Generalized helicoid
In geometry, a generalized helicoid is a surface in Euclidean space generated by rotating and simultaneously displacing a curve, the profile curve, along a line, its axis. Any point of the given curve is the starting point of a circular helix. If the profile curve is contained in a plane through the axis, it is called the meridian of the generalized helicoid. Simple examples of generalized helicoids are the helicoids. The meridian of a helicoid is a line which intersects the axis orthogonally. Essential types of generalized helicoids are ruled generalized helicoids. Their profile curves are lines and the surfaces are ruled surfaces. circular generalized helicoids. Their profile curves are circles. In mathematics helicoids play an essential role as minimal surfaces. In the technical area generalized helicoids are used for staircases, slides, screws, and pipes. Analytical representation Screw motion of a point Moving a point on a screwtype curve means, the point is rotated and displaced along a line (axis) such that the displacement is proportional to the rotation-angle. The result is a circular helix. If the axis is the z-axis, the motion of a point can be described parametrically by is called slant, the angle , measured in radian,