Question:
Consider the following statement(s) for its correctness.
A. In kinematic chain, the relative motion between the links is completely constrained.
B. A kinematic chain is known as mechanism when all of the links are fixed.
C. The mechanism forms a structure when number of degrees of freedom is zero
D. In kinematic chain, quaternary joint is equivalent to two binary joints
Choose the correct answer from the options given below:
Consider the following statement(s) for its correctness.
A. In kinematic chain, the relative motion between the links is completely constrained.
B. A kinematic chain is known as mechanism when all of the links are fixed.
C. The mechanism forms a structure when number of degrees of freedom is zero
D. In kinematic chain, quaternary joint is equivalent to two binary joints
Choose the correct answer from the options given below:
A. In kinematic chain, the relative motion between the links is completely constrained.
B. A kinematic chain is known as mechanism when all of the links are fixed.
C. The mechanism forms a structure when number of degrees of freedom is zero
D. In kinematic chain, quaternary joint is equivalent to two binary joints
Choose the correct answer from the options given below:
Show Hint
To remember joint equivalencies, think of the formula:
- Ternary joint (\(3\) links) \(\rightarrow 2\) Binary joints.
- Quaternary joint (\(4\) links) \(\rightarrow 3\) Binary joints.
It is always one less than the number of connected links.
- Ternary joint (\(3\) links) \(\rightarrow 2\) Binary joints.
- Quaternary joint (\(4\) links) \(\rightarrow 3\) Binary joints.
It is always one less than the number of connected links.
Updated On: Aug 3, 2026
- A and C only
- B and D only
- C and D only
- A and B only
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
In the theory of machines, a kinematic chain consists of links connected by joints that allow for controlled relative motion.
Understanding how these links and joints interact helps determine whether a system acts as a mechanism, a structure, or an unconstrained chain.
Step 2: Detailed Explanation:
Let us analyze the correctness of each statement:
- Statement A: "In a kinematic chain, the relative motion between the links is completely constrained."
This is correct.
By definition, a kinematic chain is an assembly of links connected by joint pairs such that the motion of any single link results in a predictable, completely constrained motion of all other links.
- Statement B: "A kinematic chain is known as a mechanism when all of the links are fixed."
This is incorrect.
A kinematic chain is called a mechanism when only one of its links is fixed to a reference frame, allowing the other links to move relative to it. If all links were fixed, no motion could occur.
- Statement C: "The mechanism forms a structure when the number of degrees of freedom is zero."
This is correct.
According to Grubler's and Kutzbach's criteria, if the degrees of freedom (DOF) of a link assembly is equal to zero, no relative motion can occur. The system becomes a statically determinate structure (rigid frame).
- Statement D: "In a kinematic chain, a quaternary joint is equivalent to two binary joints."
This is incorrect.
The equivalence formula for multi-link joints is:
\[ \text{Equivalent Binary Joints} = n - 1 \] Where \(n\) is the number of links connected at a single joint.
- For a ternary joint (3 links connected): \(3 - 1 = 2\) binary joints.
- For a quaternary joint (4 links connected): \(4 - 1 = 3\) binary joints.
Thus, a quaternary joint is equivalent to three binary joints, not two.
Therefore, only statements A and C are correct.
Step 3: Final Answer:
The correct option is (A).
In the theory of machines, a kinematic chain consists of links connected by joints that allow for controlled relative motion.
Understanding how these links and joints interact helps determine whether a system acts as a mechanism, a structure, or an unconstrained chain.
Step 2: Detailed Explanation:
Let us analyze the correctness of each statement:
- Statement A: "In a kinematic chain, the relative motion between the links is completely constrained."
This is correct.
By definition, a kinematic chain is an assembly of links connected by joint pairs such that the motion of any single link results in a predictable, completely constrained motion of all other links.
- Statement B: "A kinematic chain is known as a mechanism when all of the links are fixed."
This is incorrect.
A kinematic chain is called a mechanism when only one of its links is fixed to a reference frame, allowing the other links to move relative to it. If all links were fixed, no motion could occur.
- Statement C: "The mechanism forms a structure when the number of degrees of freedom is zero."
This is correct.
According to Grubler's and Kutzbach's criteria, if the degrees of freedom (DOF) of a link assembly is equal to zero, no relative motion can occur. The system becomes a statically determinate structure (rigid frame).
- Statement D: "In a kinematic chain, a quaternary joint is equivalent to two binary joints."
This is incorrect.
The equivalence formula for multi-link joints is:
\[ \text{Equivalent Binary Joints} = n - 1 \] Where \(n\) is the number of links connected at a single joint.
- For a ternary joint (3 links connected): \(3 - 1 = 2\) binary joints.
- For a quaternary joint (4 links connected): \(4 - 1 = 3\) binary joints.
Thus, a quaternary joint is equivalent to three binary joints, not two.
Therefore, only statements A and C are correct.
Step 3: Final Answer:
The correct option is (A).
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