Salkowski curves and spherical epicycloids

The relationship between Salkowski curves, a family of slant helices with constant curvature and non-constant torsion, and the family of spherical epicycloid curves is studied. It is shown that, for some values of the parameter defining the Salkowski curve, the curve is the image by a shear transformation along the z-axis of a spherical epicycle. Therefore, the projection of both curves on the xy-plane is the same. This result can be extended to the whole family of Salkowski curves if some parameter defining the spherical epicycle is allowed to be a complex imaginary number.