14 - Conic sections and interpenetration of solids

Abstract

There is often difficulty in handling problems involving two- and three-dimensional geometrical constructions. The examples in this chapter are included in order to provide a background in solving engineering problems connected with lines, planes, and space. Copying a selection of these examples on the drawing board or on CAD equipment will certainly enable the reader to visualize and position the lines in space which form each part of a view, or the boundary, of a three-dimensional object. It is a necessary part of draughting to be able to justify every line and dimension which appears on a drawing correctly. In this chapter examples of constructing an ellipse, a parabola and a rectangular hyperbola from a part of a cone. Many objects are formed by a collection of geometrical shapes such as cubes, cones, spheres, cylinders, prisms, and pyramids, and where any two of these shapes meet, some sort of curve of intersection or interpenetration results. It is necessary to be able to construct these curves to complete drawings in orthographic projection or to draw patterns and developments. Some of the most commonly found examples of interpenetration are also included such as a cones, cylinders and square prisms.