We are given a gear train with four gears: A, B, C, and D. Gear A drives gear B, and gears B and C are on the same shaft, so they rotate at the same speed. Gear C drives gear D. We are given the number of teeth on each gear: $N_A = 20$, $N_B = 70$, $N_C = 18$, and $N_D = 54$. We are asked to find the velocity ratio of the gear train.

1. Problem Description

We are given a gear train with four gears: A, B, C, and D. Gear A drives gear B, and gears B and C are on the same shaft, so they rotate at the same speed. Gear C drives gear D. We are given the number of teeth on each gear: $N_A = 20$, $N_B = 70$, $N_C = 18$, and $N_D = 54$. We are asked to find the velocity ratio of the gear train.

2. Solution Steps

The velocity ratio of a gear pair is the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear.

The velocity ratio of the first gear pair (A and B) is:

$VR_{AB} = \frac{N_B}{N_A} = \frac{70}{20} = \frac{7}{2} = 3.5$

The velocity ratio of the second gear pair (C and D) is:

$VR_{CD} = \frac{N_D}{N_C} = \frac{54}{18} = 3$

The overall velocity ratio of the gear train is the product of the velocity ratios of the individual gear pairs:

$VR_{total} = VR_{AB} \times VR_{CD} = 3.5 \times 3 = 10.5$

3. Final Answer

The velocity ratio of the gear train is 10.5.