Cochleoid

A concheloid with a = 1

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}

References