Inversions of Four Bar Chain Mechanism

Definition

An inversion of a mechanism is obtained by fixing different links of a kinematic chain one at a time. A four-bar chain mechanism is a fundamental kinematic chain consisting of four rigid links connected by four turning pairs (pin joints). By keeping one link stationary and allowing the others to move, we create different functional mechanisms known as inversions.

Main Content

1. Grashof’s Law

• This law states that for a four-bar mechanism to have at least one link capable of performing a full 360-degree rotation, the sum of the shortest and longest link lengths must be less than or equal to the sum of the other two link lengths.
• Mathematically: $S + L \leq P + Q$, where $S$ is the shortest link, $L$ is the longest, and $P, Q$ are the remaining links.

2. The Four-Bar Chain Structure

• The mechanism consists of four bars: the Frame (fixed), the Crank (rotating fully), the Coupler (connecting rod), and the Rocker (oscillating link).
• The behavior of the mechanism changes drastically depending on which of these links is chosen as the fixed link.

3. Types of Inversions

• Beam Engine (Crank and Lever): One link is fixed to turn a lever.
• Coupling Rod of Locomotive (Double Crank): Used to transmit rotary motion between wheels.
• Watt’s Indicator Mechanism: A modification of the four-bar chain to trace near-straight lines.

Working / Process

1. Beam Engine (Crank and Lever Mechanism)

• The frame is fixed, and the crank rotates, causing the beam to oscillate about a pivot.
• This was historically used to convert the rotary motion of a steam engine into the reciprocating motion of a pump.

2. Coupling Rod of Locomotive

• The two parallel cranks (wheels) are of equal length and are coupled by a rod.
• This ensures that both wheels rotate at the same angular velocity, maintaining synchronization.

3. Watt’s Indicator Mechanism

• This involves a four-bar chain where the links are arranged such that a point on the coupler traces a path very close to a straight line.
• This is essential for recording pressure-volume diagrams in steam engines.

       Link 2 (Crank)
          / \
         /   \
  Link 1(F)---Link 3 (Coupler)
       |       |
       \-------Link 4 (Rocker)

(Diagram of a standard four-bar chain kinematic structure)

Advantages / Applications

• Versatility: By simply changing which link is fixed, a single basic mechanism can be transformed into completely different functional tools.
• Industrial Automation: Used extensively in robotic arms, conveyor systems, and vehicle suspension systems.
• Efficiency: Four-bar linkages provide a robust and low-friction method to transmit power and motion in heavy machinery.

Summary

Inversions of a four-bar chain mechanism occur when different links are fixed to produce varied mechanical movements. These mechanisms are the building blocks of modern engineering, powering everything from locomotive wheels to precision industrial indicators.

Key terms to remember: Kinematic chain, Fixed Link, Crank, Coupler, Rocker, and Grashof's Law.