Evolute of a Catenary Ref of evolute of catenary Evolute of a Tractrix is a Catenary. What is the evolute of a Catenary? Sketched by Leonardo DaVinci Page 3, Fig 2. EDIT1: and also on Page 23, Fig 8. DaVinci_LastSupper

I actually disagree with the mathworld answer. If you take the simplest case ($a=1$), the catenary is $\alpha(t)=(t,\cosh t)$. The general formula for the evolute of a plane curve is $$\beta(t) = \alpha(t) + \frac1{\kappa(t)}N(t),$$ where $N$ is the principal normal. For the catenary, we calculate that $$\kappa = \text{sech}^2t, N = (-\tanh t,\text{sech} t),$$ so $\beta(t) = (t-\sinh t\cosh t, 2\cosh t)$. Here's a sketch:

!Catenary Evolute