Plücker’s conoid (cylindroid) C is a ruledvsurface of degree three with a finite double line. This surface plays a major role in the geometric literature since all its pedal curves are planar. It is the locus of pairs of skew lines for which a given orthogonal hyperbolic paraboloid is the bisector. In spatial kinematics, C is the locus of instantaneous screw axes of the relative motion for two rotating wheels with fixed skew axes. Finally, four concyclic generators of C are common tangents of infinitely many spheres, and we study their enveloping canal surface.
