Answer:
The appropriate number of teeth of the smallest gear should is 58 teeth.
Explanation:
The given parameters include;
The diametral pitch = 16
Number of gears = 3
Diameter of the input gear = 2 × diameter of the idler gear
Diameter of the input gear = 3 × diameter of the output gear
Height of footprint = 22 in.
Length of footprint = 15 in.
Let the size of the output gear = X
Therefore, the input gear = 3·X
The diameter of the idle gear = 2·X
Therefore, total width of the gear train = X + 2·X + 3·X = 6·X
Where 6·X = 22, X = 22/6 = 11/3 in.
Since the diametral pitch = 16 then we have;
Hence, number of teeth of the smallest gear = 16 × 11/3 = 176/3 =
The appropriate number of teeth of the smallest gear should be 58
From which we have the diameter of the smallest gear = 58/16 = 3.625
The diameter of the input gear is then 3 × 3.625 = 10.875 in.
The diameter of the idler = 2 × 3.625 = 7.25 in.
The appropriate number of teeth of the smallest gear should = 58 teeth.