Mechanical Engineering Exam > Mechanical Engineering Questions > f = 3 (n - 1) - 2j. In the Grubler's equa...
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f = 3 (n - 1) - 2j. In the Grubler's equation for planar mechanisms given, j is the
[IES-2003]
- a)Number of mobile links
- b)Number of links
- c)Number of lower pairs
- d)Length of the longest link
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
f = 3 (n - 1) - 2j. In the Grubler's equation for planar mechanism...
In general a mechanism with n number of links connected by j number of binary joints or lower pairs since it is single degree of freedom.
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f = 3 (n - 1) - 2j. In the Grubler's equation for planar mechanism...
The given equation is f = 3 (n - 1) - 2j. This equation is the Grubler's equation for planar mechanisms. It relates the number of degrees of freedom (DOF) of a planar mechanism to the number of links (n), joints (j), and the number of lower pairs.
To understand why the correct answer is option 'C', let's break down the equation and explain each term:
- f: The variable f represents the number of degrees of freedom of the mechanism. In other words, it represents the number of independent ways the mechanism can move. For example, a simple slider-crank mechanism has one degree of freedom, which allows it to move in a single plane.
- n: The variable n represents the number of links in the mechanism. A link is a rigid body that connects two or more joints. It can be thought of as a structural element of the mechanism.
- j: The variable j represents the number of joints in the mechanism. A joint is a connection between two or more links that allows relative motion between them. Joints can be classified into different types, such as revolute, prismatic, or cylindrical, depending on the type of motion they allow.
- The term 3 (n - 1): This term represents the contribution of the links to the degrees of freedom of the mechanism. Each link introduces two degrees of freedom, one for each end. However, since the mechanism is planar, one degree of freedom is constrained due to the planar nature of the mechanism. Hence, each link contributes one degree of freedom.
- The term -2j: This term represents the contribution of the joints to the degrees of freedom of the mechanism. Each joint introduces one constraint, which reduces the degrees of freedom. Hence, each joint reduces the degrees of freedom by one.
By combining the contributions of the links and joints, the Grubler's equation gives us the total number of degrees of freedom of the planar mechanism.
In this equation, the number of lower pairs (option 'C') is represented by the variable j. Lower pairs are a type of joint that allows both rotational and translational motion. Examples of lower pairs include revolute joints and prismatic joints.
Therefore, the correct answer is option 'C' because j represents the number of lower pairs in the Grubler's equation for planar mechanisms.
To understand why the correct answer is option 'C', let's break down the equation and explain each term:
- f: The variable f represents the number of degrees of freedom of the mechanism. In other words, it represents the number of independent ways the mechanism can move. For example, a simple slider-crank mechanism has one degree of freedom, which allows it to move in a single plane.
- n: The variable n represents the number of links in the mechanism. A link is a rigid body that connects two or more joints. It can be thought of as a structural element of the mechanism.
- j: The variable j represents the number of joints in the mechanism. A joint is a connection between two or more links that allows relative motion between them. Joints can be classified into different types, such as revolute, prismatic, or cylindrical, depending on the type of motion they allow.
- The term 3 (n - 1): This term represents the contribution of the links to the degrees of freedom of the mechanism. Each link introduces two degrees of freedom, one for each end. However, since the mechanism is planar, one degree of freedom is constrained due to the planar nature of the mechanism. Hence, each link contributes one degree of freedom.
- The term -2j: This term represents the contribution of the joints to the degrees of freedom of the mechanism. Each joint introduces one constraint, which reduces the degrees of freedom. Hence, each joint reduces the degrees of freedom by one.
By combining the contributions of the links and joints, the Grubler's equation gives us the total number of degrees of freedom of the planar mechanism.
In this equation, the number of lower pairs (option 'C') is represented by the variable j. Lower pairs are a type of joint that allows both rotational and translational motion. Examples of lower pairs include revolute joints and prismatic joints.
Therefore, the correct answer is option 'C' because j represents the number of lower pairs in the Grubler's equation for planar mechanisms.
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f = 3 (n - 1) - 2j. In the Grubler's equation for planar mechanism...
In general a mechanism with n no of links connected by j no of binary joints or lower pairs since it is single degree of freedom
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f = 3 (n - 1) - 2j. In the Grubler's equation for planar mechanisms given, j is the[IES-2003]a)Number of mobile linksb)Number of linksc)Number of lower pairsd)Length of the longest linkCorrect answer is option 'C'. Can you explain this answer?
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f = 3 (n - 1) - 2j. In the Grubler's equation for planar mechanisms given, j is the[IES-2003]a)Number of mobile linksb)Number of linksc)Number of lower pairsd)Length of the longest linkCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about f = 3 (n - 1) - 2j. In the Grubler's equation for planar mechanisms given, j is the[IES-2003]a)Number of mobile linksb)Number of linksc)Number of lower pairsd)Length of the longest linkCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for f = 3 (n - 1) - 2j. In the Grubler's equation for planar mechanisms given, j is the[IES-2003]a)Number of mobile linksb)Number of linksc)Number of lower pairsd)Length of the longest linkCorrect answer is option 'C'. Can you explain this answer?.
f = 3 (n - 1) - 2j. In the Grubler's equation for planar mechanisms given, j is the[IES-2003]a)Number of mobile linksb)Number of linksc)Number of lower pairsd)Length of the longest linkCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about f = 3 (n - 1) - 2j. In the Grubler's equation for planar mechanisms given, j is the[IES-2003]a)Number of mobile linksb)Number of linksc)Number of lower pairsd)Length of the longest linkCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for f = 3 (n - 1) - 2j. In the Grubler's equation for planar mechanisms given, j is the[IES-2003]a)Number of mobile linksb)Number of linksc)Number of lower pairsd)Length of the longest linkCorrect answer is option 'C'. Can you explain this answer?.
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