6.19 Branched Systems
237
K 2e = n
2
1 k 2 , K 3e = n
2
2 k 3
(c) Applying Holzer’s method
θ 4 = 1 −
n
2
1 I 6 p
2
n
2
1 k 2
= 1 −
I 6 p
2
k 2
(6.123)
θ 4 and θ 3 are related. Therefore,
θ 3 =
1
n 1
1 −
I 6 p
2
k 2
= ¯
θ 3
(6.124)
(d) Assume θ 5 = 1.
Applying Holzer’s method
θ 2 = 1 −
n
2
2 I 5 p
2
n
2
2 k 3
= 1 −
I 5 p
2
k 3
(6.125)
θ 2 is related to θ 3 of the centre gear. Therefore,
¯
θ 3 =
1
n 2
1 −
I 5 p
2
k 3
= ¯
θ
3
(6.126)
(e) In most cases, θ 3 will differ from θ
3 . Therefore, a new value of θ 5 is to be
assumed. Let this value be
θ 5 =
θ 3
θ
3
= θ 0
(6.127)
Computation is again started from the lower branch.
θ 2 = θ 5
1 −
I 5 p
2
k 3
(6.128)
Therefore,
θ
3 =
θ 5
n 2
1 −
I 5 p
2
k 3
(6.129)
Substituting the value of θ 5 from Eq. (6.128) and using the relation given in
Eqs. (6.126), (6.129) becomes
¯
θ
3 =
θ 3
¯
θ
3
× ¯
θ
3 = ¯
θ 3
(6.130)