Constructing of kinematical ruled surfaces on the base of geometrical model of complex moving for interior revolving one axoid by the another in the pairs of one-sheet hyperboloids of revolution
Abstract
Constructing of kinematical ruled surfaces on the base of geometrical model of complex moving for interior revolving one axoid by the another in the pairs of one-sheet hyperboloids of revolution
Incoming article date: 09.06.2016The geometrical model of interior revolving one axoid by another for the pairs of contacted one-sheet hyperboloids of revolution, as the methodical base for constructing of the new kinematical ruled surfaces is proposed in this article. Analytical representation of the constructed kinematical ruled surfaces is based on the previously developed model of complex moving one axoid along another. For the case of pair of contacted one-sheet hyperboloids of revolution the geometrical model of the complex moving can be represented as a superposition of some interrelated movements: rotational movement of the moving axoid around its axis; rotational movement of the moving axoid’s axis around the fixed axoid’s axis; translational movement of the moving axoid along the common generating line of both axoids. The proposed geometrical model of interior revolving one axoid by another 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. As a result of the complex moving one axoid along another the kinematical surface is generated by one of the generating lines of moving axoid. Computer graphics of the new constructed kinematical ruled surfaces has been accomplished by the previously developed software application “ArtMathGraph”.
Keywords: Mathematical Modeling, Analytical Geometry; Kinematical Ruled Surfaces, Computer Graphics