Thanks to Mike Shuter, who commented on the previous entry, for sending me his two spreadsheets with Orrery gear ratios and the “continuous fractions” method of determining wheel/pinion pairs. He has permitted me to post them here but please contact “m [dot] shuter [at] ntlworld [dot] com” if you find them useful. Please do not repost without contacting Mike as he is the creator.
This is a first public release of a Windows program for calculating compound gears (2 pair of gears) in “normal” or epicyclic arrangement. It also fully or partially automates Orrery calculations and has presets for various solar system periods, which can be modified and added to by editing the PeriodData.xml file. It allows the tolerance and min/max gear sizes to be specified as well as having various customisable presets, e.g. to only use Meccano or Lego gear sizes.
It is not fully tested and must not be distributed in its present form; it may only be downloaded from here. When it is a little more improved I will post source code and intend to permit distribution eventually. i.e. I’m only granting you a licence to use it yourself at present; a liberal Open Source licence will happen eventually.
It is written in C# and anyone interested in working on the code should contact me.
Download: Compound Gear Calculator Installer (Windows MSI, 380Kb)
If you use it, please provide feedback.
I don’t remember what made me think of it but I took a fancy to build an Orrery a little while ago. Naturally, my first recourse was to scour the web via Google for plans. I would have liked to find some dimensioned drawings in the style of engineering. What I did find was lots of other people looking for plans, designs, cad drawings etc. Noone seemed to have drawn together the following links, although a few were referenced here and there.
So, for any one else on the same quest, here is what I found…
James Ferguson: Mechanical Paradox and Sun-Earth-Moon Orrery
The so-called mechanical paradox is the basis for an orrery that differs from general practice in the way the moon is treated.
Scanned/OCR of the original account including both paradox and Orrery.
Construction notes for the paradox but not the orrery from Amateur Work Magazine Vol4.
Notes on the paradox and construction of a the orrery by Ian Coote and James Donnelly (which also appeared in the Horological Journal):
This wasn’t what I was looking for but these articles contain some ideas on approaches to construction that could be useful in designing an Orrery as well as some possible gear trains.
From the Scientific Instrument Society, two articles by Michael Whiting:
- Bulletin of the Scientific Instrument Society No. 94 (2007) has more general information
- Bulletin of the Scientific Instrument Society No. 101 (2009) focuses on a Jovilabe
Less important (IMO) is an article from Meccano Magazine.
Again, not what I was looking for… and Lego is not what I intend to use but possibly useful.
I also found a couple of other sites that might be of interest if you do plan to use Lego:
Other Useful Sites
An anonymous blogger briefly describes making an Orrery with a minimum of tools and purchased gears. This is a bit inaccurate for my taste but the design is nice and unfussy.
The SAO/NASA Astrophysics Data System (ADS) has scanned articles from 1938 detailing gear trains (using standard gears), an initial one by Roy Marshall and a subsequent one proposing improvements by Charles Balleisen.
There is also usually a book, “Making a Tellurian/Orrery” (ISBN 1905013027) for sale on ebay.
Calculating Gear Trains
If you plan to design from scratch then the question of what gear ratios to use comes into play. If you don’t mind an inaccurate Orrery then a simple pair of gears is easy to work out but compound gears don’t have quick calculator-based solutions.
The old way of doing this, based on some 19th century maths (it still works though and is elegant to those with a mathematical bent) and going under the name of the “Stern-Brocot Tree” is mainly of historical interest. The less elegant but more practical modern approach is a fairly simply computer algorithm with a bit of brute force computer power to do lots of calculations quite fast. One such algorithm appears in Robert Norton’s Book, “The Design of Machinery”, which is freely available on Scrib as an old edition or for purchase (which includes a CD/DVD).
I have almost finished writing a program in C# for Windows using the above-mentioned algorithm which I will make available via this blog in due course (including source code).