Angle θ (Orbit): 0.0°
Angle φ (Self): 0.0°
Point P(x, y): (0, 0)
Ratio (k = r_B / r_A): 1.00
Circle B (Fixed, r_B)
Circle A (Rolling, r_A)
Epicycloid Path
Speed:
1.0x
Circle Radii Parameters
Circle A Radius (r_A)
60 px
Circle B Radius (r_B)
60 px
Preset Configurations:
Display Settings
Mathematical Mechanics
An Epicycloid is traced by a point $P$ on a circle of radius $r_A$ rolling without slipping around a fixed circle of radius $r_B$.
Generalized Equations
x(θ) = (r_B + r_A)cos θ - r_A cos((1 + r_B/r_A)θ)
y(θ) = (r_B + r_A)sin θ - r_A sin((1 + r_B/r_A)θ)
No-Slip Rotation Condition
φ = θ · (1 + r_B / r_A)