Many people, at least men around my age from certain of the world's industrialized democracies, will remember the popular construction set originated by Frank Hornby and for many years produced at a facility on Binns Road in Liverpool.
Recently, I took a look at some web sites which expressed nostalgia for the various versions of the Meccano set over the years. And I learned some things I did not know about the gears that came with Meccano sets.
In order to provide the most commonly useful gear ratios in gears the centers of which would be separated by some multiple of one-half of an inch, they made at least two series of gears; one at 37 1/2 DP, and another at 38 DP; however, information on the gear ratios of some less common gears indicates to me that they also made some gears at 38 1/2 DP and 39 DP as well.
It is believed that they used a cutting tool for making gears at 40 DP, just advancing the gear a tiny bit more for each tooth, thus allowing them to make their gears using standard equipment for cutting Whitworth gears.
With two gears, the centers of which are separated by one inch, the total number of teeth on both gears, if they are the correct size to mesh, is 75 for the 37 1/2 DP gears, and is 76 for the 38 DP gears.
And, thus, some of the most common gears, which I remember having in my own Meccano set, came in the following pairs:
Pinion Spur 37 1/2 DP 25 teeth (part 25) 50 teeth (part 27) 2:1 gear ratio 38 DP 19 teeth (part 26) 57 teeth (part 27a) 3:1 gear ratio
Of course, they made quite a few other gears. I also had the worm gear, and the two sizes of contrate or crown gears: part 28 with 50 teeth, and part 29 with 25 teeth.
And thus, here is a table of the possibilities that are claimed to have been offered over the years, with part numbers in parentheses:
Series Pinion Spur Gear Ratio Center Distance 37 1/2 DP 25 (25) 50 (27) 2:1 1" 15 (26c) 60 (27d) 4:1 1" 38 DP 19 (26) 19 1:1 1/2" 38 (31) 38 1:1 1" 19 57 (27a) 3:1 1" 19 95 (27c) 5:1 1 1/2" 19 133 (27b) 7:1 2" 38 1/2 DP 7 (26z) 70 (27t) 10:1 1" 11 (26n) 66 (27h) 6:1 1" 39 DP 13 (26r) 65 (27k) 5:1 1"
The standard worm gear, which acts like a one-tooth gear, took up as much space as a 19-tooth spur gear, so it meshed with a 57-tooth spur gear in a convenient manner as well as other 38 DP gears. A narrow worm gear the size of a 15-tooth spur gear was also offered to allow a 60:1 reduction ratio, convenient for using a synchronous motor to drive a clock.
There was also Part 180, a 3 1/2" gear ring. It had 133 teeth on the outside and 95 teeth on the inside, and a Part 180a, with 95 teeth on the outside and 57 teeth on the inside.
Also, the 19, 38, and 57-tooth gears originally, in very old Meccano sets (prior to 1921), had 20, 40, and 56 (not 60!) teeth respectively.
An article in the March, 1933 issue of Meccano Magazine describes an astronomical clock made by Alexandre Rahm. It was exhibited at the Sorbonne, and another web site notes that Alexandre Rahm had a later career as a photographer; he also accompanied Thai royalty on a visit to France.
An even more famous astronomical clock built from Meccano parts was made by Jean Legros; it remains a tourist attraction in a planetarium in the city of Amiens.
Plans are still available for a somewhat less elaborate astronomical clock; the original plan is MP65, and the revised version is MP212, and they're offered by the web site Meccanoshop, which is the web site for Frizinghall Models and Railways. For all the plans in the series, though, prospective purchasers are cautioned that parts which are no longer available may be required.
Gear ratios other than those listed above could be produced by meshing gears belonging to different series; although their centers would have to be separated by an odd amount, there are plenty of ways to achieve that with a little creativity.
Still, given the arbitrary nature of the ratios between the orbital periods of the various planets in the Solar System, it would seem that it would make things simpler if one could cut one's own gears. This is not wholly impossible; leaving today's 3D printers out of consideration, the March 1972 issue of Meccano magazine featured a gear making machine designed by T. V. Vollenhoven which would produce gears out of softer materials such as nylon. It did require a 9/16" Whitworth Tap which would have to be purchased at a machine tool shop, and it only cut gears of the same sizes as existing Meccano gears, although it was noted that the model could be modified to cut gears of some other alternate sizes as well.
Amazingly, Märklin made a construction set with holes on 12.7 mm centers - in other words, 1/2" centers - and with gears of 38 DP as well. Ami-Lac (Italy), Exacto (Argentina), Stokys (Switzerland), and Temsi (Holland) also made construction sets compatible with Meccano in both these respects. For comparison, while 1/2" centers for holes were also present in the Gilbert Erector Set, such gears as they had were not compatible.