Topic: Theory of Machines
A fixed gear having 200 teeth is in mesh with another gear having 50 teeth. The two gears are connected by arm. The number of turns made by the smaller gear for one revolution of arm about the center of the bigger gear is-
- A. 4
- B. 3
- C. $3\frac{2}{4}$
- D. 5
Answer: D. 5
Explanation: Using the tabular method: Let the arm rotate by +y and gear train by +x. Fixed gear ($T_{G}=200$) turns $N_{G} = y - x(T_{P}/T_{G}) = 0$. Given $y = 1$ rev, $1 - x(50/200) = 0 \Rightarrow 1 = x/4 \Rightarrow x = 4$. The speed of the smaller gear (pinion, $T_{P}=50$) is $N_{P} = y + x = 1 + 4 = 5$ revolutions.