Consider a mechanism such as a gear train that operates so that an input torque generates an output torque. Let body EA have the input moment TA applied to it, and let body EB exert the output torque TB. Define the angular position and velocity of EA and EB by θA, ωA and θB, ωB, respectively.
Because the mechanism has one degree-of-freedom, there is a single generalized coordinate q that defines the angles θA(q) and θB(q) of the input and output of the system. The principle of virtual work requires that the generalized force associated with this coordinate be zero, thus
The negative sign on the output torque TB arises because the convention of virtual work assumes the torques are applied to the device.
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