Playground · Month 2 · kinematics
Drag the robot's hand. Watch the math move.
This is the first thing Stanford's CS223A teaches: where a robot's hand is, given its joint angles, and the harder question, which angles put the hand where you want. Here you can feel it before you read the equations.
Shaded ring: everywhere the hand can reach. Green ellipse: the directions the hand can move fast right now.
forward kinematics
x = L₁cos θ₁ + L₂cos(θ₁+θ₂) = 0.63
y = L₁sin θ₁ + L₂sin(θ₁+θ₂) = 1.30
jacobian J
det J = L₁L₂ sin θ₂ = 0.70
L₁ = 1 · L₂ = 0.75
Try this
- 1Straighten the arm all the way out. Watch det J drop to 0 and the ellipse flatten into a line.
- 2Reach the same point with elbow up, then elbow down. Two answers to one question: that's inverse kinematics.
- 3Try to touch the base. Why can't the hand get closer than 0.25?
Forward kinematics
Turn the sliders. Angles in, hand position out. One answer, always.
Inverse kinematics
Drag the hand. Position in, angles out. Often two answers, sometimes none.
The Jacobian
How fast the hand moves when the joints move. When det J hits 0, the arm loses a direction: a singularity.