Machine Design 1

Cover Machine Design 1
Machine Design 1
Forrest Robert Jones
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And since FI is any normal to OP, they are also true for all normals to OP. The diagram, therefore, can be used for any datum line between and the intersection of the curves A and B.
The above demonstration may be expressed as follows : For any given value of E — r, whatever the values of E and r, E is always a certain fixed amount larger and r another fixed amount smaller than the corresponding p, the value of d being constant.
A numerical example may serve to make this more clear. Take XY at
...a distance 4.187 above OP. This makes p' = 2 = distance from XY to the intersection of A and B, this distance being chosen simply as a convenient value.
Then L' = Z(np' + d) = 2(2tc + 10) = 32.5664.
Take #'-r' = 0.5; then n(E' + r') = V- 2 VlOO - .25 - 2(0.5)(arc sin" 1 ^) = 32.5664 - 19.975 - .0503 = 12.5411.
Therefore E' + r' = 3.992; and, since E r - r 9 = 0.5, E 9 = 2.246; E 9 - p' = 2.246 - 2 = 0.246 ; r 9 = 1.746; p 9 - r' = 2 - 1.746 = 0.254.
The values 0.246 and 0.254 show the same increase and decrease of diameters from p 9 as when p= 6.817 measured from OP as a datum line.


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