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IT-802 (C) · Robotics/Important Questions

Robotics (IT-802 (C)) - Important Questions

  1. Unit 27 Marks Low Priority

    Explain the Denavit–Hartenberg (DH) convention. Derive the homogeneous transformation $A_i$ for a single link using the DH parameters $\left(\alpha_i,\; a_i,\; d_i,\; \theta_i\right)$ and state how successive $A_i$ are composed to obtain the end-effector pose.

    Core concept: Denavit–Hartenberg convention and single-link homogeneous transform; standard exam derivation from Unit 2 kinematics.

  2. Unit 27 Marks Low Priority

    For a 2-link planar manipulator with link lengths $a_1$ and $a_2$ and joint angles $q_1$ and $q_2$, derive the forward kinematics and obtain the end-effector position coordinates $\left(x,\;y\right)$ in the base frame. Express $x$ and $y$ in terms of $a_1,\;a_2,\;q_1,$ and $q_2$.

    Standard forward kinematics derivation for a 2-DOF planar manipulator; frequent classroom exercise in Unit 2.

  3. Unit 27 Marks Low Priority

    Derive the geometric Jacobian matrix $J(q)$ for the 2-DOF planar manipulator of the previous question. Explain the physical meaning of each block of $J(q)$ and show how joint velocities $\dot q$ are related to end-effector linear and angular velocities by $v = J(q)\,\dot q$.

    Jacobian derivation and interpretation — core analytic skill in Unit 2 for velocity mapping and singularity analysis.

  4. Unit 27 Marks Low Priority

    Define a singular configuration of a robotic manipulator. Explain how singularities can be detected using the Jacobian matrix and classify common types of singularities encountered in serial manipulators (for example, workspace boundary singularities and kinematic degeneracies).

    Singularity classification and detection — typical Unit 2 theoretical question.

  5. Unit 214 Marks Low Priority

    Using the Euler–Lagrange formulation derive the equations of motion for a two degree-of-freedom planar manipulator. Show the final dynamic model in the standard form $$M\left(q\right)\,\ddot q + C\left(q,\dot q\right)\,\dot q + G\left(q\right) = \tau$$ and briefly state the physical meaning of the terms $M\left(q\right)$, $C\left(q,\dot q\right)$ and $G\left(q\right)$.

    Derivation of dynamic model using Euler–Lagrange — major derivation problem in Unit 2, typically higher marks.

  6. Unit 27 Marks Low Priority

    State and prove the principal properties of the manipulator inertia matrix $M\left(q\right)$. Explain why $M\left(q\right)$ is symmetric and positive definite for all physically realizable configurations $q$.

    Properties of inertia matrix — concise theoretical question often asked to test understanding of dynamics.

  7. Unit 27 Marks Low Priority

    Compare the Euler–Lagrange and Newton–Euler methods for computing manipulator dynamics. Discuss computational complexity, typical outputs (e.g., joint torques for given motion), and which method is preferred for recursive real-time implementations.

    Comparison of dynamic solution methods — conceptual question contrasting Euler–Lagrange and Newton–Euler methods from Unit 2.

  8. Unit 210 Marks Low Priority

    Given the DH parameters of a 3-DOF serial manipulator (revolute joints) in a typical exam table, derive the forward kinematics to obtain the end-effector pose. Then obtain the Jacobian matrix and determine the conditions (equations in $q$) under which the manipulator reaches a singular configuration.

    Applied kinematics + singularity detection: forward kinematics followed by Jacobian determinant check — common examination-style problem.

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