Mechanical Efficiency of Real Machines

A machine's mechanical efficiency is the ratio of output to input work.

For an ideal machine, the ratio is one, implying that the input and output work are equal.

For instance, in an ideal toggle vise that compresses wood, the output work due to the reaction force equals the input work due to the applied force.

In contrast, a real machine experiences friction force.

The frictional force can be obtained from the normal reaction force.

The total virtual work due to the contributing forces, when applied in the principle of virtual work, gives output work as the difference between the input work and the work due to frictional force.

Dividing output work by input work gives the mechanical efficiency. The efficiency in the absence of friction is one. However, for a non-zero coefficient of friction, the efficiency is zero when the toggle angle equals the friction angle and negative for toggle angles less than the friction angle.

This implies that a vise should be used only for a toggle angle greater than the friction angle.