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This linkage was originally designed to draw ellipses and hyperbolas. This Demonstration generalizes this too-restrictive usage. A purple Peaucellier linkage is coupled to a green trapezoidal linkage (see the Demonstration "Families of Figure-Eight Curves"). The Peaucellier cell draws a blue curve that is obtained by inversion from the red curve drawn by the trapezoidal linkage. Varying the radius of the crank (the distance been the outer black points) with the original settings will change the blue ellipse smoothly into a blue hyperbola. This is not surprising as they are both conic sections. You can create this linkage with a Meccano set; see the details.

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