Robot Arm Painting: Toolpath-Driven Brushstroke Generator

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

The brush target (x, y) on the canvas comes from a parametric generator curve, e.g. a rose curve r(θ) = R·cos(k·θ):

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

The two-link arm (lengths L₁, L₂) reaches that point with closed-form inverse kinematics — no iterative solver needed:

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

Both joints rotate about the vertical axis, exactly like a real SCARA (Selective Compliance Assembly Robot Arm) — the configuration industrial pick-and-place and painting robots actually use, because it is fast and rigid in the horizontal plane. A pen drops from the wrist down to the canvas and deposits a paint dab wherever the tool tip moves faster than a fixed dab spacing, building up the generative artwork instance by instance.

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 instance buffer and coverage counter.

Link 1 / Link 2 Paint dabs

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