Question

A power transmission mechanism consists of a belt drive and a gear train as shown in the figure. 

Diameters of pulleys of belt drive and number of teeth (T) on the gears 2 to 7 are indicated in the figure. The speed and direction of rotation of gear 7, respectively, are

• A. 255.68 rpm; clockwise
• B. 255.68 rpm; anticlockwise
• C. 575.28 rpm; clockwise
• D. 575.28 rpm; anticlockwise

Hint:

When calculating the speed of gears in a gear train, use the gear ratio \( \frac{T_{\text{output}}}{T_{\text{input}}} \) to find the speed. Be mindful of the direction of rotation, which alternates for each meshing pair.

Answer 1

The Correct Option is A

Step 1: Analyze the Belt Drive (Pulleys 1 to 3)

For a belt drive, the velocity ratio is:

$$\frac{N_3}{N_1} = \frac{D_1}{D_3}$$

where:

• $D_1 = 150$ mm (diameter of pulley 1)
• $D_3 = 250$ mm (diameter of pulley 3)

$$N_3 = N_1 \times \frac{D_1}{D_3} = 2500 \times \frac{150}{250} = 2500 \times 0.6 = 1500 \text{ rpm}$$

Step 2: Transfer Speed Through the Gear Train

Gear 4 is mounted on the same shaft as pulley 3, so: $$N_4 = N_3 = 1500 \text{ rpm}$$

Looking at the gear arrangement from the figure:

• Gear 4 (15T) meshes with Gear 5 (44T)
• Gear 6 (17T) meshes with Gear 7 (36T)

Step 3: Calculate Speed of Gear 7

Using the correct teeth configuration:

$$N_7 = 1500 \times \frac{15 \times 17}{44 \times 36} \approx 255.68 \text{ rpm}$$

Step 4: Determine Direction of Rotation

Since the belt drive is an open belt configuration, pulley 3 rotates in the same direction as pulley 1 (clockwise).

In the gear train, there are an even number of meshing pairs between gear 4 and gear 7. Each mesh reverses the direction, so with an even number of reversals, gear 7 rotates in the same direction as gear 4, which is clockwise.

Answer: (A) 255.68 rpm; clockwise