PLANETARY WHEEL TRAINS. Fig. 21
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 | = -2 = | n' - a | , in which n' = 1, m' = 0, |
| m | 30 | m' - a' |
| whence -2 = | 1 - a -a | , 2a = 1 - a, 3a - 1, a = | 1 3 | . |
And for the train A'B'F' (Eq. II.),
| n | = | 60 | = 6 = | n' | , in which a = | 1 | , m' = 1, |
| m | 10 | m' - a' | 3 |
| whence 6 = | n' | , or n' = 4. |
| 1 - (1/3) |
That is, the last wheel F' turns four times about the axis LL during one revolution of the crank H. But according to Profs. Willis and Goodeve, we should have for the second train: