What are the inversions of single slider-crank mechanism?

Short Answer:

The inversions of a single slider-crank mechanism are obtained by fixing different links of the chain one at a time. There are four possible inversions in this mechanism. They are:

  1. Reciprocating engine mechanism (first inversion),
  2. Rotary engine mechanism (second inversion),
  3. Oscillating cylinder mechanism (third inversion), and
  4. Hand pump mechanism (fourth inversion).

Each inversion changes the motion of the links and produces different types of mechanical movements used in various machines like engines, pumps, and compressors.

Detailed Explanation:

Inversions of Single Slider-Crank Mechanism

The single slider-crank mechanism is a modification of the four-bar chain, where one of the turning pairs is replaced by a sliding pair. It has four links — the frame (fixed link), crank, connecting rod (coupler), and slider. This mechanism is used to convert rotary motion into reciprocating motion or vice versa.

When different links of the single slider-crank chain are fixed one at a time, four different mechanisms are obtained. Each of these mechanisms is called an inversion of the single slider-crank chain. The motion and function of each inversion vary depending on which link is fixed.

  1. First Inversion – Reciprocating Engine Mechanism

In the first inversion, the frame (link 1) is fixed. The crank (link 2) rotates about a fixed point, and the slider (link 4) moves in a straight line within the guide of the frame. The connecting rod (link 3) connects the crank and the slider.

As the crank rotates continuously, it causes the slider to move back and forth along a straight path. This inversion converts rotary motion into reciprocating motion.

Example Applications:

  • Internal combustion engines
  • Reciprocating compressors
  • Steam engines

This is the most commonly used inversion and is found in nearly all piston-type mechanical systems where linear motion of the piston is converted to rotary motion of the crankshaft.

  1. Second Inversion – Rotary Engine Mechanism

In this inversion, the connecting rod (link 3) is fixed. The crank (link 2) and frame (link 1) both rotate around the fixed connecting rod. The slider (link 4) moves along a circular path instead of a straight line.

In this type of inversion, the slider and the frame rotate about the same center. The mechanism is mainly used to obtain rotary motion of both the crank and the frame while keeping the connecting rod stationary.

Example Applications:

  • Rotary internal combustion engines
  • Crank-type rotary pumps
  • Certain types of mechanical drives used in aircraft engines

This inversion helps to generate rotary motion with fewer moving parts and is often used in compact mechanisms.

  1. Third Inversion – Oscillating Cylinder Mechanism

In this inversion, the crank (link 2) is fixed. The slider (link 4) moves along a straight guide attached to an oscillating cylinder. The connecting rod (link 3) connects the slider and the oscillating cylinder.

As the slider moves back and forth, it causes the cylinder to oscillate (swing) about a pivot point. The cylinder does not rotate fully but moves through a limited angular range.

Example Applications:

  • Cradle-type steam engines
  • Oscillating cylinder engines used in ships
  • Small steam pumps

This inversion is useful in cases where a full rotation is not required and oscillatory motion is sufficient for operation.

  1. Fourth Inversion – Hand Pump Mechanism

In the fourth inversion, the slider (link 4) is fixed. The crank (link 2) is rotated manually or by a motor. The connecting rod (link 3) and the frame (link 1) move to produce an oscillatory motion.

This mechanism converts rotary motion of the crank into oscillatory motion of the frame or connecting rod. The fixed slider acts as a pivot point for the connecting rod, allowing the crank to rotate and create a pumping or lifting action.

Example Applications:

  • Hand-operated reciprocating pumps
  • Small lifting devices
  • Manual water pumps

This inversion demonstrates how fixing the slider changes the motion type from linear to oscillatory while maintaining the same linkage system.

Summary of Inversions:

  1. First Inversion: Frame fixed → Reciprocating engine mechanism
  2. Second Inversion: Connecting rod fixed → Rotary engine mechanism
  3. Third Inversion: Crank fixed → Oscillating cylinder mechanism
  4. Fourth Inversion: Slider fixed → Hand pump mechanism

Each inversion is a practical form of the same kinematic chain, but the function changes as the fixed link changes. These inversions are highly useful in the design of machines where motion conversion is required.

Conclusion

The inversions of the single slider-crank mechanism show how versatile a simple four-link system can be. By fixing different links, engineers can create mechanisms that generate rotary, reciprocating, or oscillatory motion. These inversions form the basis for several important mechanical systems like engines, pumps, and compressors. Understanding them helps in designing machines that efficiently convert one type of motion into another according to practical requirements.