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The spur gears of identical pitch, tp = 3 inches, are assembled as shown below to transmit power from gear A to gear C. The gear A-Gear B center distance is 7 inches. The gear A rotates counter-clockwise (CCW) at a speed of ch.g rpm, and the number of teeth on gear A is N = 12T. Find the number of teeth on gear B. [10 pts]
Assume that gear B receives 7878 lb.in torque from gear A, and gear C receives 5252 lb.in torque from gear B. Find the torque transmitted by gear C to the city of Gear C. [10 pts]
Solution:
1. To find the number of teeth on gear B, we can use the formula for gear ratio:
Gear Ratio = Number of Teeth on Gear B / Number of Teeth on Gear A
Since the gear ratio is 1:1 (since they are identical gears), we can set up the equation:
1 = Number of Teeth on Gear B / 12
Cross-multiplying, we get:
Number of Teeth on Gear B = 12
Therefore, the number of teeth on gear B is 12.
2. To find the torque transmitted by gear C to the city of Gear C, we can use the formula for torque:
Torque = Force x Distance
Since the torque received by gear B is 7878 lb.in and the distance between gear B and gear C is 7 inches, we can set up the equation:
Torque received by gear C = 7878 lb.in x 7 inches
Simplifying, we get:
Torque received by gear C = 55146 lb.in
Therefore, the torque transmitted by gear C to the city of Gear C is 55146 lb.in.
