Despite its name, this type of pulley system does not use
a differential gear. Instead, it uses an upper group with
two independent pulleys that can rotate at various speeds
in opposite directions. This is made possible by using two
separate axles, one for each pulley, or by replacing one of the
pulleys with some circular LEGO piece with a pin hole rather
than an axle hole, as shown in Figure 6-22.
As you see, the lower group is fairly simple, while the
upper one includes two pulleys of various diameters, one
made of a wedge belt wheel and another made of a small
rim (#42610). The rim has a pin hole, so it can rotate freely
on the axle, regardless of the speed and direction of the
other pulley, and it has a deep central groove with an inner
diameter of roughly 9 mm. The arrangement of the string is no less interesting: It’s tied in a loop, first coming off the reel,
going over the large upper pulley and the lower pulley, and
then coming back to be wrapped around the small upper pulley.
Upon coming off, it’s tied to the section of string between
the reel and the large upper pulley.
When we rotate the reel, it pulls the string on both
the large and small upper pulleys, making them rotate in
opposite directions at various speeds. The difference in
speeds is balanced by the rotations of the lower pulley.
The interesting thing is how much mechanical advantage
we can gain in this system.
If R is the radius of the large upper pulley and r is
the radius of the small upper pulley, then the mechanical
advantage of the whole system is equal to
2×R
R − r
In our example, R is 10.5 and r is 4.5, which gives a
mechanical advantage equal to 21/6, which is 3.5. As you
see from this formula, the mechanical advantage is bigger
if the difference in the upper pulleys’ sizes is very small.
But the pulley sizes cannot be the same because that would
stop the lower group from moving up or down.
Let’s check the mechanical advantage given by other
pulley combinations. For example, with the Micromotor pulley
(R = 4.5) and a half bush (r = 2.9), we can get 9/1.6, which
is equal to 5.63—quite a result from such small pieces.
The combination of another freely rotating rim (#56902),
shown in Figure 6-23, with a deep central groove and an
inner diameter of 10 mm (R = 5), and the Micromotor pulley
(r = 4.5) grants a mechanical advantage of 10/0.5, which is
equal to 20.