Engineering Drawing Principles and Applications

Introduction

The term ‘intersection of surfaces’ is used when the surfaces of two solids intersect each other, such as of cylinders, cones, prisms, pyramids, etc. The term ‘interpenetration of solids’ is used when three-dimensional solids such as cylinders, cones, prisms, pyramids, etc., intersect each other. The term ‘intersection of surfaces’ is used for all situations, irrespective of the fact that the solids interpenetrating each other have plane or curved surfaces.

When two solids interpenetrate each other, their surfaces meet in a common line called the line or curve of intersection. This line of intersection of two surfaces may be joined by determining key points and joining these points in the correct order. The resulting line may be straight or curved depending upon the nature of the intersecting surfaces. Determination of the line of intersection between two solids is important, as their development into flat patterns is otherwise not possible. The term ‘development’ refers to the unfolded sheet from which the required objects can be formed without stretching the material, i.e., hoppers, pipe joints, etc. In view of the above mentioned applications, intersection of surfaces may be classified into three categories:

• (i) Intersection of two plane surfaces, viz. prism and prism, prism and pyramid.

• (ii) Intersection of two curved surfaces, viz. cone and cylinders, cylinder and cylinder, cone and cone.

• (iii) Intersection of a plane surface and a curved surface, viz. prism and cylinder, pyramid and cylinder, etc.

Methods of Determining Line of Intersection

The following two methods may be used to find the line of intersection:

• (i) Line Method or Piercing Point Method

• (ii) Cutting Plane Method

• (i) Line Method or Piercing Point Method:When two solids meet each other, elements on one solid intersect with the surface of the other solid. Points of intersection of these solids with the surface of the other solid are then located. These points are the vertices of the line of intersection. These points are more easily located from the view in which the lateral surface of the solid appears edgewise, i.e., a line. Then, these points from one view are projected on to the other view. The curve joining these points will be a line of intersection.

• (ii) Cutting Plane Method:This is the general method of finding the line of intersection of any two surfaces. In this method, the solids are assumed to be cut by a series of cutting planes.