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Thank you everyone who either offered to make a PDF file or went ahead and
made one and mailed it to me.
Here is the PDF version of the spreadsheet.
http://www.brickshelf.com/gallery/GJansson/Diagonals/legogearsanddiagonals.pdf
I suggest that you print it out and try out some of the diagonals.
For the new 12 and 20 tooth gears, there often doesn't even exist a good
vertical or horizontal way of laying out the gears. For example, lets say
you want to mesh a 20 tooth with a 40 tooth gear. The ideal spacing is 3.75
LEGO Units. With a quick glance at the chart I found as many as 4 possible
diagonal arrangements.
The chart is also designed to find acceptable diagonals that can be used for
beams. Everyone knows about the 3:4:5 right triangle combinations, but did
you know that you can also place a beam at the diagonal of a horizontal
offset of 6 LEGO Units and a vertical offset of 3.6 LEGO Units? The
diagonal will have a length of 7 with an error of -0.29% of one LEGO unit
(that is .0029 LEGO Units!) Besides this one I found several more,
especially when you can accept horizontal and diagonal lengths which include
a half LEGO Unit.
Enjoy!
Gus Jansson
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