Abstract: With the help of the orthographic projection method, the two projective pencils of
planes with solid lines as the base are systematically expressed for the first time. When moving or
revolving one of them, various types of quadric cylinders, quadric cones, unparted hyperboloids
and hyperbolic paraboloids can be produced. When an appropriate cutting plane is selected, two
pairs of corresponding contract harnesses can be obtained. Whether or not the harnesses are
coplanar is the sufficient and necessary condition for the existence of circular section in quadric
surface.

Key words: two projective pencils of planes, cone, one-sheet hyperboloid, circular section;
hyperbolic paraboloid