A gear train is formed by mounting gears on a frame so that the teeth of the gears engage.
The mechanical advantage of a pair of meshing gears for which the input gear has NA teeth and the output gear has NB teeth is given by This shows that if the output gear G has more teeth than the input gear G, then the gear train amplifies the input torque.
And, if the output gear has fewer teeth than the input gear, then the gear train reduces the input torque.
If the output gear of a gear train rotates more slowly than the input gear, then the gear train is called a speed reducer.
Let the angle θ of the input gear be the generalized coordinate of the gear train, then the speed ratio R of the gear train defines the angular velocity of the output gear in terms of the input gear, that is The formula for the generalized force obtained from the principle of virtual work with applied torques yields The mechanical advantage of the gear train is the ratio of the output torque T to the input torque T, and the above equation yields Thus, the speed ratio of a gear train also defines its mechanical advantage.
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