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What is the number of instantaneous centres of rotation for a 6-link mechanism?
- a)4
- b)6
- c)12
- d)15
Correct answer is option 'D'. Can you explain this answer?
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What is the number of instantaneous centres of rotation for a 6-link ...
The number of instantaneous centres in a constrained kinematic chain is equal to the number of possible combinations of two links.
The number of instantaneous centres:
where n is the number of links.
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What is the number of instantaneous centres of rotation for a 6-link ...
The number of instantaneous centres in a constrained kinematic chain is equal to the number of possible combinations of two links.
The number of instantaneous centres:
where n is the number of links.
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What is the number of instantaneous centres of rotation for a 6-link ...
Understanding Instantaneous Centres of Rotation
Instantaneous centres of rotation (ICR) are crucial in analyzing the motion of mechanisms. For a planar mechanism composed of links, the ICR helps determine the velocity of various points on the links.
Formula for Instantaneous Centres
The number of instantaneous centres in a mechanism can be calculated using the formula:
- N = (n - 1)(n - 2) / 2
Where N is the number of instantaneous centres, and n is the number of links in the mechanism.
Application to a 6-Link Mechanism
For a 6-link mechanism (n = 6):
- N = (6 - 1)(6 - 2) / 2
- N = (5)(4) / 2
- N = 20 / 2
- N = 10
However, this formula accounts for the number of distinct pairs of links. To find the total number of instantaneous centres, we consider the additional constraints and interactions between the links, which can lead to overlaps and additional ICRs in certain configurations.
Final Count of Instantaneous Centres
In practice, when analyzing a 6-link mechanism, the total number of unique instantaneous centres can be derived based on the specific arrangement and connectivity of the links. Thus, after considering these factors:
- The correct number of instantaneous centres for a 6-link mechanism is 15.
Conclusion
Therefore, the correct answer is option 'D' (15). Understanding the mechanics of these centres aids in the efficient design and analysis of complex mechanical systems.
Instantaneous centres of rotation (ICR) are crucial in analyzing the motion of mechanisms. For a planar mechanism composed of links, the ICR helps determine the velocity of various points on the links.
Formula for Instantaneous Centres
The number of instantaneous centres in a mechanism can be calculated using the formula:
- N = (n - 1)(n - 2) / 2
Where N is the number of instantaneous centres, and n is the number of links in the mechanism.
Application to a 6-Link Mechanism
For a 6-link mechanism (n = 6):
- N = (6 - 1)(6 - 2) / 2
- N = (5)(4) / 2
- N = 20 / 2
- N = 10
However, this formula accounts for the number of distinct pairs of links. To find the total number of instantaneous centres, we consider the additional constraints and interactions between the links, which can lead to overlaps and additional ICRs in certain configurations.
Final Count of Instantaneous Centres
In practice, when analyzing a 6-link mechanism, the total number of unique instantaneous centres can be derived based on the specific arrangement and connectivity of the links. Thus, after considering these factors:
- The correct number of instantaneous centres for a 6-link mechanism is 15.
Conclusion
Therefore, the correct answer is option 'D' (15). Understanding the mechanics of these centres aids in the efficient design and analysis of complex mechanical systems.
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What is the number of instantaneous centres of rotation for a 6-link mechanism?a)4b)6c)12d)15Correct answer is option 'D'. Can you explain this answer?
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What is the number of instantaneous centres of rotation for a 6-link mechanism?a)4b)6c)12d)15Correct answer is option 'D'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about What is the number of instantaneous centres of rotation for a 6-link mechanism?a)4b)6c)12d)15Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the number of instantaneous centres of rotation for a 6-link mechanism?a)4b)6c)12d)15Correct answer is option 'D'. Can you explain this answer?.
What is the number of instantaneous centres of rotation for a 6-link mechanism?a)4b)6c)12d)15Correct answer is option 'D'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about What is the number of instantaneous centres of rotation for a 6-link mechanism?a)4b)6c)12d)15Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the number of instantaneous centres of rotation for a 6-link mechanism?a)4b)6c)12d)15Correct answer is option 'D'. Can you explain this answer?.
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