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Hi Everyone,
I just created a spreadsheet that I think will be useful to many of us. It
shows the lengths of possible diagonals in terms of LEGO Units. I created it
because I often find myself searching by trial and error for possible
diagonal arrangements for various gear combinations. The spreadsheet
includes a small chart that shows the ideal distance between axles for
different gear combinations. After you have that distance, you can look at
the big chart and find close matches to that ideal measurement.
All the diagonal measurements are rounded to either the nearest quarter of a
unit or half of a unit if the diagonal is greater then 5 units. For each
measurement, I also show the error of the rounding in terms of the
percentage of one Lego unit.
For example, lets say you want to mesh a 40 tooth gear with one of the new
12 tooth gears. When you look at the gear chart, you will see that the
ideal distance between the axles is 3.25 Lego units. Now you can look at
the diagonals chart and find a few close matches. With a vertical offset of
3.2 LU and a horizontal offset of 0.5 LU, there is an excellent fit with a
diagonal whose length is only 1.12% of a LU off. Another close fit can be
found at the vertical offset of 1.2 LU and horizontal offset 3 LU. This one
has an error of 1.89%.
My testing shows that errors as great as 5% are usually no problem for
gears. If the error is more then that, it may be too tight and jam or so
loose that the gears risk skipping.
LEGO Unit terminology:
In my terminology, one LEGO Unit (LU) is the width of a one stud block. It
is also the distance between the studs on a block and the distance between
axles holes on a beam. The height of a plate is .4 LU. Thus a standard
LEGO brick, which is the same height as three plates, is 1.2 LU high. If
you put two beams on top of each other without plates in between, the
vertical distance between the holes of the two beams will be 1.2 LU apart.
If you put two beams together with two plates in between them, then the
vertical distance between the holes will by 2 LU, 1.2 from the height of the
beams and another .8 from the two plates.
The reason that I have horizontal offsets in .5 increments is because it is
possible to combine standard beams with beams that have the holes offset by
half of an LU. Such as the 2 hole length 2 beam. Vertically, I have
increments in .4 of a unit, the same as the height of a plate. I round to
the nearest quarter of a unit when the diagonal is less then 5 because of
the possible gear combinations that need them. Since the greatest distance
between gears is 5 LU, I round to nearest half of LU above that.
Here is the Excel spreadsheet:
http://www.brickshelf.com/gallery/GJansson/Diagonals/legogearsanddiagonals.xls
The spreadsheet is formated to print on one piece of paper in landscape
orientation.
Please, if anyone has the means to create Adobe Acrobat .pdf files, please
let me know. I would really like to convert this to a pdf file to make it
easier for people to look at/print.
Gus Jansson
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Message has 4 Replies:
 | | Re: Length of Diagonal Spreadsheet
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| (...) ---...--- snip ---...--- (...) Gus I can't download the sheet nor can I open it online. If you can email it to me I can convert and return the pdf via email, providing the document isn't too large for your mail box. Dave (23 years ago, 7-Apr-01, to lugnet.robotics)
| | | Re: Length of Diagonal Spreadsheet
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| (...) For gear spacings, you might try: (URL) My testing shows that errors as great as 5% are usually no problem for (...) That *can't* be right. The tolerable error for two 40t gears is no different from the error for two 8t gears - so it's (...) (23 years ago, 8-Apr-01, to lugnet.robotics)
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