The body of each piece is a section of a cone: basically a cone with the top cut off. The pieces are fabricated by bending two pieces of metal tubing: one for the base and one for the neck, and then wrapping a piece of sheet metal around the two rings.



The rough shape of the sheet metal cutout (you can barely see the black-sharpie line -- TODO get a better picture) is pretty simple if you think about it for a few seconds --imagine you took the cone above and rolled it on its side for one rotation. Determining the exact measurements is a straightforward exercise in high-school level geometry....well, it would have been if any of us were still in high school and actually remembered any of that stuff! Fortunately Stephen came to our rescue and was able to walk Tim through it over an IM session (it's a good thing Yahoo IM has that "Doodle" tool!).

Basically, given r1, r2 and h (see diagram above) we needed to determine the radius of the top and bottom arcs and the arc-angle phi. We also calculated the X and Y dimensions of the shape so that we could make sure our sheet stock was big enough.



Once we had worked out the formulas, we built a very simple excel spreadsheet that would output the results for a given set of dimensions -- this let us quickly calculate results for the larger pieces, and it also let us quickly recalculate things when the as-bent ring radiuses were slightly different from the expected ones.

CONTINUE to Building the First Pawn

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