Quick and accurate angle setting

In other writings on this forum I've advocated the use of a "blue collar" sine bar, i.e., one that can be used in the mill vise while milling without feeling guilty about mistreating a precision instrument.

If you're not inclined to build such a device, there is a simpler way to build a device that will serve as an accurate single angle reference and has the further advantage of not requiring the use of a spacer block to set the angle.

If I take two cylinders of diameters d1 (smaller) and d2 (larger) and lay them in contact with each other on a horizontal plate, a flat plate placed across them will form an angle, theta, with the horizontal given by:

d1/d2 = (1-sin(theta/2))/(1+sin(theta/2))

So, the procedure goes like this: Using your required angle, calculate the value of the right side of the equation above (a scientific calculator is a great shop tool) then pick a convenient angle for d2. Multiply d2 by the calculated value to find d1. Machine a cylinder to that diameter. Pack the two cylinders in the mill vise and lay the work across them. Tighten the vise and mill away.

Update: A more complete discussion of this procedure has been published here...

http://www.homemadetools.net/forum/a...6608#post84001