Inversion of Single-Slider-Crank Chain:

Single-slider-crank chain is a kinematic chain that consists of four links connected by revolute joints. The four links are crank, connecting rod, slider, and frame. This chain is widely used in reciprocating engines, pumps, compressors, and other mechanisms. The motion of the chain is characterized by the rotation of the crank about its axis, which causes the connecting rod to oscillate and the slider to reciprocate along a straight line.

There are several inversions of the single-slider-crank chain, which are obtained by fixing different links of the chain and making the remaining links as the input and output. Each inversion has its own kinematic and dynamic properties, which make it suitable for certain applications. The following are some of the inversions of the single-slider-crank chain:

1. Crank-rocker mechanism: In this inversion, the crank is fixed, and the rocker is the output. The connecting rod and the slider form the input. This mechanism is used in windshield wipers, oscillating fans, and other devices that require a rocking motion.

2. Double-rocker mechanism: In this inversion, both the crank and the slider are fixed, and the two rockers form the input and output. The connecting rod is a floating link. This mechanism is used in walking machines, oscillating pumps, and other devices that require a back-and-forth motion.

3. Drag-link mechanism: In this inversion, the slider is fixed, and the crank and the connecting rod form the input and output. The frame is a floating link. This mechanism is used in steering systems, throttle controls, and other devices that require a rotational motion.

4. Whitworth quick-return mechanism: In this inversion, the crank and the connecting rod are fixed, and the slider forms the input and output. The frame is a floating link. This mechanism is used in shaping machines, slotting machines, and other devices that require a fast return stroke.

5. Hand pump: In this inversion, the connecting rod and the slider are fixed, and the crank and the frame form the input and output. This mechanism is used in hand-operated pumps, such as water pumps, oil pumps, and air pumps.

Conclusion:

The hand pump is an inversion of the single-slider-crank chain, in which the connecting rod and the slider are fixed, and the crank and the frame form the input and output. This mechanism is commonly used in hand-operated pumps, where the reciprocating motion of the handle is converted into the pumping action of the piston. The hand pump is a simple and reliable device that can generate high pressures and flow rates with low input power.