Kinematics & Dynamics

Two joints, two link lengths, and high-school trig. Compute where the end-effector is, plot the reachable workspace, and you've unlocked the foundation of every arm problem.

~15 min

Rotations and poses in 3D, without trig soup. Learn SO(3), SE(3), homogeneous matrices, and quaternions — and when to use each.

~18 min

DH was the standard arm-kinematics formulation for 50 years. It still shows up in textbooks and FK code. Here's how it works, why it survives, and what modern textbooks (and URDFs) prefer.

~13 min

The clean replacement for Denavit-Hartenberg. Each joint contributes a screw axis; kinematics is the product of their matrix exponentials. Same answers as DH, with dramatically less bookkeeping.

~18 min

Given a target (x, y), find the joint angles. Closed-form IK for a 2-DOF planar arm, the two-solution trap (elbow up vs elbow down), and when closed-form falls apart.

~14 min

When closed-form IK doesn't exist (7+ DOF, redundant arms), you iterate. Damped least squares, null-space projection, and the practical recipes that make Jacobian-based IK actually converge.

~14 min

The matrix that connects joint speeds to end-effector velocities — and joint torques to end-effector forces. Master it once and most arm-control intuition follows.

~13 min

From kinetic + potential energy to the equation of motion. M(q)q̈ + C(q,q̇)q̇ + g(q) = τ — the canonical form behind every torque-control loop and feedback-linearization scheme.

~15 min

Three wheel configurations cover almost every wheeled robot. Each has different kinematics, different motion constraints, and different planners. The full comparison in one lesson.

~12 min

Four propellers, six degrees of freedom, four control inputs. Underactuated, fast, and gorgeous to control. The minimal model, the controller hierarchy, and the differential-flatness trick that makes it work.

~14 min