Question Bank • QB_FM_014 NAT • 2 Marks

Section 2: Farm Machinery

Machine Design

Subtopic: Design and selection of machine elements – gears, pulleys, chains and sprockets and belts

Question Statement:

A roller chain drive on a fertilizer broadcaster has a driving sprocket with $Z = 18$ teeth and a chain pitch of $p = 19.05\text{ mm}$. The pitch diameter of the sprocket in $\text{mm}$ is ________ (round off to 1 decimal place).

Answer Key:

109.7

Step-by-Step Solution & Explanation

The pitch diameter $D$ of a roller chain sprocket is given by: $D = \frac{p}{\sin\left(\frac{180^\circ}{Z}\right)}$ Given $p = 19.05\text{ mm}$ and $Z = 18$ teeth: $\frac{180^\circ}{Z} = \frac{180^\circ}{18} = 10^\circ$ $\sin(10^\circ) \approx 0.17365$ $D = \frac{19.05}{0.17365} \approx 109.703\text{ mm} \approx 109.7\text{ mm}$
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