I'm trying to make a nomogram for finding the maximum pressure angle on cycloidal cams with radial followers. See image for the nomogram.
I've obtained the paper from E.C. Varnum where he first created the nomogram. Reference is: "Varnum, E.C. Circular nomogram theory and construction technique. Product Engineering; v 22, n 8; p 152-156, ago 1951"
Since the paper is old and not available on the internet, I've attached the excerpt that contains the problem.
Summing up the paper, in order to create a nomogram to find the maximum pressure angle, the author needs the equation for the angle, which he fully deducts. I'm following the paper deductions, but I'm stuck on how the author turned equation 4 into equation 8.
I am not sure if he used the answer he got from equation 7 to solve for B into equation 4. It doesn't seem so.
Perhaps he made any assumptions and ignored part of equation 4 to make the simplification. The paper is quite old, but the nomogram is widely used in cam theory and I believe there is no mistake on the author's findings. Also, his math from equations 5 to 7 are correct and I've checked them. I don't want to simply accept equation 8 since I want to deduct the equations for harmonic cams and others, and I believe this simplification will be needed for other cams.
Oh well, I made it. I had to use the involute function after all. Thanks anyway.
Solution