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A vehicle's manual transmission operates in first gear using a compound gear train. The input shaft gear with 15 teeth drives a countershaft cluster gear with 30 teeth. On the same countershaft, another gear with 10 teeth meshes with and drives a mainshaft output gear with 40 teeth. If the engine rotates the input shaft at 2,400 RPM, what is the resulting rotational speed of the mainshaft?

  1. A
    1,200 RPM
  2. 300 RPMAnswer
  3. C
    600 RPM
  4. D
    4,800 RPM

Answer

300 RPM
The correct answer is 300 RPM because a manual gearbox in lower gears utilizes a two-step compound reduction. The first mesh between the 15-tooth input gear and 30-tooth countershaft gear yields a 2:1 reduction ratio (30÷15=230 \div 15 = 2). The second mesh between the 10-tooth countershaft gear and 40-tooth mainshaft gear yields a 4:1 reduction ratio (40÷10=440 \div 10 = 4). Multiplying both stage ratios gives an overall gear ratio of 8:1 (2×4=82 \times 4 = 8). Dividing the engine input speed of 2,400 RPM by the total ratio of 8 yields an output mainshaft speed of 300 RPM.

Step-by-Step Solution

1
Calculate the first-stage gear reduction from the input shaft to the countershaft
Gear Ratio 1 = 30 teeth ÷ 15 teeth = 2:1 reduction; Countershaft speed = 2,400 RPM ÷ 2 = 1,200 RPM
The input shaft drives the larger gear on the countershaft, reducing rotational speed by half.
2
Calculate the second-stage gear reduction from the countershaft to the mainshaft
Gear Ratio 2 = 40 teeth ÷ 10 teeth = 4:1 reduction
The smaller driving gear on the countershaft turns the larger driven gear on the mainshaft.
3
Determine total transmission gear reduction and compute the final output speed
Overall Gear Ratio = 2 × 4 = 8:1; Mainshaft output speed = 2,400 RPM ÷ 8 = 300 RPM
Compound gear ratios multiply across successive mesh stages to determine total drivetrain mechanical advantage and output shaft speed.

Key Concept

Compound gear ratios and mechanical power flow in manual transmissions
Estimated Time:1m 30s
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Topics

Clutches and Transmissions

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