To obtain the evolute of the catenary, we start with the catenary locus, and draw in the normals to points on the locus.

Click the diagram below to activate the applet, and then click the ‘Animate’ button, or manually drag the red driver point along the x-axis. Both methods give a good representation of the evolute. Do you recognize the evolute? Can you name it? describe it?

In a sense this has been a trick question. For although the evolute of the catenary resembles a tractrix, it appears to be a different curve called a cissoid, with different equation and properties.


Bibliography

Equations: http://mathworld.wolfram.com/CatenaryEvolute.html