3 April 2004
Meccano gears come in many different sizes and can be combined to form many different ratios. They all mesh with one another without problems (bevel gears, helical gears and large-toothed quadrants being obvious exceptions). Clearly the system was well-planned to allow this. Or was it?
Looks are deceiving. Meccano gears aren't as compatible as they appear. Below is a table of all the main gears, and the distance between each tooth (all distances in inches):
Part Teeth Radius Circ Tooth spacing DP #27b 133 1.750 10.9956 0.0827 38 #27c 95 1.250 7.8540 0.0827 38 #27d 60 0.800 5.0265 0.0838 37.5 #27a 57 0.750 4.7124 0.0827 38 #27 50 0.667 4.1888 0.0838 37.5 #31 38 0.500 3.1416 0.0827 38 #25 25 0.333 2.0944 0.0838 37.5 #26 19 0.250 1.5708 0.0827 38 #26c 15 0.200 1.2566 0.0838 37.5
(Diametral Pitch[?] (DP) is a good method of describing classes of compatible gears, namely the number of teeth divided by the diameter.)
As one can see, they are close, but not exact. They break down into two distinct families. First there's the "odd" family including the ratios 1:3:5:7 with a spacing of 0.0827 inches between teeth on all gears and pinions (38 DP). Then there's the "even" family including the ratios 1:2:4 with a slightly wider spacing of 0.0838 inches between teeth on all gears and pinions (37.5 DP). Technically members of one family shouldn't really be meshed with members of the other family.
In order to make the existing system work, it's quite possible that Meccano left the tooth spacing uniform, but instead adjusted the gear radii. Thus the 1:2:4 family of gears would all be a little too small. However it would take pretty sensitive equipment to measure which route (or combination of routes) they took.
A computer search reveals that this incompatibility would vanish had the #26c been created with 12 teeth, the #26 with 15 and so on (all gears with 30 DP). All teeth would have been 25% larger, the tooth-spacing would have been uniform on all gears, and all the current ratios would have been unaffected.
Finally there are two more gears of note: racks.
Part Teeth Radius Circ Tooth spacing DP #129 112 1.500 9.4248 0.0841 37.3 (4x rack segments) #110 42 '0.557' '3.5000' 0.0833 37.7 (straight rack)
(The radius and circumference numbers for #110 are the equivalents if the rack were twisted into a circle.)
The 'gear' made out of four rack segments has an even wider spacing of 0.0841 inches between its teeth (37.8 DP). It has an obvious explanation. This 'gear' should have 114 teeth. With 114 teeth the spacing exactly matches the gears in the "odd" family (which is usually what one would mesh it with). It also means that the resulting ratios are nice round numbers. However 114 isn't divisible by 4, so Meccano's dentists removed two teeth when they made the quadrants and hoped nobody would notice.
The straight rack strips all have a spacing of 0.0833 inches between teeth (37.7 DP). In this case, there was no choice but to make an approximate match. Meccano's geometry is governed by its hole spacing of half an inch, whereas gear geometry is governed by Pi[?]. These two incompatible systems collide on straight racks. No possible arrangement could have made this work exactly.
Does any of this make any difference to the real world? Probably not. These discrepancies are close enough never to be noticed. But it was interesting to discover that the Meccano gear system is sightly flawed.
A couple of weeks after posting this article, Bernard Champoux of Montreal wrote with his thoughts on the issue. Mr Champoux is very well known for his gear cutting abilities.
A friend sent me a copy of you essay on Meccano gears. I was surprised that you didn't mentionned the "worm". To my opinion, Hornby based the system on it, for the following reasons. I saw some pictures of the early machine shop when Hornby started to fabricate Meccano parts. There are no elaborate machine, just basic lathe, one "turrett lathe" for parts production in brass and a simple milling machine on which the gears were cut.
If you buy at the hardware store "ironmongers" in England a bolt 9/16"-12 tpi B.S.W.which is very srandard in England, This is the dimensions of the Meccano worm. Cutting 12 threads/inch on a lathe to make a worm is very easy. But that implies that the gears that will operate with this worm must have a circular pitch of 1/12" = 0.08333...
Remember that the early 1" Dia. gear had 40 th. and the 1/2" pinion had 20 teeth. but they would not fit the worm properly.
The closer standard gear cutter that could be bought at that time was 40DP. The 1" 40 th. gear cut with a 40DP. cutter had an equivalent circular pitch of 3.14159/40=0.07854"= 12.732 TPI, difference of 0.00479" per tooth. very impractical to make on a lathe.
But if on the 1" Dia. at the pitch circle, you cut 38 teeth with the 40 DP. cutter then you have a circular pitch equivalent to 3.14159/38=0.08267 the error is now only 0.00066... very good enough for Meccano gears.
I bet that that's what Hornby did, because the price for special gears cutter pitches is very high, and it requires 8 cutters to cut all the gear sizes from the rack to gear 12 tooth.
Now, you cut the worm on a simple lathe, you buy standard cutters, The 1" gear becomes 38 teeth, the 1/2" 19teeth, 57, 95, 133, etc any multiple of 19
That is not a gear system but a thread system being based on the BSW threading system.
I found a set of gear-cutters 40DP a few years ago, I bought them $40.00/cutter, 8 to the set. They fit the teeth perfectly. It is not a hasard, Hornby used 40 DP. cutters.