Watch a game character walk up uneven stairs. Every step, the engine knows exactly where the foot has to land — but the animation was made on flat ground. Someone has to answer: given where the foot ends up, what angles should the hip and knee take? That question has a name, and by the end of this page you'll drag it around with your mouse.
press play — 90 seconds ↓Plays like the video — one caption at a time, the picture animating under it — and it pauses when it's your turn. Skip around with the dots or arrow keys. The full lab comes after.
Here's the classic robot-arm diagram: joints with angles
q1, q2, q3, links with fixed lengths, and an End Effector
— the hand — at the tip. Given the angles, finding where the hand is is pure
plug-and-chug: walk down the chain adding up rotations. That's
Forward Kinematics. Turn the knobs and watch the numbers.
The HARD question is the reverse.
Now the reverse: you pick where the hand must be, and the arm has to discover its own angles. Drag the red ✛ anywhere. The solver here is FABRIK — embarrassingly simple: snap the hand to the target and pull the chain backwards, then snap the base home and pull the chain forwards. Repeat until the error is tiny. Turn on show solve steps to literally see it reach.
This is the whole chapter in one diagram. Going right is Forward Kinematics — you did it with three sliders. Going left is Inverse Kinematics — you did it by dragging a crosshair while an algorithm scrambled to keep up.
Back to the hook. The body just slides along — nobody animated these legs. Each foot raycasts straight down to find the ground, the swing foot lerps along an arc to its next landing spot (chapter 02!), and a two-bone analytic IK (law of cosines) tells each knee what to do. Planted feet stick while the body passes over the bumps. Press walk.
FABRIK doesn't care how many dimensions it works in — the same slide-to-target, slide-to-base trick from above runs here on a 3-bone arm chasing a flying target. Orbit around it and watch the elbow decide.
Click any moment on the right — it takes you straight there (in place when this site is served over http, on YouTube when opened as a local file).