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Mechanism for Drawing a Logarithmic Spiral

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This Demonstration shows a mechanism for drawing a logarithmic spiral . A pivot point holds a rod with a sharp wheel at the far end. The axis of the wheel is at an angle to the rod; is chosen such that . As the wheel digs into the plane, it gradually pulls away from the pivot point and traces the spiral.

Contributed by: Izidor Hafner (January 2013)
Open content licensed under CC BY-NC-SA

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For , the derivative with respect to is . For the angle between the radius vector to a point and its tangent, we have . For the angle , we have . (If , the curve is a circle; as , the curve tends to the straight line .)

Reference

[1] A. A. Savelov, Plane Curves (in Croatian), Zagreb: Školska knjiga, 1979 p. 265.

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