Robot Arm Painting: Toolpath-Driven Brushstroke Generator (2D)

Toolpath

Pattern

Petal / frequency k 5

Arm speed 1.0×

Live readouts

Shoulder θ₁

0.0°

Elbow θ₂

0.0°

Tool speed

0.0 u/s

Canvas coverage

How it works

This is an independent 2D top-down model of the same SCARA painting robot as the 3D version: a two-link arm (lengths L₁, L₂) is driven by closed-form analytic inverse kinematics to keep its brush exactly on a parametric generator curve.

rose:      x = R·cos(kθ)·cos(θ), y = R·cos(kθ)·sin(θ)
lissajous: x = A·sin(aθ+π/2),   y = A·sin(bθ)
spiral:    x = R·(θ/θmax)·cos(θ), y = R·(θ/θmax)·sin(θ)

d  = √(x² + y²)
α  = acos( (d² + L1² − L2²) / (2·L1·d) )   // shoulder offset
φ  = atan2(y, x)                            // direction to target
θ1 = φ − α                                  // shoulder angle (elbow-up branch)
elbow = L1·(cos θ1, sin θ1)
θ2 = atan2(y − elbow.y, x − elbow.x)        // absolute angle of link 2

Every frame recomputes the target point from θ, solves the same law-of-cosines IK the 3D engine uses, and stamps a paint dab wherever the tool tip has moved at least the fixed dab-spacing distance since the last one — the dab buffer is a fixed-size ring, so once it is full, new dabs overwrite the oldest ones rather than growing forever, exactly like the 3D instanced mesh. Drag the canvas to pan and scroll to zoom the view; nothing about the physics changes, only what you're looking at.

Pattern / k — changes the target curve the IK solver is asked to track.
Arm speed — scales how fast the parameter θ advances, which changes both joint angular velocity and dab spacing.
Clear canvas — resets the paint-dab ring buffer and coverage counter.
Drag / scroll — pans and zooms the view; the arm and coverage stats are unaffected.

Link 1 / Link 2 Paint dabs

Drag to pan, scroll to zoom