Rolling curve / 02

Double hypotrochoid

Geometry

Two hypotrochoids are added point by point: (x, y) = (x₁, y₁) + (x₂, y₂). Each is a circle of radius rᵢ rolling inside a fixed circle Rᵢ carrying a pen at distance dᵢ.

xᵢ(t) = (Rᵢ − rᵢ)·cos t + dᵢ·cos((Rᵢ − rᵢ)/rᵢ · t)
yᵢ(t) = (Rᵢ − rᵢ)·sin t − dᵢ·sin((Rᵢ − rᵢ)/rᵢ · t)

The sum shows the interference between the two rolling motions.

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