392 APPLIED MECHANICS 
A simple method which may be adopted in solving problems on 
epicyclic trains will now be illustrated on a fairly complex example. 
Fig. 616 shows an epicyclic reverted train known as Humpage’s gear. 
A is a fixed wheel, that is, a wheel which 
is not allowed to rotate. Lis fixed to the 
shaft H, and D is fixed to the shaft K. 
B and C are fixed or cast together, but 
i) {] 
"Ys; Uy 
G 
4 
turn freely on an arm EF, which can Vx 
rotate about the common axis of the Ks 
shafts H and K. The wheels B and C 
and the arm EF are duplicated, as shown, 
for the sake of balance and pure torque. A 
Let the numbers of teeth in the different 
wheels be as follows: A, 48; B, 40; C, 
25; D,12; and L, 40. First suppose the 
whole system to be turned once round in 
the direction S. The wheels A, L, and D 
have therefore made one revolution in the direction 8. If now A is turned 
back through one revolution in the direction T, the arm EF being at rest, 
the various wheels will then occupy the positions which they would have 
occupied had A been fixed while the arm EF turned once in the direc- 
tion 8S. In turning A back through one revolution in the direction T 
the wheel L will evidently turn in the direction T through nx a = 
But L previously made one revolution in the direction 
of a revolution. 
8, therefore the actual motion of L is 1- o=i of a revolution in the 
direction S. Again, in turning A back through one revolution in the 
direction T, the arm EF being at rest, the wheel D will make eo4 
revolutions in the direction 8. But D previously made one revolution in 
the direction §, therefore the actual motion of D is 4+1=5 revolutions 
in the direction S. Hence the speed of L is to the speed of D as 13, 
or as | is to 20. 
The working of the above problem may be tabulated as follows :— 
Arm EF. Wheel A. Wheel D. Wheel L. 
+1 +1 +1 +1 Revolutions. 
48 48 25 8 
0 = —_—= -—_ moe ae ee 
1 + ip +4 40 x 40 z ” 
1 
+1 0 +5 + Z ” 
or +4 0 +20 +1 Bs 
Problems on epicyclic trains become quite simple when worked by the 
above method. 
