The correct answer is option 'A': the Whitworth quick return mechanism is contained by the inversion of a slider-crank mechanism.

Explanation:
The Whitworth quick return mechanism is a well-known mechanism used in machines such as shapers and slotting machines. It is used to convert the rotary motion of a crank into a reciprocating motion of a slider.

The mechanism consists of four main links: the crank, the connecting rod, the slider, and the fixed frame. The crank is connected to the connecting rod, which in turn is connected to the slider. The fixed frame provides a reference point for the other links.

The key feature of the Whitworth quick return mechanism is that the slider's motion is not symmetrical with respect to the rotation of the crank. During one half of the crank's rotation, the slider moves slowly in one direction, while during the other half of the rotation, the slider moves quickly in the opposite direction. This non-uniform motion is useful for certain machining operations.

In order to achieve this motion, the slider-crank mechanism needs to be inverted. In the standard slider-crank mechanism, the crank is driven by a motor, and the slider provides the output motion. However, in the Whitworth quick return mechanism, the slider is driven by an external force, such as a cutting tool. This external force causes the slider to move in a non-uniform manner, as desired.

By inverting the slider-crank mechanism, the Whitworth quick return mechanism is created. This inversion allows for the desired non-uniform motion of the slider, making it suitable for applications where a quick return stroke is required.

In conclusion, the Whitworth quick return mechanism is contained by the inversion of a slider-crank mechanism. This inversion allows for the non-uniform motion of the slider, which is a key feature of the Whitworth mechanism.