Short Answer:

Inversions of a single slider-crank mechanism are obtained by fixing different links one at a time out of the four available links — frame, crank, connecting rod, and slider. Each inversion gives a different type of motion and application. There are mainly four inversions of the single slider-crank mechanism, and each serves a unique function in mechanical devices.

These inversions are commonly used in various machines such as engines, pumps, and shaping machines. By fixing different links, the mechanism produces different motion characteristics useful for performing specific mechanical operations like reciprocating, rotary, or oscillatory motion.

Detailed Explanation :

Inversions of Single Slider-Crank Mechanism

A single slider-crank mechanism consists of four links — the frame (fixed link), crank (rotating link), connecting rod (coupler), and slider (reciprocating link). When one link is fixed, the relative motion between the remaining three changes, resulting in a new type of mechanism. Each of these different mechanisms formed by fixing different links is called an inversion of the single slider-crank mechanism.

There are four main inversions of the single slider-crank mechanism. Each inversion has its own motion characteristics and industrial applications. The inversions are as follows:

1. First Inversion – Reciprocating Engine or Pump Mechanism

In the first inversion, the frame (link 1) is fixed. This is the most common inversion and is used in engines and pumps.

• The crank (link 2) rotates continuously about a fixed point.
• The connecting rod (link 3) transmits the motion between crank and slider.
• The slider (link 4) reciprocates in a straight path inside the cylinder.

Applications:

• Reciprocating engines: Converts reciprocating motion of piston into rotary motion of crankshaft.
• Reciprocating pumps: Converts rotary motion of crank into reciprocating motion of the piston to lift water.

Example: Internal Combustion (IC) engine mechanism, steam engine mechanism.

This inversion is widely used because of its smooth conversion of rotary motion to linear motion, making it suitable for generating power or fluid displacement.

2. Second Inversion – Whitworth Quick Return Mechanism

In the second inversion, the crank (link 2) is fixed. The other three links (frame, connecting rod, and slider) are free to move relative to it.

In this arrangement, the mechanism converts rotary motion into a reciprocating motion, but with a quick return stroke. That means the tool returns faster than it moves during the forward stroke, which increases the machine’s working efficiency.

Working Principle:

• The connecting rod and frame form a crank-like motion, and the slider reciprocates with unequal time for forward and return strokes.

Applications:

• Used in shaping machines, slotting machines, and slotted crank mechanisms where the tool must move quickly during the return stroke to save time.

This inversion is especially useful in metal-cutting machines where productivity can be increased by reducing idle time during the return stroke.

3. Third Inversion – Rotary Engine or Crank and Slotted Lever Mechanism

In the third inversion, the connecting rod (link 3) is fixed. The crank and slider both move relative to this fixed link.

Working Principle:

• As the crank rotates, the frame and slider move in a way that the output becomes rotary in nature.
• The mechanism can be designed to convert reciprocating motion into rotary motion for continuous operation.

Applications:

• Used in rotary engines where all links rotate continuously and power is transmitted to the output shaft.
• Also used in crank and slotted lever quick return mechanisms for shaping and slotting operations.

This inversion is particularly important in systems requiring rotary output without complete reciprocating parts, allowing compact and continuous energy transmission.

4. Fourth Inversion – Oscillating Cylinder Engine

In the fourth inversion, the slider (link 4) is fixed. This means the slider does not move, and the crank and connecting rod move relative to it.

Working Principle:

• The crank rotates and causes the cylinder (frame) to oscillate or swing back and forth.
• The piston remains stationary while the cylinder performs an oscillating motion.

Applications:

• Used in oscillating cylinder steam engines and beam engines.
• Common in small marine engines and compact pumping units where oscillating movement is needed instead of full rotation.

This inversion provides a unique motion suitable for small and compact power systems where space and mechanical balance are important.

Summary of Inversions

Inversion	Fixed Link	Example/Application
First Inversion	Frame (Link 1)	Reciprocating engine or pump
Second Inversion	Crank (Link 2)	Whitworth quick return mechanism
Third Inversion	Connecting Rod (Link 3)	Rotary engine mechanism
Fourth Inversion	Slider (Link 4)	Oscillating cylinder engine

Each inversion gives a new application depending on which link is fixed, making this mechanism highly versatile for industrial use.

Conclusion

The inversions of a single slider-crank mechanism demonstrate how one basic mechanism can produce different motions and machine functions by simply changing the fixed link. Each inversion has unique applications — from reciprocating engines to shaping machines and rotary engines. This versatility makes the single slider-crank mechanism one of the most important mechanical systems in engineering design and industrial applications.