T-118
Table 13-2 Equations of Speed Ratio for a Solar Type
–1 1
Speed Ratio = ––––––––– = ––––––––
(13-12)
za za
– ––– – 1 ––– + 1
zc zc
Note that the directions of rotation of input and output axes are the same.
Example: za = 16, zb = 16, zc = 48, then the speed ratio = 1/1.3333333.
(c) Star Type
This is the type in which Carrier D is fixed. The
planet gears B rotate only on fixed axes. In a strict
definition, this train loses the features of a planetary
system and it becomes an ordinary gear train. The
sun gear is an input axis and the internal gear is the
output. The speed ratio is:
za
Speed Ratio = – –––
(13-13)
zc
Referring to Figure 13-6(c), the planet gears are
merely idlers. Input and output axes have opposite
rotations.
Example: za = 16, zb = 16, zc = 48;
then speed ratio = –1/3.
13.4 Constrained Gear System
A planetary gear system which has four gears, as in Figure 13-5, is an example of a
constrained gear system. It is a closed loop system in which the power is transmitted from
the driving gear through other gears and eventually to the driven gear. A closed loop gear
system will not work if the gears do not meet specific conditions.
Let z1, z2 and z3 be the numbers of gear teeth, as in Figure 13-7. Meshing cannot
function if the length of the heavy line (belt) does not divide evenly by circular pitch.
Equation (13-14) defines this condition.
z1q 1 z2(180 +zq1 +q2) z3q2
–––– + ––––––––––––––––– + ––––– = integer
(13-14)
180 180 180
where q1 and q2 are in degrees.
Sun Gear A
za
Planet Gear B
zb
Internal Gear C
zc
Carrier D
No.
Description
+1
– 1
0
(fixed)
1
2
3
Rotate sun gear A once
while holding carrier
System is fixed as a
whole while rotating
+(za /zc)
Sum of 1 and 2
za
– –––
zb
– 1
za
– ––– – 1
zb
za
– –––
zc
– 1
za
– ––– – 1
zc
0
– 1
– 1
Fig. 13-6(c)
Star Type
Planetary Gear
Mechanism
(Fixed)
C
B
A
