(140:128;54:45) · F=(35/32,42/32) · nsymm=7
The Math Behind This Curve

Every number below updates live as you change the wheels, so this always describes exactly what's on screen.

The mechanism

The equations

With your current numbers

Why it looks the way it does

Label the parts on canvas

Turning this on (and "Show gear mechanism" in the settings panel) draws the actual wheels to scale, labeled, and lets you watch them turn while it draws.

Show equations on canvas

Prints the live x(t) and y(t) equations underneath the drawing itself — independent of the part labels above, and included in downloaded images.

Gears — outer ring (n0), wheel (n1)
Hoop (n2), pen wheel (n3)
More squiggles
Hoop & pen
Hoop offset (h)0.480
Pen distance (p)0.800
Pen phase (φ)0°
Pen hole3.0mm
Display
Show gear mechanism
Show symmetry rays
Show base curve (no pen offset)
Pen style
Solid Color
#f2a65a
Color cycles2.0
Brightness0.90
Line width1.6
Glow intensity8
Curve detail512
Glow
Canvas layers

Keep the current drawing, tweak the gears, and draw a new one on top — like the physical toy, without erasing what's already there. Click a kept layer below to load its parameters back into every control and keep tweaking it in place, without disturbing the others.

Motion
Reveal animation
Loop continuously (live drawing)
Speed1.0x
Advanced: frequency & similarity
Frequency inversion — solve gears from F=(T1/T,T3/T)
Derived & similarity
Presets (34)
Explore

Second-order roulette (gear-in-hoop-in-wheel) construction after glagolj (the optional n4/n5 third level extends that same construction one level further). Live-drawing & compositing workflow inspired by Abel Vincze's HTML Spirograph.

Drag to pan · Scroll to zoom · Double-click to reset view
Gear = tweak the wheels · Σ = explain the math