A vintage printing press utilizes a compound gear train to feed paper. Shaft 1 is the inpu… — Armed Services Vocational Aptitude Battery (ASVAB)

A vintage printing press utilizes a compound gear train to feed paper. Shaft 1 is the input and is driven at $120$ RPM in a counter-clockwise direction. Gear A ( $40$ teeth) is mounted on Shaft 1 and meshes directly with Gear B ( $20$ teeth), which is mounted on Shaft 2. Also rigidly mounted on Shaft 2 is Gear C ( $50$ teeth). Gear C meshes directly with Gear D ( $25$ teeth) mounted on Shaft 3. Based on this configuration, what is the rotational speed and direction of Shaft 3?

$480$ RPM, counter-clockwiseAnswer
B
$480$ RPM, clockwise
C
$30$ RPM, counter-clockwise
D
$120$ RPM, counter-clockwise

Answer

The output shaft rotates at

480

RPM in a counter-clockwise direction.

In a compound gear train, mechanical advantage and speed ratios are multiplied across stages. In the first stage (Gears A to B), a

40

-tooth gear drives a

20

-tooth gear, doubling the speed to

240

RPM and reversing the direction to clockwise. Both gears on Shaft 2 rotate together. In the second stage (Gears C to D), a

50

-tooth gear drives a

25

-tooth gear, doubling the speed again to

480

RPM and reversing the direction back to counter-clockwise.

Step-by-Step Solution

Calculate the rotational speed of Shaft 2.

Speed =

120 \times (40 / 20) = 240

RPM.

The speed ratio between meshing gears is inversely proportional to their tooth count. A smaller driven gear rotates faster than the driving gear.

Determine the rotational direction of Shaft 2.

Clockwise.

When two external gears mesh, they rotate in opposite directions. Since Shaft 1 is counter-clockwise, Shaft 2 must be clockwise. Because Gears B and C are on the same shaft, Gear C also rotates at

240

RPM clockwise.

Calculate the rotational speed of Shaft 3.

Speed =

240 \times (50 / 25) = 480

RPM.

Applying the speed ratio principle again from Gear C (driving) to Gear D (driven).

Determine the rotational direction of Shaft 3.

Counter-clockwise.

Gear C (clockwise) meshes with Gear D, forcing Gear D to rotate in the opposite direction.

Key Concept

Compound Gear Trains and Speed Ratios

Question

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Step-by-Step Solution

Key Concept

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