# NPTEL Robotics Week 4 Assignment Answers

NPTEL Robotics Week 4 Assignment Answers:- In this post, we have provided the answers to the NPTEL Robotics Week 4. All the answers are provided here on the basis of data available on the internet.

## NPTEL Robotics Week 4 Assignment Answers 2022

Q1. A 2 dof serial manipulator with the links having lengths of L and Lz has the joint angles represented by 6, and 02. The end-effector’s coordinates are represented by (qx4y), where

4xL cOSs6, + Lącos (0, + 0,)
4 Lsin 0, + Lzsin (0, +0,)

The Jacobian matrix for the given configuration will be as follows:

`Answer:- d`

Q2. Which one(s) of the following statements is/are Correct with respect to Jacobian matrix? Statement-1: Jacobian matrix is nothing but multi-dimensional form of derivative. Statement-2: Jacobian matrix relates the Cartesian velocity of a manipulator with its joint velocity. Statement-3: Jacobian matrix helps to determine singularity condition of a manipulator.

• a. Only Statement-1 is correct.
• b. Only Statement-2 is correct.
• c. Only Statement-3 is correct.
• d. All the Statements-1, 2 and 3 are correct.
`Answer:- d`

Q3. Forward Kinematics of a Serial Manipulator

• a. aims to determine the position and orientation of its end-effector with respect to the base coordinate system for the given joint angles/link-offset values.
• b. aims to determine the joint angles/link-offset values for the given position and orientation information of its end-cffector with respect to the base coordinate system.
• c. is more difficult to solve compared to its inverse kinematics problem.
• d. will yield multiple solutions.
`Answer:- a`

Q4. Which one of the following statements is TRUE?

• a. Robot’s trajectory planning problem aims to determine its collision-free path among the obstacles present in the environment.
• b. Robot’s motion planning problem aims to ensure smooth variations at different robotic joints.
• c. Robot’s trajectory planning problem aims to ensure smooth variations at different robotic joints.
• d. Robot’s trajectory planning problem and its motion planning problem are the same.
`Answer:- c`

Q5. To determine fifth-order polynomial trajectory for a manipulator joint, we need to know

• a. Joint position only at initial and final states.
• b. Joint position and velocity at initial and final states.
• c. Joint velocity and acceleration at initial and final states.
• d. Joint position, velocity and acceleration at initial and final states.
`Answer:- d`

Q6. Which one of the following statements is True?

• a. Computational complexity of Cartesian scheme of trajectory planning is more as compared to its joint-space scheme.
• b. Computational complexity of joint-space scheme of trajectory planning is more as compared to its Cartesian scheme.
• C. Computational complexity of Cartesian scheme and joint-space scheme of trajectory planning is not comparable.
• d. Joint-space scheme is never used in robot’s trajectory planning.
`Answer:- a`

Q7. The parabolic blends are used at two ends of linear trajectory function in order to

• a. generate linear movement of the end-effector of the manipulator.
• b. make it computationally faster compared to pure linear trajectory function.
• C. avoid infinite acceleration and deceleration at the beginning and end of the linear trajectory function, respectively.
• d. develop intelligent robot.
`Answer:- c`

Q8. The initial and final positions of a rotary joint of a manipulator are 10 and 40 degrees, respectively. The link connected to this joint starts from rest and reaches its final position in 3.0 seconds and becomes motionless. Ift and 6 represent the time and angular position of the joint, respectively, the suitable third- order polynomial trajectory function will be given by

• a. 6 10+ 10t2-3
• b. 5+5t +20t2
• c. 0 10 +20t +2
• d. 10 – 10t2 +3
`Answer:- a`

Q9. Trajectory planning aims to

• a. develop an autonomous robot.
• b. determine a collision-free path for the robot.
• C. ensure the smooth variations of displacement, velocity and acceleration at each of the robotic joints.
• d. determine the force/torque required at each of the robotic joints.
`Answer:- c`

Q10. For a 5 dof serial manipulator, which of the following statements are correct?

Statement-1: Its forward kinematics has a unique solution.
Statement-2: Its inverse kinematics has a unique solution.
Statement-3: Its inverse kinematics has multiple solutions.
Statement-4: Its forward kinematics has multiple solutions.

• a. Statements-1 and 3 are correct.
• b. Statements-2 and 3 are correct.
• C. Statements-2 and 4 are correct.
• d. Statements-1, 3 and 4 are correct.
`Answer:- a`