Gentle persons:

Kirk and others may find the following references to be useful:

1) "The Involute Curve, Drafting a Gear in CAD and Applications," by 
Nick Carter. http://www.cartertools.com/involute.html

2)  "Direct Gear Design for Spur and Helical Involute Gears," by 
Alexander L. Kapelevich and Roderick E. Kleiss. 
http://www.akgears.com/pdf/direct.pdf

Regarding calculating tables of values of Kirk's representation of an 
involute of a circle, or any other parametric equations, don't forget 
that OpenOffice Calc is a fully functional spreadsheet application that 
has all the necessary mathematical machinery including trig functions 
like sine, cosine, and arctangent. OpenOffice is available for and runs 
in Linux, Winders, etc. Like Microsoft Excel, it can generate various 
forms of plots, although I personally don't like either for generating 
publication-ready graphs. It should be easy to code up Calc and/or Excel 
programs to automate the calculations discussed in the above papers.

As for displaying mathematical functions easily, one can take advantage 
of the OpenOffice Math interface, but since I'm an old-fart (it's 
official, even the Social Security Administration says so), I use LaTeX, 
which has been around since the days when all we had were mainframe 
computers (and had to walk barefoot through the snow to hand over our 
punched card decks to the operator at the counter). Now that MathML is 
fairly mature, there is a lot of interest in MathML-based tools. See, 
for example, the following MIT pages on displaying mathematics:

http://web.mit.edu/acs/faq/webmath/contents.html and 
http://web.mit.edu/ist/topics/webpublishing/mathml/

Finally, regarding the Machinery's Handbook, just find the cheapest 
price for any recent edition. I bought my 26th Edition (2002) copy on 
eBay in 2005 for about $35. With the exception of a torn fly leaf, it 
was in pristine condition. Sometimes eBay is cheapest, sometimes 
abebooks.com, sometimes amazon.com. Like everything else, you have to be 
patient.

Regards,
Kent

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