Now, there is no conceivable sense in which the motion of T can be
said to be added to the rotation of F about its axis, and the
expression "absolute revolution," as applied to the motion of the last
wheel in this train, is absolutely meaningless.
Nevertheless, Prof. Goodeve states (Elements of Mechanism, p. 165)
that "We may of course apply the general formula in the case of bevel
wheels just as in that of spur wheels." Let us try the experiment;
when the train-arm is stationary, and A released and turned to the
right, F turns to the left at the same rate, whence:
n
--- = -1; also m' = 0 when A is fixed,
m
and the equation becomes
n' - a
------ = -1, [therefore] n' = 2a:
- a
or in other words F turns _twice_ on its axis during one revolution of
T: a result too palpably absurd to require any comment. We have seen
that this identical result was obtained in the case of Fig. 15, and it
would, of course, be the same were the formula applied to Figs. 5 and
6; whereas it has never, so far as we are aware, been pretended that a
miter or a bevel wheel will make more than one rotation about its axis
in rolling once around an equal fixed one.
Again, if the formula be general, it should apply equally well to a
train of screw wheels: let us take, for example, the single pair shown
in Fig. 8, of which, when T is fixed, the velocity ratio is unity.
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