nephroid : evolute

NEPHROID : Evolute

We next ask: what is the evolute of the nephroid? At each point of the nephroid locus we draw the normal to the curve. The evolute occurs as the envelope of these normals.

Click the diagram below to activate the applet, and then click the ‘Animate’ button to generate the evolute. Clicking the little red x at bottom right will clear the drawing from the applet window. Now drag the red point Q slowly along the segment. Can you describe the construction? Have we seen this curve before?

Interestingly, the evolute here is another nephroid, half the size, and rotated from the original through 90°.

Bibliography

http://mathworld.wolfram.com/NephroidEvolute.html