Lab
Epitrochoid Spirograph
A circle rolling inside or outside a fixed circle traces curves called hypotrochoids and epitrochoids. A pen attached to the rolling circle draws the pattern. Adjust the radii and pen offset to produce an infinite family of curves — from cardioids and nephroids to deltoids, astroids, and roses. Layer multiple curves in different colors.
Curve type
Hypotrochoid
Rolling inside
Petals / Cusps
—
R/r ratio
Period
—
Rotations to close
Layers
0
Saved curves
Actions
Mode
Parameters
Fixed radius (R)
150
Rolling radius (r)
50
Pen offset (d)
30
Line width
1.5
Pen color
Presets
Equations
x(t) = (R − r) cos(t) + d cos((R − r)t / r)
y(t) = (R − r) sin(t) − d sin((R − r)t / r)
y(t) = (R − r) sin(t) − d sin((R − r)t / r)