is 0.5000 or smaller. If the inner dimension is greater than 0.5000 then the dimension from A to B will be smaller.