The
directional relation, however, depends upon the direction in which the
wheels are twisted: so that in applying the formula, we shall have
_n/m_ = +1, if the helices of both wheels are right handed, and
_n_/_m_ = -1, if they are both left handed. Thus the formula leads to
the surprising conclusion, that when A is fixed and T revolves, the
planet-wheel B will revolve about its axis twice as fast as T moves,
in one case, while in the other it will not revolve at all.
[Illustration: PLANETARY WHEEL TRAINS. Fig. 18]
A favorite illustration of the peculiarities of epicyclic mechanism,
introduced both by Prof. Willis and Prof. Goodeve, is found in the
contrivance known as Ferguson's Mechanical Paradox, shown in Fig. 18.
This consists of a fixed sun-wheel A, engaging with a planet-wheel B
of the same diameter. Upon the shaft of B are secured the three thin
wheels E, G, I, each having 20 teeth, and in gear with the three
others F, H, K, which turn freely upon a stud fixed in the train-arm,
and have respectively 19, 20, and 21 teeth. In applying the general
formula, we have the following results:
n 20 n' - a 1
For the wheel F, --- = ---- = ---------, [therefore] n' = - ---- a.
m 19 -a 19
n n' - a
" " " H, --- = 1 = --------, [therefore] n' = 0.
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