The spur gears shown in the figure have a diametral pitch of 5 and a 20° pressure angle. The pinion 2 rotates at 1000 rev/min clockwise and transmits 200 hp to gear 3 on shaft b. Gears 3 and 4 are located on shaft b, where 75 hp is extracted for external use. The remaining 125 hp is transmitted to shaft c through gears 4 and 5. Gearing ratio between first set of gears is 2 and the second set is 2.5. a. Determine the minimum number of teeth on all gears to avoid interference. b. Determine the magnitude and direction forces on all gears. c. Determine the magnitude, direction and location of forces on all shafts. Assume origin is located on shaft a and full depth tooth gears.

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The spur gears shown in the figure have a diametral pitch of 5 and a 20° pressure angle. The pinion 2 rotates at 1000 rev/min clockwise and transmits 200 hp to gear 3 on shaft b. Gears 3 and 4 are located on shaft b, where 75 hp is extracted for external use. The remaining 125 hp is transmitted to shaft c through gears 4 and 5. The gearing ratio between the first set of gears is 2 and the second set is 2.5.

**Tasks:**

a. Determine the minimum number of teeth on all gears to avoid interference.

b. Determine the magnitude and direction of forces on all gears.

c. Determine the magnitude, direction, and location of forces on all shafts.

Assume the origin is located on shaft a and full depth tooth gears.

**Diagram Explanation:**

- The diagram depicts four gears arranged on three shafts labeled a, b, and c.
- Gear 2 is on shaft a and engages with gear 3 on shaft b.
- Gear 3 and 4 are positioned along shaft b. Gear 4 interacts with gear 5 on shaft c.
- The x and y axes cross at the origin on shaft a.
- The rotational directions, power transmission paths, and gearing ratios are symmetric around these coordinates, setting the stage for problem-solving related to gear systems and mechanical power transmission.
Transcribed Image Text:The spur gears shown in the figure have a diametral pitch of 5 and a 20° pressure angle. The pinion 2 rotates at 1000 rev/min clockwise and transmits 200 hp to gear 3 on shaft b. Gears 3 and 4 are located on shaft b, where 75 hp is extracted for external use. The remaining 125 hp is transmitted to shaft c through gears 4 and 5. The gearing ratio between the first set of gears is 2 and the second set is 2.5. **Tasks:** a. Determine the minimum number of teeth on all gears to avoid interference. b. Determine the magnitude and direction of forces on all gears. c. Determine the magnitude, direction, and location of forces on all shafts. Assume the origin is located on shaft a and full depth tooth gears. **Diagram Explanation:** - The diagram depicts four gears arranged on three shafts labeled a, b, and c. - Gear 2 is on shaft a and engages with gear 3 on shaft b. - Gear 3 and 4 are positioned along shaft b. Gear 4 interacts with gear 5 on shaft c. - The x and y axes cross at the origin on shaft a. - The rotational directions, power transmission paths, and gearing ratios are symmetric around these coordinates, setting the stage for problem-solving related to gear systems and mechanical power transmission.
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