Instantaneous centers of a six bar linkage

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In summary: I can try to help you out. In summary, the velocities of P 2,6 and slider D are equal, but can someone explain how this can be proven? As far as I understand, if P 2,6 is considered as a point on the extended link 2 then it has the same linear velocity as link 6, but why are the velocity directions the same? Is this because P 2,6 can be thought of as moving tangentially on a body and the tangent is horizontal? Also, couldn't the point P 2,6 on an extension of link 2 rotate about the slider D?Given the diagram, it appears that the three shaded regions labelled 1 form parts of the same rigid body, and these
  • #1
Andrew1235
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Homework Statement
Find the velocity of link 6 as a function of the rotational speed of link 2.
Relevant Equations
The velocity of P 2,6 can be determined by multiplying the angular speed of link 2 by the distance from the ground to P 2,6.
20210215_223531.jpg


I am not sure how to relate the velocities of P 2,6 and slider D. The textbook solution states that they are equal but can someone explain how this can be proven? As far as I understand if P 2,6 is considered as a point on the extended link 2 then it has the same linear velocity as link 6 but why are the velocity directions the same? Is this because P 2,6 can be thought of as moving tangentially on a body and the tangent is horizontal? Also couldn't the point P 2,6 on an extension of link 2 rotate about the slider D?
 
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You will need to provide a lot of explanation of the diagram.

I take it that the three shaded regions labelled 1 form parts of the same rigid body, and these count as one of the six links.

Labels 2 and 5 are next to what look like links.
Label 4 appears to refer to the line from P1,4 towards P1,5, but if that is all one rigid link then together with links 1 and 2 it forms a triangle, so no movement would be possible.

Label 3 is next to a block. Is that considered a link?

What does the small rectangle around P4,5 represent?

I have been quite unable to make any sense of the Pm,n notation. How does that work?
I do get that the dashed arrows with @∞ mean the label refers to a point at infinity in that direction.
 
  • #3
Andrew1235 said:
Homework Statement:: Find the velocity of link 6 as a function of the rotational speed of link 2.
Relevant Equations:: The velocity of P 2,6 can be determined by multiplying the angular speed of link 2 by the distance from the ground to P 2,6.
I am not sure how to relate the velocities of P 2,6 and slider D.
Welcome, Andrew! :cool:
Do you still need help with this problem?
 

Related to Instantaneous centers of a six bar linkage

1. What is the concept of instantaneous centers in a six bar linkage?

The concept of instantaneous centers in a six bar linkage refers to the point where two links in the linkage have zero relative velocity at a specific instant in time. This point is important in analyzing the motion and forces of a six bar linkage.

2. How are instantaneous centers determined in a six bar linkage?

Instantaneous centers in a six bar linkage can be determined by drawing perpendicular lines from the centers of rotation of each link to the adjacent link. The point where these lines intersect is the instantaneous center for that particular instant in time.

3. What is the significance of instantaneous centers in a six bar linkage?

Instantaneous centers play a crucial role in determining the velocity and acceleration of each link in a six bar linkage. They also help in understanding the forces acting on each link and how they contribute to the overall motion of the linkage.

4. Can instantaneous centers change during the motion of a six bar linkage?

Yes, instantaneous centers can change as the six bar linkage moves through different positions. This is because the relative velocity and acceleration of each link changes at different positions, resulting in different instantaneous centers.

5. How are instantaneous centers used in practical applications?

Instantaneous centers are used in practical applications such as designing machinery and mechanisms that require precise and controlled motion. They are also used in robotics, biomechanics, and other fields that involve the analysis of complex linkages and their motion.

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