- In geometry, a
hypotrochoid is a
roulette traced by a
point attached to a
circle of
radius r
rolling around the
inside of a
fixed circle of
radius R, where...
-
interior circle. A
hypotrochoid for
which r = d A
hypotrochoid for
which R = 5, r = 3, d = 5 The
parametric equations for the
hypotrochoids are: x ( θ ) =...
-
epicycloid with d = r. The
classic Spirograph toy
traces out
epitrochoid and
hypotrochoid curves. The
paths of
planets in the once po****r
geocentric system of...
- case of the epitrochoid)
Hypotrochoid Hypocycloid (special case of the
hypotrochoid)
Spirograph (special case of the
hypotrochoid) Jacobi's
elliptic functions...
-
parallelogram instead of a rectangle. The
ellipse is a
special case of the
hypotrochoid when R = 2 r {\displaystyle R=2r} , as
shown in the
adjacent image. The...
-
straight line
traced by the
classic Tusi couple, are
special cases of
hypotrochoids. Murray's
Hypocycloidal Engine,
utilising a Tusi
couple as a substitute...
-
produces mathematical roulette curves of the
variety technically known as
hypotrochoids and epitrochoids. The well-known toy
version was
developed by British...
- (another orbit)
around ( x 0 , y 0 ) {\displaystyle (x_{0},y_{0})} (the
hypotrochoid/epitrochoid case), x ′ = x 0 + r 2 cos ( ω 2 t + ϕ 2 ) , y ′ = y...
-
generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids,
hypotrochoids, and involutes. On a
basic level, it is the path
traced by a
curve while...
- used in this
instance is
called a
spirograph in mathematics, that is, a
hypotrochoid generated by a
fixed point on a
circle rolling inside a
fixed circle...
