Leminscates are Inversions (in Circles) of
Hyperbolas
Lemniscates can also be drawn by a three rod drawing mechanism
Modify the curve
Position on middle rod: 0.05 ... 0.95
Rotating rod length: 0.5 ... 1.3
Lemniscates can be parametrized by inverting parametrized
Hyperbolas.
Here we use the mechanical construction: The right rod is rotating and the
position of the other joint is obtained by intersecting two circles. The drawing
pen is the dot on the middle rod.
Tangent construction for mechanically generated curves. Turn demo on!
The green circle, the intersection of the lines of the outer two rods, is
the momentary fixed point of the rotating
movement of the "moving plane" attached to the middle rod of the drawing
mechanism. All points of the moving
plane have velocities orthogonal to their connection with this momentary
fixed point. The tangent at the current
point of each curve is therefore orthogonal to this generalized "radius":
a very simple tangent construction.