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
# tparameter
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
# tparameter
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
# tparameter
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)

