NPTEL Advanced Robotics Week 4 Assignment Answers 2025
1. The end-effector velocity and joint velocity is related by
- Rotation matrix
- Jacobian matrix
- Null-space of Jacobian matrix
- Homogeneous transformation matrix
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2. If the determinant of the Jacobian matrix is equal to zero then
- Joint velocity becomes maximum
- Joint velocity becomes minimum
- Joint velocity becomes infinity
- Joint velocity becomes zero
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3. Singularities are points in the workspace where
- determinant of Jacobian becomes zero.
- determinant of Jacobian becomes positive.
- determinant of Jacobian is undefined.
- energy is minimum.
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4. For a two link 2 DoF (2R) palner manipulator as shown below has singu-
larities at
- θ1=−90∘
- θ1=270∘
- θ2=90∘
- θ2=0∘,180∘
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5. The maximum energy configuration for the 2 DoF (2R) manipulator of Q4
is
θ1=90∘,180∘
θ2=90∘
θ2=0∘,180∘
θ1=0∘,90∘
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6. For the 2 link manipulator (2R) given below, a force F3=[110] acts at the end-effector. Find the torque (moment) acting at joint 2. (l2=1)
- [001]
- [011]
- [110]
- [111]
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7. Manipulation ability is defined as
- ease of moving in a particular direction
- ease of moving in all directions
- ease of moving in two orthogonal directions
- determinant of the rotation matrix
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8. The major axis of the velocity ellipsoid is found by (J is the Jacobian matrix)
- the square root of determinant of JJT
- determinant of J
- Singular Value Decomposition of J−1
- Singular Value Decomposition of J
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9. Singular values of a non-square matrix ′A′ are the
- trace of A.
- square roots of eigen values of A.
- Square roots of the non-zero eigen values of AAT.
- Square roots of the non-zero diagonal elements of A.
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10. Singular value decomposition of a matrix breaks it up into
- a diagonal matrix and a rectangular matrix.
- a diagonal matrix and two rotation matrices.
- a diagonal matrix and two orthogonal matrices.
- a diagonal matrix and a non-singular matrix
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