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Problem 3.39

As covered in earlier problems, the torque relationship for meshing gears is:

The angle of twist for shaft CD is:

The relationship between the angles that the gears turn through can be computed by realizing that both gears turn through the same arc lengths, since they are touching (and not slipping):

So gear B turns through three times the angle that gear C does. In addition, there is the twist of A relative to B:

Therefore, the angle through which A rotates relative to the fixed point D is 0.0310 + 3(0.0359) = 0.1387 rad, or 7.94o.

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