Perspective drawing of tube with trunnions
Here's the idea, you fill in the blanks. You want to cut out a strip of paper that has the exact same circumference as the trunnion. One edge of the stip will be flat, and the other will have a curve that will be the curve needed to make the trunnion mate with the main telescope tube. (hope that makes some sense).
Top view of telescope tube.
Side view of telescope tube.
S is the length along the circumferance of the trunnion starting from the top side of the telescope tube. Notice that the x in this and the x in the previous drawings are the same.
Ok, here are the equations
The first equation comes from the first drawing, and the second from the second drawing.
Put the 1st and 2nd equations together and you get the third. The last equation is the angle, Theta, expressed as a funtion of the circumferance along the trunnion. Plug this into the third equation and plot S from zero to 2*pi*r and you'll get a plot that looks some thing like this:
