A portable hand-cranked emergency generator utilizes a compound gear train to step up the … — Armed Services Vocational Aptitude Battery (ASVAB)

A portable hand-cranked emergency generator utilizes a compound gear train to step up the rotational speed of its internal rotor. The hand crank is directly attached to the driving gear (Gear A), which has $60$ teeth. Gear A meshes with Gear B, which has $15$ teeth. Gear B is fixed to the same solid shaft as Gear C, which has $45$ teeth. Finally, Gear C meshes with Gear D, which has $10$ teeth and is attached to the generator's rotor.

If a person turns the hand crank at a steady speed of $40\text{ RPM}$ , what is the resulting speed of the generator's rotor in $\text{RPM}$ ?

Answer: 720 RPM

Answer

720

In a compound gear train, the overall mechanical advantage (or speed ratio) is found by evaluating each meshing pair separately. The first pair (A to B) increases the speed by a factor of

4

(since

60/15 = 4

). The input speed is

40\text{ RPM}

, so Gear B spins at

160\text{ RPM}

. Because Gear B and Gear C are fixed to the same shaft, Gear C also spins at

160\text{ RPM}

. The second meshing pair (C to D) increases the speed by a factor of

4.5

(since

45/10 = 4.5

). Multiplying Gear C's speed by this ratio gives

160 \times 4.5 = 720\text{ RPM}

Step-by-Step Solution

Determine the rotational speed of Gear B.

160\text{ RPM}

Gear A (

60

teeth) drives Gear B (

15

teeth). The speed multiplier is

60 / 15 = 4

. Therefore, Gear B spins at

40 \times 4 = 160\text{ RPM}

Determine the rotational speed of Gear C.

160\text{ RPM}

Gears mounted on the exact same solid shaft rotate at the same speed, regardless of their size.

Determine the rotational speed of Gear D (the rotor).

720\text{ RPM}

Gear C (

45

teeth) drives Gear D (

10

teeth). The speed multiplier is

45 / 10 = 4.5

. Therefore, Gear D spins at

160 \times 4.5 = 720\text{ RPM}

Key Concept

Compound Gear Train Speed Ratios

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