Most modellers are familiar with the Meccano helical
gears, PN 211a and PN 211b. The pinion and wheel
can only be meshed together with shafts at right
angles, and are known to run smoothly and quietly
because of the sliding action of their teeth.

The ratio between the gears is the ratio of their
teeth, 35 to 14 or 2.5:1. As would be expected, the
ratio of the diameters is also 2.5 to 1. But this is not
always the case with helical gearing.

The instance where the diameter ratio matches the
teeth ratio only applies if the helix angle is
45 degrees on both gears. (Helix angle is the slope
angle between the gear teeth and the shaft it is
mounted on.) The helix angle can be different for the
pinion and wheel, provided both angles add up to
90 degrees. If the helix angles are not both
45 degrees an interesting phenomenon happens.

If the helix angle of a pinion is made greater than
45 degrees, then the pinion’s diameter will increase.
Similarly, if the helix angle of a wheel is made less
than 45 degrees, the wheel’s diameter will reduce.

Let’s consider the case of the Meccano gears with
2.5:1 ratio. If the pinion and wheel were made with
helix angles of 68.2 and 21.8 degrees respectively,
the two gears would end up being the same diameter!
It is also possible for the pinion to be much larger
than the wheel, and a good example of this is the
speedo drive fitted into the gearbox of older cars with
cable-driven speedos. If you’ve ever pulled an older
gearbox apart you will have seen that the pinion gear
can be as much as twice the diameter of the wheel,
despite the gears being speed reducing.

Taking this further, a Meccano worm gear can be
considered as a one-tooth gear with a high helix
angle of about 86 degrees. A mating 19 tooth pinion
should therefore have a helix angle of about
4 degrees. It doesn’t, but that is presumably because
Meccano engineers made the decision to use straightcut
spur gears (helix angle 0 degrees) throughout the
range. There is sufficient slack in the meshing to
permit this mis-match of helix angles with worm
gears. (Industrial worm and pinion gears would have
the required helix angle on the pinion’s teeth.)

The important point though, is that a Meccano
worm and 19 tooth gear give a considerable 19:1
ratio using two gears of approximately equal size.
Meccano reproduction suppliers have increased
the range of helical gears in recent years.

Meccano Spares in UK have a range of helical gears listed on
their website, covering ratios from 1:1 to 4:1; all
pairs meshing at 1″ centres. As well, left hand
helicals are also available in some sizes, allowing
helical gears to mesh with their shafts parallel.