The cycloid describes the motion of a point on the perimeter of a wheel.

The tractoria  (or tractrix) is a curve where the length of the tangent from the tangentialpoint to the x-axis has a constant length a. Its evolute is the chainline

y = a cosh(x/a).

a particle P attached to a string PQ pulled through Q along a given curve at right angle to thee initialposition of PQ traces out a curve called dog-curve.

The equation for this curve is x= a ln{[a+{[a+&sqrt;(a²–²)]/y }- &sqr;(a²-y²)