For a simple gear train with gears 1, 2, and 3 in series (gear 2 is an idler), the overall velocity ratio i_ 13 between gear 1 (input) and gear 3 (output) is:

Home › MCQs › Mechanical Engineering › Question #2460

Mechanical Engineering QUESTION #2460

Question 1

For a simple gear train with gears 1, 2, and 3 in series (gear 2 is an idler), the overall velocity ratio \(i_{13}\) between gear 1 (input) and gear 3 (output) is:

\(i_{13} = -\frac{N_3}{N_1}\) (idler gear 2 only affects sign, not magnitude)✔️
\(i_{13} = -\frac{N_2 N_3}{N_1^2}\)
\(i_{13} = \frac{N_1}{N_3}\)
\(i_{13} = \frac{N_1 N_2}{N_2 N_3}\)

Correct Answer Explanation

For a simple gear train: \(i_{13}=\left(-\frac{N_2}{N_1}\right)\left(-\frac{N_3}{N_2}\right)=-\frac{N_3}{N_1}\). The idler gear 2 cancels out in magnitude but reverses the direction sign once.

More Options