Studying The Intersection Of Rotational Cylinders Analytically And Graphically To Obtain The Unfolding Of The Intersection Curve

Abstract

The problem of intersection between rotational cylindrical bodies is considered as a problem of special importance, either in theoretical studies, or in practical applications, such that in water supply projects, irrigation projects, oil and gas projects and other industrial projects that involves piping and cylindrical tanks works.In this paper we will study the problem of intersection between rotational cylindrical bodies. We will solve this problem using the analyticalmethod and the graphical method. The analytical solution includes acquiring the equations of the resulting intersection curve, whereas in the graphical solution, which relies on descriptive geometry and the method of auxiliary spheres, the result is acquiring the shape of the intersection curve and determining its projections. In spite of the importance of reaching the intersection curve, the acquiring of the unfolding of the intersection curve and its graphical plot is more important and it is the aim of this research. We will demonstrate this issue via a numerical practical example including various cases of studied intersection