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Two gear system in static equilibrium

  1. Dec 14, 2013 #1
    1. The problem statement, all variables and given/known data

    Two solid steel shafts are coupled together using meshed gears. Determine the angle of twist of end A. Shaft DC is fixed at D.

    2. Relevant equations

    angle of twist = torque * shaft length / ( polar moment of inertia * shear modulus)

    balance of forces where the two gears mesh:
    150mm * Fab = 0.75mm * Fcd

    3. The attempt at a solution

    I know the solution, but am puzzled about what is wrong with the following approach:

    The sum of forces and moments on the system must equal zero since the system is at static equilibrium. Since torque exerted on the system at A is 45Nm, the torque exerted on the system at D must therefore be -45 Nm.

    However, balancing forces at where the two gears mesh shows that torque at D is really -22.5 Nm.
     

    Attached Files:

  2. jcsd
  3. Dec 14, 2013 #2

    Simon Bridge

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    To balance torques, they must be about the same axis.
     
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