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Question 15.22: An epicyclic, gear train, as shown in Fig.15.26 is composed ...

An epicyclic, gear train, as shown in Fig.15.26 is composed of a fixed annular wheel A having 150 teeth. The wheel A is meshing with wheel B which drives wheel D through an idle wheel C, D being concentric with A. The wheels B and C are carried on an arm which revolves clockwise at 100 rpm about the axis of A and D. If the wheels B and D have 25 teeth and 40 teeth respectively, find the number of teeth on C and the speed and sense of rotation of C.

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Given:    z_{b}=25, z_{d}=40 .

Table 15.20 is used to find the speed of gears.

For A to be fixed,                x + y = 0, y = -100 rpm, x = +100 rpm.

Table 15.20
Revolutions of Operation
Gear D, 40 Gear C Gear B, 25 Gear A, 150 Arm

+\frac{z_{a}}{z_{d}}=\frac{150}{40}

=\frac{+15}{4}

-\frac{z_{a}}{z_{c}}=-\frac{150}{z_{c}} +\frac{z_{a}}{z_{b}}=\frac{150}{25}=+6 +1 0 1. Arm fixed, +1
revolutions
given to gear A,
ccw
\frac{-15 x}{4} \frac{-150 x}{z_{c}} +6x +x 0 2. Multiply by x
y+\frac{15 x}{4} y-\frac{150 x}{z_{c}} y + 6x y+x y 3. Add y

Now    \frac{d_{a}}{2}=d_{b}+d_{c}+\frac{d_{d}}{2} .

For same module,    \frac{z_{a}}{2}=z_{b}+z_{c}+\frac{z_{d}}{2} .

\frac{150}{2}=25+z_{c}+\frac{40}{2} .

z_{c}=30 .

n_{c}=-100-150 \times \frac{100}{30}=-600 \text { rpm, i.e., } 600 rpm cw .

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