"Mathematical modeling and computer graphics of kinematical ruled surfaces on the base of interior revolving one axoid by another in the pairs of contacted cylinders and cones "
Abstract
"Mathematical modeling and computer graphics of kinematical ruled surfaces on the base of interior revolving one axoid by another in the pairs of contacted cylinders and cones "
Incoming article date: 09.06.2016On the base of geometrical model of interior revolving one axoid by another for the pairs of contacted cylinders and cones analytical representations, and computer visualization of the new constructed kinematical surfaces is developed in this research. The described geometrical model corresponds to the case when one axoid is located in the interior of another axoid. As this takes place, there are two possible variants of mutual arrangement of moving and fixed axoids. In the first variant, the moving axoid is located in the interior of the fixed axoid. In the second variant, the fixed axoid is located in the interior of the moving axoid. In the first variant, the outside surface of the moving axoid revolves around the interior surface of the fixed axoid. In the second variant, the interior surface of the moving axoid revolves around the outside surface of the fixed axoid. For pairs of axoids “cylinder – cylinder” or “cone – cone” both variants of geometrical model for constructing kinematical ruled surfaces are considered on the base of rolling one axoid along another one. As a result of the moving one axoid along another the kinematical ruled surface is generated by one of the generating lines of moving axoid. Computer graphics of the new constructed kinematical ruled surfaces based on the proposed geometrical models has been accomplished by the previously developed software application “ArtMathGraph”.
Keywords: Mathematical Modeling, Analytical Geometry; Kinematical Ruled Surfaces, Computer Graphics