PLANETARY WHEEL TRAINS. Fig. 15
To illustrate: Take the simple case of two equal wheels, Fig. 15, of which the central one A is fixed. Supposing first A for the moment released and the arm to be fixed, we see that the two wheels will turn in opposite directions with equal velocities, which gives n/m = -1; but when A is fixed and T revolves, we have m' = 0, whence in the general formula
| n' - a -a | = -1, or n' = 2 a; |
which means, being interpreted, that F makes two rotations about its axis during one revolution of T, and in the same direction. Again, let A and F be equal in the 3-wheel train, Fig. 16, the former being fixed as before. In this case we have:
| n m | = 1, m' = 0, which gives |
| n' - a -a | = 1, ∴ n' = 0; |
that is to say, the wheel F, which now evidently has a motion of circular translation, does not rotate at all about its axis during the revolution of the train-arm.
PLANETARY WHEEL TRAINS. Fig. 16
All this is perfectly consistent, clearly, with the hypothesis that the motion of circular translation is a simple one, and the motion of revolution about a fixed axis is a compound one.