Linkage for the Cissoid

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 , with the length of the four shorter rods, the length of the two long rods.