Robotics Nptel Week 3 Assignment Answers and Solutions
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Robotics Nptel Week 3 Assignment Answers and Solutions (July-Dec 2025)
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Question 1. Translation along x axis by p units, that is, TRANS(X, p) is given by
Question 2. Which one of the following statements about the rotation matrix is FALSE?
a) ROT(X,θ₁) ROT(Y,θ₂) = ROT(Y,θ₂) ROT(X,θ₁)
b) ROT(X,θ₁) ROT(Y,θ₂) = ROT(Y,θ₂) ROT(X,θ₂)
c) ROTᵀ(X,θ) = ROT⁻¹(X,θ)
d) Each row/column of a rotation matrix is a unit vector
Question 3. A 4 x 4 matrix representing rotation about X axis by an angle θ, and translation along the X, Y and Z axes by a, b and c units, respectively, is given by
Question 4. Cartesian coordinate system can be used to represent
a) the position of end-effector only of a manipulator with respect to its base coordinate system.
b) the orientation of end-effector only of a manipulator with respect to its base coordinate system.
c) both the position and orientation of end-effector of a manipulator with respect to its base coordinate system
d) neither the position nor orientation of end-effector of a manipulator with respect to its base coordinate system
Question 5. According to Denavit-Hartenberg’s notations, length of ith link, that is, aᵢ is defined as
a) mutual perpendicular distance between two consecutives X axes.
b) mutual perpendicular distance between two consecutives Z axes.
c) mutual perpendicular distance between two consecutives Y axes.
d) can never be equal to zero.
These are Robotics Nptel Week 3 Assignment Answers and Solutions
Question 6. According to Denavit-Hartenberg notations, link-offset, that is, dᵢ is defined as
a) the distance between two consecutives Y-axes measured along Z-axis.
b) the distance between two consecutives Z-axes measured along X-axis.
c) the distance between two consecutives X-axes measured along Z-axis.
d) the distance between two consecutives Z-axes measured along Y-axis.
Question 7. According to Denavit-Hartenberg’s notation, angle of twist of ith link, that is, αᵢ is defined as
a) the angle between two consecutive Z axes measured about X axis.
b) the angle between two consecutive X axes measured about Y axis.
c) the angle between two consecutive X axes measured about Z axis.
d) the angle between two consecutive Y axes measured about Z axis.
Question 8. According to Denavit-Hartenberg notations, joint angle (θᵢ) is defined as
a) the angle between two consecutives Y axes measured about Z axis.
b) the angle between two consecutives Y axes measured about X axis.
c) the angle between two consecutives X axes measured about Z axis.
d) the angle between two consecutives Z axes measured about X axis.
These are Robotics Nptel Week 3 Assignment Answers and Solutions
Question 9. The concept of Roll, Pitch and Yaw angles has been used to represent the rotation of a frame (B) with respect to the reference frame (U). Let us suppose that the above rotation can also be expressed by a 3 x 3 rotation matrix, as given below. [10000.50.86600.8660.5]\begin{bmatrix} 1 & 0 & 0 \\ 0 & 0.5 & 0.866 \\ 0 & 0.866 & 0.5 \end{bmatrix}
The angles of rolling (α), pitching (β) and yawing (γ) are found to be as follows:
a) α = 45°, β = 60°, γ = 0°
b) α = 0°, β = 60°, γ = 45°
c) α = 0°, β = 30°, γ = 45°
d) α = 60°, β = 0°, γ = 0°
These are Robotics Nptel Week 3 Assignment Answers and Solutions
Question 10. The concept of Euler angles has been used to represent the rotation of a frame (B) with respect to the reference frame (U). Let us suppose that the above rotation can also be expressed by a 3 x 3 rotation matrix as given below. [0.86600.50100.500.866]\begin{bmatrix} 0.866 & 0 & 0.5 \\ 0 & 1 & 0 \\ 0.5 & 0 & 0.866 \end{bmatrix}
The Euler angles (α, β, γ) are found to be as follows:
a) α = 0°, β = 30°, γ = 0°
b) α = 45°, β = 0°, γ = 60°
c) α = 30°, β = 30°, γ = 30°
d) α = 45°, β = 45°, γ = 45°
These are Robotics Nptel Week 3 Assignment Answers and Solutions
