We are to design a linkage which describes an ellipse.
The linkage consists of three bars
and
The extremeties of the two outer bars are fixed in points
The lengths
and
are the same and remain constant, and the length
remains constant during the motion.
-
Construct a circle with center
and a point
moving around the circle.
-
Build an animation button making
moving round the circle.
-
Pick any point
lying inside the circle and mark the vector
-
Translate the line segment into
by the vector
-
Taking
as mirror of symmetry, reflect
into
-
The required linkage consists of
and the intersection of
and
traces an ellipse with
as foci.
Modify the previous linkage making it to draw the lemniscate of Bernoulli.
Modify the previous linkage to construct the hyperbola.
Construct an animation showing two identical ellipses one rolls upon the
other.
Construct an animation showing that the intersection of any line passing
through the cusp of the cardioid intersects the cardioid in a segment of
constant length.
Take the longest line segment lying inside a deltoid and show how to rotate it
by
360
while moving continuously inside the deltoid.
