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Hypotrochoid

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

The parametric equations for a Hypotrochoid are:

Use the folowing script to plot function Hypotrochoid:

# Example
# 2D. Hypotrochoid

scale = 8

# z must be zero
z = 0

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

# Constant
a = 5.0
b = 3.0
d = 5.0

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. Hypotrochoid with d = r: Hypocycloid

# Example
# 2D. Hypotrochoid

scale = 8

# z must be zero
z = 0

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

# Constant
a = 5.0
b = 3.0
d = 3.0

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. Hypotrochoid with R = 2r: Ellipse

# Example
# 2D. Hypotrochoid

scale = 8

# z must be zero
z = 0

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

# Constant
a = 6.0
b = 3.0
d = 5.0

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

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