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Gears and Gear Ratios

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Question 21Question →

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 rpm120\text{ rpm}.

Click a left item, then click its matching right item

Items

20-tooth driving gear meshing directly with a 60-tooth driven gear
40-tooth driving gear meshing with a 15-tooth idler, which meshes with a 20-tooth driven gear
60-tooth driving gear meshing directly with a 20-tooth driven gear
10-tooth driving gear, a 50-tooth idler, a 20-tooth idler, and a 10-tooth driven gear meshing in sequence

Matches

Show answer & explanation

Answer

The correct matches are: the 20-to-60 tooth train outputs 40 rpm40\text{ rpm} counter-clockwise; the train with one idler outputs 240 rpm240\text{ rpm} clockwise; the 60-to-20 tooth train outputs 360 rpm360\text{ rpm} counter-clockwise; and the train with two idlers outputs 120 rpm120\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

1
Evaluate the 20-tooth to 60-tooth gear train.
Matches with '40 rpm40\text{ rpm}, counter-clockwise'.
The output ratio is determined by driver/driven: 20/60 = 1/3. Output speed is 120×1/3=40 rpm120 \times 1/3 = 40\text{ rpm}. A single mesh reverses the initial clockwise direction to counter-clockwise.
2
Evaluate the 40-tooth to 20-tooth train with one idler.
Matches with '240 rpm240\text{ rpm}, clockwise'.
The idler's tooth count does not affect the ratio. Ratio is 40/20 = 2. Output speed is 120×2=240 rpm120 \times 2 = 240\text{ rpm}. Two meshes mean the direction is reversed twice, resulting in clockwise rotation.
3
Evaluate the 60-tooth to 20-tooth gear train.
Matches with '360 rpm360\text{ rpm}, counter-clockwise'.
The output ratio is 60/20 = 3. Output speed is 120×3=360 rpm120 \times 3 = 360\text{ rpm}. A single mesh reverses the direction to counter-clockwise.
4
Evaluate the 10-tooth to 10-tooth train with two idlers.
Matches with '120 rpm120\text{ rpm}, counter-clockwise'.
The idlers are ignored for speed. Ratio is 10/10 = 1. Output speed is 120×1=120 rpm120 \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.
Question 22Question →

A heavy-duty drawbridge mechanism employs a compound gear train to safely operate its primary lifting drum. The driving electric motor is directly connected to Gear W (14 teeth), which rotates at 640 rpm640\text{ rpm} in a counter-clockwise direction. Gear W meshes with Gear X (56 teeth). Gear X and Gear Y (18 teeth) are rigidly mounted to the same central axle. Gear Y meshes with the final output Gear Z (90 teeth), which turns the lifting drum. Based on this configuration, what is the rotational speed and direction of Gear Z?

Show answer & explanation

Answer: 32 rpm32\text{ rpm}, counter-clockwise

Answer

The final output Gear Z rotates at 32 rpm32\text{ rpm} in a counter-clockwise direction.
The system features a two-stage reduction. In the first stage, Gear W drives Gear X, yielding a 4:1 reduction (640 rpm640\text{ rpm} divided by 4 equals 160 rpm160\text{ rpm}) and a direction change to clockwise. Gear Y shares the axle with Gear X, so it also rotates at 160 rpm160\text{ rpm} clockwise. In the second stage, Gear Y drives Gear Z, creating a 5:1 reduction (160 rpm160\text{ rpm} divided by 5 equals 32 rpm32\text{ rpm}) and reversing the direction back to counter-clockwise.

Step-by-Step Solution

1
Calculate the speed and direction of Gear X.
Gear X rotates at 160 rpm160\text{ rpm}, clockwise.
Gear W (14 teeth) drives Gear X (56 teeth). The gear ratio is 56/14 = 4. Since the driven gear is larger, the speed is reduced: 640/4=160 rpm640 / 4 = 160\text{ rpm}. Meshing gears rotate in opposite directions, so Gear X turns clockwise.
2
Determine the speed and direction of Gear Y.
Gear Y rotates at 160 rpm160\text{ rpm}, clockwise.
Gear X and Gear Y share the same solid axle. Compound gears on the same axle always rotate at the exact same speed and in the same direction.
3
Calculate the speed and direction of Gear Z.
Gear Z rotates at 32 rpm32\text{ rpm}, counter-clockwise.
Gear Y (18 teeth) drives Gear Z (90 teeth). The gear ratio is 90/18 = 5. The speed is reduced again: 160/5=32 rpm160 / 5 = 32\text{ rpm}. Meshing gears reverse direction, so Gear Z turns counter-clockwise.

Key Concept

Compound Gear Trains and Speed Ratios
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