Solving Four Bar Chain Problems

Table of Contents

1. Introduction
2. Understanding the 4 Bar Chain
3. Configuration Diagram
   • Determining the Scale
   • Drawing the fixed link AD
   • Plotting angle BAD
   • Drawing the crank AB
   • Drawing the connecting link BC
4. Velocity Diagram
   • Analyzing the direction of the crank rotation
   • Calculating the angular velocity of the crank AB
   • Finding the velocity of point B with respect to point A
   • Plotting the velocity diagram
   • Determining the velocity of point C with respect to point D and point B
5. Angular Velocity Calculation
   • Measuring the length of link CD
   • Calculating the angular velocity of link CD
6. Conclusion

Introduction

In this article, we will Delve into the mechanics of the 4 Bar Chain and explore how it works. Specifically, we will focus on finding the velocity and acceleration of different lengths of the 4 Bar Chain. By understanding the concept of angular velocity and the configuration of the chain, we can accurately determine the motion characteristics of the system.

Understanding the 4 Bar Chain

The 4 Bar Chain is a mechanism consisting of four links connected by revolute joints. It is commonly used in various engineering applications, such as in the design of linkages and mechanical systems. The four links are typically labeled as AB, BC, CD, and AD, where AB is the crank, BC and AD are the coupler links, and CD is the rocker link. The motion of the chain is determined by the rotation of the crank AB.

Configuration Diagram

Before we can proceed with calculating the velocity and acceleration, we need to first draw the configuration diagram of the 4 Bar Chain. This diagram provides a visual representation of the system and allows us to accurately analyze its motion. Here are the steps involved in drawing the configuration diagram:

Determining the scale

To draw an accurate configuration diagram, we need to determine an appropriate scale Based on the lengths of the links. In this case, the lengths are given as 150 mm, 40 mm, and 80 mm. By selecting a suitable scale, we can ensure that the diagram is clear and concise.

Drawing the fixed link AD

The fixed link AD is always positioned at the bottom of the configuration diagram. It represents the ground or any fixed component of the system. In this case, the length of AD is 150 mm. Using the selected scale, we can draw the fixed link AD accurately.

Plotting angle BAD

The angle BAD is given as 60 degrees in the question. To accurately represent this angle in the diagram, we can use a protractor or measuring tool. By measuring and plotting the angle, we can ensure that the diagram reflects the given conditions.

Drawing the crank AB

The crank AB is the link that rotates and drives the motion of the chain. Its length is given as 40 mm. Using the selected scale, we can draw the crank AB and position it at the appropriate angle based on the given conditions.

Drawing the connecting link BC

The connecting link BC is of equal length to AD, which is 80 mm. This link connects the crank AB to the rocker link CD. By drawing the link BC accurately, we can establish the complete configuration of the 4 Bar Chain.

Velocity Diagram

Once we have the configuration diagram, we can proceed with drawing the velocity diagram. This diagram helps us analyze the motion of the chain by considering the velocities of different points. Here are the steps involved in drawing the velocity diagram:

Analyzing the direction of the crank rotation

In the question, it is Mentioned that the crank AB rotates clockwise at 120 rpm. This information informs us about the direction of the crank's rotation. Knowing the direction is crucial when determining the velocities of different points in the chain.

Calculating the angular velocity of the crank AB

To calculate the angular velocity of the crank AB, we can use the formula: omega = 2 Pi n / 60, where omega represents the angular velocity and n represents the rotational speed in rpm. By substituting the given values, we can determine the angular velocity of the crank AB.

Finding the velocity of point B with respect to point A

To find the velocity of point B with respect to point A, we need to consider the perpendicular distance between point B and the crank AB. This distance corresponds to the length of AB. By multiplying the length of AB with the angular velocity, we can calculate the velocity of point B with respect to point A.

Plotting the velocity diagram

Using the obtained values for the velocity of point B with respect to point A, we can plot the vector in the diagram. By selecting a suitable scale, we can accurately represent the magnitudes and directions of the velocities. This will give us a comprehensive velocity diagram.

Determining the velocity of point C with respect to point D and point B

Point C is connected to both point B and point D in the 4 Bar Chain. Therefore, there are two velocities to consider: the velocity of point C with respect to point B and the velocity of point C with respect to point D. These velocities are perpendicular to the respective links. By plotting these velocities in the diagram, we can analyze their magnitudes and directions.

Angular Velocity Calculation

Once we have the velocity diagram, we can proceed with the calculation of the angular velocity of the link CD. To calculate this, we need to measure the length of the link CD and convert it into meters. Using the given length, we can determine the angular velocity by dividing the length by the time unit. By applying the appropriate formula, we can determine the angular velocity accurately.

Conclusion

In conclusion, understanding the mechanics of the 4 Bar Chain and its motion characteristics is crucial in various engineering applications. By accurately drawing the configuration and velocity diagrams, we can analyze the velocities and accelerations of different points in the system. Through these calculations, we can gain valuable insights into the dynamics of the 4 Bar Chain and its performance.