Short Answer:

A mechanism inversion is obtained when one link of a kinematic chain is fixed, and the relative motion between the remaining links is studied. By fixing different links one at a time, different mechanisms can be produced from the same kinematic chain. Each fixed-link arrangement gives a new inversion of that chain.

In simple words, mechanism inversion helps in obtaining various useful mechanisms from a single chain by changing which link is held stationary. For example, the four-bar chain gives three inversions, while single slider-crank and double slider-crank chains also give multiple inversions used in practical machines.

Detailed Explanation :

Mechanism Inversion

A mechanism inversion is a fundamental concept in kinematics of machines that explains how multiple mechanisms can be obtained from a single kinematic chain by fixing different links in turn. When a kinematic chain is formed by connecting links through pairs, none of the links is fixed initially. But to convert a chain into a useful mechanism, one of the links must be held stationary. The process of fixing different links of the same kinematic chain, one at a time, to obtain different mechanisms is called inversion of mechanism.

In simple terms, when we change the fixed link of a kinematic chain, we get a new set of relative motions between the remaining links. This new arrangement behaves as a different mechanism though it is derived from the same basic chain. Each such mechanism obtained from the same chain is known as an inversion.

Basic Concept

A kinematic chain consists of several links connected by kinematic pairs that allow relative motion between them. The purpose of such a chain is to transmit motion or force from one point to another in a machine. However, when one of these links is fixed, it converts the chain into a mechanism that performs useful work.

If we fix different links of the same chain, we get different types of relative motion, and therefore, different mechanisms. This process is called mechanism inversion.

For example, a four-bar chain consists of four links connected by four turning pairs. When one link is fixed, it becomes a four-bar mechanism. If another link is fixed instead, we get another form of four-bar mechanism with different motion characteristics.

Definition

Mechanism inversion can be defined as:

“The process of obtaining different mechanisms by fixing different links of a kinematic chain, one at a time, is known as inversion of mechanism.”

This definition emphasizes that the geometry of the chain remains the same, but the motion characteristics and application change depending on which link is fixed.

Purpose of Mechanism Inversion

The main purpose of inversion is to derive various useful mechanisms from one basic chain. Each inversion may serve a different practical application, even though they are built from the same set of links. This allows engineers to use the same basic structure for multiple machines by slightly altering the configuration.

Example of Mechanism Inversion

Four-Bar Chain Inversions
The four-bar chain is one of the most commonly studied kinematic chains. It consists of four links and four turning pairs. Depending on which link is fixed, we can obtain three possible inversions:
- First inversion: When the shortest link is fixed, it gives a double crank mechanism (or drag-link mechanism).
- Second inversion: When any link adjacent to the shortest link is fixed, it gives a crank and rocker mechanism.
- Third inversion: When the link opposite the shortest link is fixed, it gives a double rocker mechanism.

Each inversion finds different applications such as in engines, pumps, and couplings.

Single Slider-Crank Chain Inversions
The single slider-crank chain consists of one sliding pair and three turning pairs. It gives four different inversions:
- First inversion: Used in reciprocating engines.
- Second inversion: Used in rotary internal combustion engines.
- Third inversion: Used in oscillating cylinder engines.
- Fourth inversion: Used in hand pumps.

These inversions demonstrate how the same basic link combination can perform different types of motion by simply changing the fixed link.

Double Slider-Crank Chain Inversions
The double slider-crank chain has two sliding pairs and two turning pairs. It produces three important inversions:
- Elliptical trammel (used to draw ellipses).
- Scotch yoke mechanism (used to convert rotary motion into reciprocating motion).
- Oldham’s coupling (used to connect two shafts that have a small lateral misalignment).

Each of these inversions serves a unique industrial or mechanical purpose.

Importance of Mechanism Inversion

Simplifies Machine Design:
By using the concept of inversion, designers can develop several machine mechanisms without creating new link systems.
Reduces Manufacturing Cost:
Since the same links can be used in different ways, it saves material, time, and production cost.
Provides Motion Versatility:
Different types of motion such as rotary, reciprocating, or oscillating can be achieved from one basic chain.
Used in Practical Machines:
Mechanism inversions are the foundation of many mechanical devices like engines, compressors, pumps, and couplings.

Working Principle

When one link in a kinematic chain is fixed, the other links move relative to it. By changing which link is fixed, the direction and type of motion change. However, the length of links and the type of joints remain constant.
This change in fixed link alters the motion transfer pattern within the chain, leading to new functional mechanisms. Therefore, the geometry remains constant, but the kinematics (motion characteristics) of the mechanism change.

Applications

Used in designing engines, reciprocating pumps, and compressors.
Applied in coupling mechanisms like Oldham’s coupling.
Used in drawing devices like elliptical trammel.
Applied in shaping and slotting machines for controlled linear motion.
Used in robotic arms and linkages for specific motion control.

Conclusion

Mechanism inversion is the process of obtaining different mechanisms by fixing different links of the same kinematic chain. It is an essential concept in machine design and kinematics, as it helps in deriving multiple practical mechanisms from one basic structure. Each inversion gives a new mechanism that can serve a distinct purpose, such as rotary, reciprocating, or oscillating motion. Therefore, understanding mechanism inversion is key to developing efficient and versatile machines used in various mechanical systems.