How was h’ calculated?

[Sergiulzr]

Hello,

I would like to know how was h’ (in the below) calculated step-by-step.

Can anyone help me, please?
Thanks!

 

[Steven G]

In the 1st diagram I feel that the result for h is wrong. It would imply that j_min=0 and D_min=d_max and this last statement can't be true. What is j_min anyways????


Diagram 2: What is j₁ and j₂??

 

[Sergiulzr]

For the 1st diagram:
j_min=D_min-d_max


For the 2nd diagram:
j₁=D_1min-d_1max
j₂=D_2min-d_2max

Here is a little engineering. It is called lower deviation. If you want to introduce a bar into a hole(like in this technical drawing) you can have there a diameter diference. So, the hole diameter is bigger than the bar diameter. This difference is called lower deviation and the value of deviation is about few micrometeres.

 

[Steven G]

I still do not see how the result for h was obtained. I think it is wrong!

 

[Sergiulzr]

Why? There are two similar triangles (ABC and ADE). Then he wrote the relations for the sinus and consinus for the angle α. Then he wrote sin^2 (x) + cos^2(x) = 1. From this relationship he calculated h.