Match each simple gear train configuration to its resulting output rotation speed and dire… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each simple gear train configuration to its resulting output rotation speed and direction. Assume the driving gear in each configuration rotates clockwise at $120\text{ rpm}$ .

20-tooth driving gear meshing directly with a 60-tooth driven gear $40\text{ rpm}$ , counter-clockwise
40-tooth driving gear meshing with a 15-tooth idler, which meshes with a 20-tooth driven gear $240\text{ rpm}$ , clockwise
60-tooth driving gear meshing directly with a 20-tooth driven gear $360\text{ rpm}$ , counter-clockwise
10-tooth driving gear, a 50-tooth idler, a 20-tooth idler, and a 10-tooth driven gear meshing in sequence $120\text{ rpm}$ , counter-clockwise

Answer

The correct matches are: the 20-to-60 tooth train outputs

40\text{ rpm}

counter-clockwise; the train with one idler outputs

240\text{ rpm}

clockwise; the 60-to-20 tooth train outputs

360\text{ rpm}

counter-clockwise; and the train with two idlers outputs

120\text{ rpm}

counter-clockwise.

The output speed of a simple gear train is calculated by dividing the number of teeth on the driving gear by the number of teeth on the driven gear, and multiplying that ratio by the input speed. Any intermediate gears, known as idlers, exist solely to bridge gaps or change the rotational direction of the driven gear; their tooth counts do not influence the final output speed. Additionally, each physical mesh between gears reverses the direction of rotation.

Step-by-Step Solution

Evaluate the 20-tooth to 60-tooth gear train.

Matches with '

40\text{ rpm}

, counter-clockwise'.

The output ratio is determined by driver/driven: 20/60 = 1/3. Output speed is

120 \times 1/3 = 40\text{ rpm}

. A single mesh reverses the initial clockwise direction to counter-clockwise.

Evaluate the 40-tooth to 20-tooth train with one idler.

Matches with '

240\text{ rpm}

, clockwise'.

The idler's tooth count does not affect the ratio. Ratio is 40/20 = 2. Output speed is

120 \times 2 = 240\text{ rpm}

. Two meshes mean the direction is reversed twice, resulting in clockwise rotation.

Evaluate the 60-tooth to 20-tooth gear train.

Matches with '

360\text{ rpm}

, counter-clockwise'.

The output ratio is 60/20 = 3. Output speed is

120 \times 3 = 360\text{ rpm}

. A single mesh reverses the direction to counter-clockwise.

Evaluate the 10-tooth to 10-tooth train with two idlers.

Matches with '

120\text{ rpm}

, counter-clockwise'.

The idlers are ignored for speed. Ratio is 10/10 = 1. Output speed is

120 \times 1 = 120\text{ rpm}

. Three meshes alternate the direction (CW to CCW to CW to CCW).

Key Concept

Calculating output speed and tracking rotational direction in simple gear trains involving idler gears.

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