kinematics
4 lessons tagged kinematics: free, quiz-checked micro-lessons.
The Jacobian and Velocity Kinematics
Connect joint velocities to end-effector velocity through the Jacobian matrix. Learn how to build J, spot singularities where det J = 0, invert J with the pseudoinverse for velocity control, and measure manipulability — with NumPy code for the 2-link arm.
Inverse Kinematics: From Pose to Joint Angles
Flip the FK problem: given a desired end-effector pose, find the joint angles that achieve it. Master analytical closed-form IK for the 2-link arm, the elbow-up/elbow-down duality, atan2 arithmetic, and the basics of numerical IK via the Jacobian.
Forward Kinematics and DH Parameters
Translate a list of joint angles into an end-effector pose. Learn the four Denavit-Hartenberg parameters, build per-link transforms, multiply them into T_0^n, and implement FK for a 2-link planar arm in NumPy.
Coordinate Frames and Homogeneous Transforms
Master how roboticists describe rigid-body pose. Build rotation matrices from scratch, pack them into 4x4 homogeneous transforms, and compose multiple frames with NumPy to track every link in a robot arm.