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Epitrochoid

Epitrochoid is a is a curve traced by a point attached to a circle of radius r rolling around the outside of a fixed circle of radius R, where the point is a distance d from the center of the exterior circle.

The parametric equations for an Epitrochoid are

You can draw function online using the folowing script for Epitrochoid:

# Example
# 2D. Epitrochoid

# z must be zero
z = 0

# t-parameter
tmin = 0
tmax = 6*pi
tgrid = 400

# Constant
a = 6.0
b = 1.0
d = 0.75

k = a + b
m = (a + b) / b

# Calculations
x = k * cos(t) - d * cos(m * t)
y = k * sin(t) - d * sin(m * t)

Special case. Epitrochoid with d = r: Epicycloid

# Example
# 2D. Epitrochoid

# z must be zero
z = 0

# t-parameter
tmin = 0
tmax = 6*pi
tgrid = 400

# Constant
a = 6.0
b = 0.5
d = 0.5

k = a + b
m = (a + b) / b

# Calculations
x = k * cos(t) - d * cos(m * t)
y = k * sin(t) - d * sin(m * t)