A cochleoid is a snail-shaped curve similar to a strophoid which can be represented by the polar equation

\( r=\frac{a \sin \theta}{\theta} \)

the Cartesian equation

\( (x^2+y^2)\arctan\frac{y}{x}=ay \)

or the parametric equations

\( x=\frac{a\sin t\cos t}{t} \)
\( y=\frac{a\sin^2 t}{t} \)