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Zorluk: ZorGears and Gear Ratios

Match each gear system configuration with its resulting mechanical properties.

  • Simple train: 15-tooth drive gear directly meshing with a 60-tooth driven gear.Torque is multiplied by 4; rotational direction is reversed.
  • Idler train: 60-tooth drive gear, 25-tooth idler gear, and 15-tooth driven gear.Output speed is 4 times the input speed; rotational direction is unchanged.
  • Compound train: 20-tooth drive gear driving a 40-tooth gear on a countershaft; a 10-tooth gear on the same countershaft drives a 30-tooth final gear.Overall mechanical advantage is 6; final gear rotates in the same direction as the input gear.
  • Rack and pinion: 12-tooth pinion gear meshed directly with a flat, toothed rack.Rotational motion is converted into linear motion.

Cevap

The simple train multiplies torque by 4 and reverses direction. The idler train quadruples speed and keeps the same direction. The compound train provides a mechanical advantage of 6 and keeps the same direction. The rack and pinion converts rotational motion to linear motion.
Each specific gear arrangement produces distinct mechanical outcomes based on the ratio of teeth between the driving and driven gears, the number of intermediary gears, and the physical shape of the gears involved.

Adım Adım Çözüm

1
Determine the mechanical properties of the simple train.
Matches with: Torque is multiplied by 4; rotational direction is reversed.
A 15-tooth gear driving a 60-tooth gear has a ratio of 4:1. The driven gear is 4 times larger, multiplying torque by 4. Two meshing gears turn in opposite directions.
2
Determine the mechanical properties of the idler train.
Matches with: Output speed is 4 times the input speed; rotational direction is unchanged.
The 25-tooth idler gear does not change the ratio. The 60-tooth drive gear directly relates to the 15-tooth driven gear, meaning the output is 1/4 the size and spins 4 times as fast. An odd number of gears (3) preserves the rotational direction.
3
Determine the mechanical properties of the compound train.
Matches with: Overall mechanical advantage is 6; final gear rotates in the same direction as the input gear.
Calculate the ratio of each pair: 40/20 = 2, and 30/10 = 3. Multiply them: 2 * 3 = 6. This is the mechanical advantage. There are two gear meshes, causing the direction to reverse twice, returning to the original input direction.
4
Determine the mechanical properties of the rack and pinion.
Matches with: Rotational motion is converted into linear motion.
A round pinion turning against a straight rack is the standard mechanism for converting rotational motion into linear motion.

Anahtar Kavram

Calculating gear ratios and tracking rotational direction across simple, idler, compound, and rack-and-pinion trains.
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