WOLFRAM|DEMONSTRATIONS PROJECT

Linkage for the Cissoid

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rotation angle pink point
4.801
length of four short rods
2.4
length of two long rods
3.4
radius pink circle
0.975
zoom
3.
show geometry
This linkage is an application of Peaucellier's inversor. Varying the radius of the rods gives rise to a family of cissoids with a bump, a cusp, and a loop.
Click on "show geometry". The points P and Q are fixed points nailed to the board. Point O rotates around P. Point Q' is the inverse of point Q in the dashed inversion circle centered at O. A pencil anchored in Q' draws the cissoid. The radius of the dotted circle is
2
b
-
2
a
, with
a
the length of the four shorter rods,
b
the length of the two long rods.