PRINCIPLES OP MECHANISM.

4-1

Similarly we have,

Q™ + 1 — ^2 x Si

Qi Qj Q2

which may he expressed in language as follows:— The ratio ofthe synchronal rotation of the first and last axes, is equal tothe product of the separate synchronal ratios of the successivepairs of axes.

The number of axes in this combination is always one morethan the number of pairs of wheels.

It is evident, from eq. (1), that the drivers and followers maybe placed in any order in a train of wheel-work without chang-ing the velocity ratios of the first and last axes.

Example. —Let the number of pairs of drivers and followersbe 3, that is, let m =3, n, = 16, n 2 = 15, n 3 = 14, n Y = 7,n 2 = 6, n z = 5; required the least number of synchronal rota-tions of the first and last axes in the train of wheels.

Here by eq. (1) we have—

q 4 16 x 15 x 14 _ 16.

Q,= 7x6x5 “ T’

that is, whilst the first axis makes one revolution, the last willmake sixteen.

58. If the number of teeth in a driving wheel be some exactmultiple of the number of teeth in the follower, then the sameteeth will come into contact in every revolution of the driver.Thus if the driver contains 30 teeth and the follower 6, thenthe same teeth will come into contact at every revolution of thedriver. This arrangement of teeth is preferred by the clockand watchmaker ; but the millwright would add one tooth, calledthe Hunting Cog, to the large wheel, that is, he would have31 teeth in the driver and 6 in the follower, because 31 and 6,being prime to each other, and at the same time nearly in thesame ratio as 30 and 6, the same pair of teeth would not comeagain into contact until the large wheel had made 6 revolutions,and the small one 31.

59. Eq. (3), Art. 53, enables us readily to find the number ofrevolutions which the wheels must make in order that the sameteeth may come again into contact with each other; for it is only

x ... (2),