Rolling curves / 02

Dual spirograph

Geometry

Two wheels of radii r_A and r_B roll without slipping inside a fixed circle of radius R. A bright dot on each rim leaves a persistent hypocycloid contour.

P(θ) = (R − r)(cos θ, sin θ) + r(cos φ, sin φ)
φ = −(R/r − 1)θ

Reverse flips that wheel's rolling direction, mirroring its orbit. Changing a radius or pressing Reset clears both contours and restarts them from the rightmost point.

Both wheels roll inside the same fixed circle · CW / CCW reverses direction · traces persist until reset