Understanding solution method for finding accelerations in a mechanical linkage

In summary, the conversation is about a discrepancy in using equations between the person and Chegg. The person is wondering why their equation gave a different answer and questions the accuracy of neglecting the cross product term. It is then explained that in the Chegg problem, the angular acceleration is zero and the velocities are constant, leading to no rotation between the bars. The person then realizes their mistake and thanks the other person for explaining.
  • #1
whitejac
169
0

Homework Statement


I was checking my work and Chegg uses the equations differently. Can somebody tell me why? Maybe I'm misunderstanding how/why to use the equation I chose.
Steps 1-3.JPG
Steps 4-5.JPG

Homework Equations


They say aB = -ω2ABRB/Ai
I used aB = aA + αk x r - ω2rB/A

The Attempt at a Solution


So obviously mine will be a different answer, I only found aB but it gave me an i and j component because of that cross product. Which one is correct and why? Why can they neglect the cross product?
 
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  • #2
The cross product term involves angular acceleration of the rod connecting A and B. In the Chegg problem, the angular acceleration is apparently zero.
 
  • #3
How do they justify there being no angular acceleration? It doesn't say this is a static situation, so these bars should be rotating towards one another.
 
  • #4
whitejac said:
How do they justify there being no angular acceleration? It doesn't say this is a static situation, so these bars should be rotating towards one another.

I figured it out. The problem states that the velocities are constant and therefore the angular accelerations are zero.
Man, reading is important. Thank you for explaining this to me!
 

FAQ: Understanding solution method for finding accelerations in a mechanical linkage

What is a mechanical linkage?

A mechanical linkage is a system of interconnected mechanical components that work together to transmit motion or force from one point to another.

How do you find accelerations in a mechanical linkage?

To find accelerations in a mechanical linkage, you need to first identify all the components in the linkage and determine their relative positions and velocities. Then, you can use the equations of motion, such as Newton's laws, to calculate the accelerations of each component.

What are some common solution methods for finding accelerations in a mechanical linkage?

Some common solution methods for finding accelerations in a mechanical linkage include graphical methods, such as the velocity and acceleration polygons, and analytical methods, such as the use of equations and mathematical modeling.

Are there any limitations to using solution methods for finding accelerations in a mechanical linkage?

Yes, there can be limitations to using solution methods for finding accelerations in a mechanical linkage. These methods may not be accurate for complex or nonlinear linkages, and they may require assumptions and simplifications that can affect the accuracy of the results.

How can understanding solution methods for finding accelerations in a mechanical linkage be beneficial?

Understanding solution methods for finding accelerations in a mechanical linkage can be beneficial for engineers and designers as it allows them to analyze the performance and behavior of mechanical systems. This knowledge can help in the design and optimization of linkages for various applications in industries such as automotive, aerospace, and robotics.

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