Geometric Constructions 8

Demonstrate
how the lemniscate can be drawn with the crossed parallelogram.

Construct
the lemniscate with a linkage different from the previous one.

Design
a linkage to draw the ellipse.

Design
a linkage to draw the cardioid.

Design
a linkage to draw the nephroid.

Construct
Peaucellier's linkage converting straight line motion to circular motion.

Construct
Hart's linkage converting straight line motion to circular motion.

Construct
two circles of the same radius with each rotating about a point not located
at the center while remaining tangent to each other.

Can you
change the above construction to allow two circles of different radii?

Instead
of two circles tangent to each other externally, make the two circles tangent
to each other internally.

Construct
two identical ellipses with each rotating about one of its two foci while
remaining tangent to each other.