Astronomical gear train/gear ratio calculation tool for linux?

[BastardNamban]

I already searched through all the stickies and program database for anything I thought might help me, and found nothing I can figure will, so I'm asking here.

I am looking to plan out some special clocks, and while I know what ends I need to achieve, I don't know of any program for linux
that could help me calculate the special gear train ratios I need.

See, these are going to be astronomical clocks, for my own personal use. They involve some more complicated gear ratios that are non-standard,
and thus, not easy for me to calculate without software- I can, but it is arduous to say the least.

For example, I'm trying to make a new solar-sidereal gear train, and need to create a gear ratio of exactly 1:1.0027379.
I know others have done this with between 4-20 some odd gears, but I need to create something new.

Basically, what I need is something that can take a given final ratio, and show me what in whole numbers in the form of fractions
what numbers for a given number of gears can make the ratios I need.

For example, here's a version of what watchmaker Breguet came up with:

(51 teeth/82 teeth) x (79 teeth/49 teeth) = 1: 1.00273768 (solar:sideral ratio; the true ratio for the spacial relation is 1:1.0027379)

Using that kind of clockmaker's layout, I need something that can help me calculate for, given the number of fractions (each a gear and pinion combo)
I choose to use, and a final given ratio, whole numbers that will produce the result.

I'm sure this would be simple for some sort of existing software, probably some form of spreadsheet calculation, but I am a novice in such matters,
and am not sure what would work best for this.

Can anyone point me in the right direction for what can do this? Any sort of astronomical phenomena calculation program suggestions would be welcome too.
I just haven't been able to find much despite looking for a few years on and off now!

[radioboy]

Looks like some sort of constrained optimization problem...
Check here: http://wiki.cacr.caltech.edu/danse/i...ion_Algorithms

[BastardNamban]

Thanks for the reply, but I have no idea whatsoever what anything on that page can do for me.

I understand what an optimization problem is, and I agree- but finding a way to implement such a layout in software is what confuses me.

Any mathematicians out there that can sugguest a simple solution for something like this? A program that solves for ratios with a simple fractional layout like that listed above would be a huge boon to clockmakers. That layout is needed for us to do whole number gears in proper ratios.

[oldfred]

clockgear.pyI created a brute force try all combinations and only print out the ones with small error. It trys all gears in a range so for a set you get your answer 4 times as each gear can be 51, each gear can be 82 etc.

I print calculated ratio, error, and the four gears. You will see all those with exponent of 7 are the same four gears. I am trying to teach myself python so I do not expect this to be considered "good" code.

fred@fred-desktop:~/Projects/PyAssetTrakkr$ python clockgear.py
1.00273768044 2.19561971271e-07 51.0 79.0 49.0 82.0
1.00273768044 2.19561971271e-07 51.0 79.0 82.0 49.0
1.00273972603 1.82602739729e-06 54.0 61.0 45.0 73.0
1.00273972603 1.82602739729e-06 54.0 61.0 73.0 45.0
1.00273972603 1.82602739729e-06 60.0 61.0 50.0 73.0
1.00273972603 1.82602739729e-06 60.0 61.0 73.0 50.0
1.00273972603 1.82602739729e-06 61.0 54.0 45.0 73.0
1.00273972603 1.82602739729e-06 61.0 54.0 73.0 45.0
1.00273972603 1.82602739729e-06 61.0 60.0 50.0 73.0
1.00273972603 1.82602739729e-06 61.0 60.0 73.0 50.0
1.00273972603 1.82602739729e-06 61.0 66.0 55.0 73.0
1.00273972603 1.82602739729e-06 61.0 66.0 73.0 55.0
1.00273972603 1.82602739729e-06 61.0 72.0 60.0 73.0
1.00273972603 1.82602739729e-06 61.0 72.0 73.0 60.0
1.00273972603 1.82602739729e-06 61.0 78.0 65.0 73.0
1.00273972603 1.82602739729e-06 61.0 78.0 73.0 65.0
1.00273972603 1.82602739729e-06 66.0 61.0 55.0 73.0
1.00273972603 1.82602739729e-06 66.0 61.0 73.0 55.0
1.00273972603 1.82602739729e-06 72.0 61.0 60.0 73.0
1.00273972603 1.82602739729e-06 72.0 61.0 73.0 60.0
1.00273972603 1.82602739729e-06 78.0 61.0 65.0 73.0
1.00273972603 1.82602739729e-06 78.0 61.0 73.0 65.0
1.00273768044 2.19561971271e-07 79.0 51.0 49.0 82.0
1.00273768044 2.19561971271e-07 79.0 51.0 82.0 49.0
done

Newer version info several posts down updated Jun16 2010

[BastardNamban]

Oldfred, thank you very much! What program did you use to do this?

It looks like you found a way to use the same 4 numbers, in different orders, to come up with the first number, the ratio. Then what is the second decimal number
each time? (ie: in 1.00273768044 2.19561971271e-07 51.0 79.0 49.0 82.0, the 2.19561971271e-07 part.)

It's crucial that I use whole numbers only for the gears in the sequence.
Also, I need that exact end ratio, and I'm willing to not limit myself to 4 gears- up to 20, if need be. More accurate is better.

Finally, the 4 gears I used above aren't quite accurate- they were the ones Breguet used (I gave them only as an example, I would not use the same solution as he), and his train was off by 10 seconds or so a year, I believe.

Much higher levels of accuracy are obtainable, but more gears must be used.

I really appreciate you trying whatever you did, and I'd like to know what you used. I'd like to learn how to use it, and continue on my own with even more gears!

Finally, is there a way to make a gui program to calculate gear ratios in this way for clockmakers/watchmakers (ie: gear tooth numbers in whole numbers only for a desired result)? I would think linux can do it- I'd just need someone to make it for me. Can I pay someone to make a program to do this? I would!

[oldfred]

The second value is error, you see it changed to exponential since it was so small. Whatever simple logic I used only gave errors to 6 or 7 decimals.

I attached the program, it is just python. copy it to your system and make it executeable. I had it in desktop so I changed to this:

fred@fred-desktop:~$ python clockgear.py

This only uses 2 gears sets and when I had 0 to 100 on all 4 it took forever to run. It would be relatively easy to add more but may take too long to run. not sure how to add optimization to make it easier to run.

Look at program, it is short enough to understand I think for just about anyone as it is not complex.