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Zorluk: OrtaGears and Gear Ratios

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?

  1. 32 rpm32\text{ rpm}, counter-clockwiseCevap
  2. B
    512 rpm512\text{ rpm}, counter-clockwise
  3. C
    32 rpm32\text{ rpm}, clockwise
  4. D
    800 rpm800\text{ rpm}, counter-clockwise

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

Compound Gear Trains and Speed Ratios
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Konular

Gears and Gear Ratios

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