CBSE Book Class 11 Engineering Graphics Development of Surfaces

Chapter 8

DEVELOPMENT OF SURFACES

8.1 INTRODUCTION

We brush our teeth daily but have you ever noticed the shape of packing box of tooth paste. Is it similar to a square prism? Let us open the box from its joints and lay down it on a plane surface. What do you observe? It is a piece of hard paper, having a rectangular shape with crease/folds on all bends. This shape is known as TRUE SHAPE of object/box and the process of unfolding of surfaces of a solid is called Development of Surfaces.

Can we take more examples? Yes, every packing box, birthday cap etc. can be opened up in the same way. Steel almirahs, buckets, storage vessels etc are bulky and complicated but these are also made up of sheet metal or plates from the TRUE SHAPE of objects. In this chapter, we are going to study about the development of surfaces to find out the true shape of objects required to produce the three dimensional object. The knowledge of development of surfaces not only gives us the model of the object but also helps in the estimation of costing and process of manufacturing i.e. blanking, stamping, pressing, welding, riveting etc.

8.2 DEVELOPMENT OF SURFACES

If the surface of a solid is opened out and laid on a plane surface. The true shape of the surface area of the solid is obtained. It is known as the development of that solid. The technique used in making a development from the orthographic views of a given object, is to find out the true shape of the surfaces and correct placement of one surface with respect to another adjacent element. “A development is a plane surface, which represents the unfolded surface of the object” Figure 8.1 explains the unfolding process of a cube to get its development. Fig. 8.1

8.3 METHODS TO DRAW DEVELOPMENT OF SURFACES

The group of developments, classified according to the type of surface involved to construct the development are as follows :-

1. Parallel line developments

2. Radial line developments

8.3.1 PARALLEL LINE (RECTANGULAR) METHOD

In this method development of surfaces of prisms and cylinders is drawn with the help of parallel lines. In this method the lateral surfaces of a solid are divided into a number of convenient rectangles. The true length of each of the side of the rectangles is found out from the orthographic views of the solid. Using these true lengths the rectangles are drawn, sequentially, one besides the other. Usually, as the height of the Front View and development is the same, the development is drawn in horizontal alignment with the Front View. The addition of two end surfaces to the lateral surface gives the complete development of the solid. Development of the cylinder is obtained by dividing the cylindrical surface into “equal” parts with the help of generators.

8.3.1.1 CUBE

The development of the surface of a cube consists of six equal squares of side equal to the edge of the cube.

Example 8.1 : Draw the development of surface of a cube of side 40 mm. 

Solution : Refer to fig. 8.2

Steps :

1. Draw the Front View and Top View of the cube.

2. Draw the base line in horizontal alignment to the Front View and on it draw four faces (i.e. squares) of the cube.

3. Draw two faces (squares) of the cube on the first and last face. Fig. 8.2

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