19. This
device, as is well known, was employed by the illustrious inventor as
a substitute for the crank, which some one had succeeded in patenting.
It consists merely of two wheels A and F connected by the link T; A
being keyed on the shaft of the engine and F being rigidly secured to
the connecting-rod. Suppose the rod to be of infinite length, so as to
remain always parallel to itself, and the two wheels to be of equal
size.
Then, according to Prof. Willis' analysis, we shall have--
n' - a n -s
-------- = --- = -1, n' = 0, [therefore] -------- = -1, whence
m' - a m m' - a
-a = a - m', or m = 2a.
The other view of the question is, that F turns once backward in its
bearings during each forward revolution of T; whence in Eq. 2 we
have--
n' n
-------- = --- = -1, n' = -a,
m' - a m
-a
[therefore] -------- -1, which gives -a = a - m', or m' = 2a,
m' - a
as before.
It is next to be remarked, that the errors which arise from applying
Eq. I. to incomplete trains may in some cases counterbalance and
neutralize each other, so that the final result is correct.
[Illustration: PLANETARY WHEEL TRAINS. Fig. 20]
For example, take the combination shown in Fig. 20. This consists of a
train-arm T revolving about the vertical axis OO of the fixed wheel A,
which is equal in diameter to F, which receives its motion by the
intervention of one idle wheel carried by a stud S fixed in the arm.
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