In Fig. 21 is shown a combination consisting also of two distinct
trains, in which, however, there is but one train-arm T turning freely
upon the horizontal shaft OO, to which shaft the wheels A', F, are
secured; the train-arm has two studs, upon which turn the idlers B B',
and also carries the bearings of the last wheel F'; the first wheel A
is annular, and fixed to the frame of the machine. Let it be required
to determine the results of one revolution of the crank H, the numbers
of teeth being assigned as follows:

A = 60, F = 30, A' = 60, F' = 10.

We shall then have, for the train ABF (Eq. I.),

n 60 n' - a
--- = - ---- = -2 = --------, in which n' = 1, m' = 0,
m 30 m' - a'

1 - a 1
whence -2 = -------, 2a = 1 - a, 3a = 1, a = ---.
-a 3

And for the train A'B'F' (Eq. II.),

n 60 n' 1
--- = ---- = 6 = --------, in which a = ---, m' = 1,
m 10 m' - a' 3

n'
whence 6 = -----------, or n' = 4.
1 - (1/3)