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A linkage is shown below in the figure in which links ABC and DEF are ternary Jinks whereas AF, BE and CD are binary links. The degrees of freedom of the linkage when link ABC is fixed are (a) 0 (b) 1 (c) 2 (d) 3?
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A linkage is shown below in the figure in which links ABC and DEF are ...
Linkage and Degrees of Freedom
Linkage is a mechanical system composed of links and joints connected together to perform a specific function. The degrees of freedom (DOF) of a linkage refer to the number of independent variables required to describe the motion of the system. In other words, it represents the number of ways in which a linkage can move.
Given Linkage
In the given linkage, there are two ternary links (ABC and DEF) and three binary links (AF, BE, and CD). Ternary links have three joints, whereas binary links have two joints. The joints in the linkage are labeled as A, B, C, D, E, and F.
Fixed Link ABC
When link ABC is fixed, it means that it is held stationary and cannot move. This implies that joint A is fixed, and hence, it does not contribute to the DOF of the system.
Calculating Degrees of Freedom
To calculate the DOF of the linkage when link ABC is fixed, we need to determine the number of independent variables required to describe the motion of the system.
1. The fixed joint A does not contribute to the motion, so it does not add any DOF.
2. Ternary link DEF has three joints (D, E, and F), which can independently move. Therefore, it adds 3 DOF.
3. Binary link AF has two joints (A and F), but joint A is fixed. So, it contributes only 1 DOF.
4. Binary link BE has two joints (B and E), which can independently move. Thus, it adds 2 DOF.
5. Binary link CD has two joints (C and D), but joint D is already considered in link DEF. So, it does not add any additional DOF.
Calculating Total Degrees of Freedom
To calculate the total DOF, we need to sum up the contributions from each link.
Total DOF = DOF of ternary link DEF + DOF of binary link AF + DOF of binary link BE + DOF of binary link CD
Total DOF = 3 + 1 + 2 + 0
Total DOF = 6
Answer
Therefore, the degrees of freedom of the linkage when link ABC is fixed are 6. Option (d) is the correct answer.
Linkage is a mechanical system composed of links and joints connected together to perform a specific function. The degrees of freedom (DOF) of a linkage refer to the number of independent variables required to describe the motion of the system. In other words, it represents the number of ways in which a linkage can move.
Given Linkage
In the given linkage, there are two ternary links (ABC and DEF) and three binary links (AF, BE, and CD). Ternary links have three joints, whereas binary links have two joints. The joints in the linkage are labeled as A, B, C, D, E, and F.
Fixed Link ABC
When link ABC is fixed, it means that it is held stationary and cannot move. This implies that joint A is fixed, and hence, it does not contribute to the DOF of the system.
Calculating Degrees of Freedom
To calculate the DOF of the linkage when link ABC is fixed, we need to determine the number of independent variables required to describe the motion of the system.
1. The fixed joint A does not contribute to the motion, so it does not add any DOF.
2. Ternary link DEF has three joints (D, E, and F), which can independently move. Therefore, it adds 3 DOF.
3. Binary link AF has two joints (A and F), but joint A is fixed. So, it contributes only 1 DOF.
4. Binary link BE has two joints (B and E), which can independently move. Thus, it adds 2 DOF.
5. Binary link CD has two joints (C and D), but joint D is already considered in link DEF. So, it does not add any additional DOF.
Calculating Total Degrees of Freedom
To calculate the total DOF, we need to sum up the contributions from each link.
Total DOF = DOF of ternary link DEF + DOF of binary link AF + DOF of binary link BE + DOF of binary link CD
Total DOF = 3 + 1 + 2 + 0
Total DOF = 6
Answer
Therefore, the degrees of freedom of the linkage when link ABC is fixed are 6. Option (d) is the correct answer.
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A linkage is shown below in the figure in which links ABC and DEF are ternary Jinks whereas AF, BE and CD are binary links. The degrees of freedom of the linkage when link ABC is fixed are (a) 0 (b) 1 (c) 2 (d) 3?
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A linkage is shown below in the figure in which links ABC and DEF are ternary Jinks whereas AF, BE and CD are binary links. The degrees of freedom of the linkage when link ABC is fixed are (a) 0 (b) 1 (c) 2 (d) 3? 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 A linkage is shown below in the figure in which links ABC and DEF are ternary Jinks whereas AF, BE and CD are binary links. The degrees of freedom of the linkage when link ABC is fixed are (a) 0 (b) 1 (c) 2 (d) 3? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A linkage is shown below in the figure in which links ABC and DEF are ternary Jinks whereas AF, BE and CD are binary links. The degrees of freedom of the linkage when link ABC is fixed are (a) 0 (b) 1 (c) 2 (d) 3?.
A linkage is shown below in the figure in which links ABC and DEF are ternary Jinks whereas AF, BE and CD are binary links. The degrees of freedom of the linkage when link ABC is fixed are (a) 0 (b) 1 (c) 2 (d) 3? 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 A linkage is shown below in the figure in which links ABC and DEF are ternary Jinks whereas AF, BE and CD are binary links. The degrees of freedom of the linkage when link ABC is fixed are (a) 0 (b) 1 (c) 2 (d) 3? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A linkage is shown below in the figure in which links ABC and DEF are ternary Jinks whereas AF, BE and CD are binary links. The degrees of freedom of the linkage when link ABC is fixed are (a) 0 (b) 1 (c) 2 (d) 3?.
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