Kinematical ruled surfaces based on interrelated movements in triads of contacted axoids

Abstract

Kinematical ruled surfaces are constructed by generating the line's motion of a moving ruled surface during its movement along a fixed ruled surface [Spr02a]. The main condition of constructing kinematical ruled surfaces is that a moving axoid contacts with a fixed axoid along their common generating line in each of their positions during the movement of one axoid along another. A lot of well-known kinematical ruled surfaces are constructed on the base of certain pairs of contacted axoids such as “plane – cylinder”, “plane – cone”, “cylinder – cylinder”, “cone – cone”, etc. [Kri06a]. A new model of constructing kinematical ruled surfaces based on interrelated movements in the triads of contacted axoids is proposed in this research. Geometrical models, analytical representations, and computer visualization of the new constructed kinematical surfaces for some cases of triads of contacted axoids “plane – cylinder – cylinder”, “plane – cone – cone”, “cylinder – cylinder – cylinder”, “cone – cone – cone” (Fig. 1), and for matched triads of one-sheet hyperboloids of revolution are developed in this paper. Figures of the triads of contacted axoids and corresponding constructed kinematical ruled surfaces have been developed with the help of the software application AMG (“ArtMathGraph”) [Con07a].