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Kinematics (FK / IK)

Forward & inverse kinematics, Jacobians.

mediumControl & Motion

Why it matters in robotics

Kinematics is the bread-and-butter screening topic for any manipulation, arm, or humanoid role: interviewers expect you to map joint angles to end-effector pose (FK) and back (IK), and to reason about the Jacobian on the spot. Expect to derive or sketch a Jacobian, explain singularities and redundancy, and contrast analytical vs. numerical IK (Newton / damped least squares), including why IK can have no solution or infinitely many. Fluency with frames, the product-of-exponentials formula, and Jacobian-based velocity control signals genuine hands-on robotics maturity.

Application focus

The same topic, tailored to the robot you're building. Your choice is remembered across the roadmap and every topic.

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At a glance

Joint anglesĪø (config space)Forwardkinematics T(Īø)End-effectorpose / twistJacobian Jv = J·θ̇θposeinversekinematicsJ⁻¹ / DLS(velocity IK)

FK maps joint angles to end-effector pose; IK inverts it; the Jacobian links joint and end-effector velocities.

What to study

  • āœ“Forward kinematics: DH parameters and the product-of-exponentials (PoE) formula in space and body frames
  • āœ“Velocity kinematics: the space/body Jacobian, singularities, manipulability, and statics duality (force = J^T wrench)
  • āœ“Inverse kinematics: closed-form/analytical solutions vs. numerical Newton-Raphson and damped least squares (pseudoinverse)
  • āœ“Redundancy and null-space control: handling >6-DOF arms and using the Jacobian for resolved-rate motion control

Study by time budget

Pick the path that fits the time you have before your interview.

  1. ā–¶Modern Robotics, Chapter 4: Forward Kinematics (lecture playlist)↗VideoKevin Lynch / NorthwesternĀ· ~45 min
  2. āœŽForward and Inverse Kinematics: Jacobians and Differential Motion↗ArticleReality BytesĀ· ~30 min

Where to practice coding

Prerequisites

Practice questions (2)