Neil's News

Diametral Pitch

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.

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