# DEVELOPMENT OF SURFACES CLASS NOTES FOR ENGINEERING

## CLASS NOTES FOR ENGINEERING

### METHODS OF DEVELOPMENT OF SURFACES

#### Fig. Development of a truncated cylinder

Procedure

Draw the front and top views of the cylinder. Divide the top view into 12 equal parts. Project the points to the front view. Take the length of line 1-1 equal to πD (circumference of the cylinder). Divide it in 12 equal parts equal to chord length ab, using a bow divider. Make  the generators. Draw horizontal lines through points a’, b’ to meet the generators at points A, B etc.. Draw a smooth curve through these points. the portion 1ABCD….A1-1 is the final development.

#### (b) Radial line development of surfaces Fig. Development of a Square Pyramid (Radial Method)

#### (d) Approximate method of development

Used in the development of double or multi curved surfaces like a spherical solid. Use an approximate method for its development. Divide the surfaces of such a solid into number of narrow conical or cylindrical segments. Do their approximate development. There are two different methods of development of a sphere. These are

(i) Zone Method Fig. Sphere Development by Zone Method

In this, cut the sphere into number of horizontal zones. Consider each of these a frustum of a cone. Its apex is at the intersections of the extended chords. Now develop each zone by the radial line method. In Fig. top half of a sphere is divided into four zones A, B, C & D by lines ST, RU, QV and PW. For the development of zone C, Join QR and UV. Produce these lines to meet at point O (center of development). From O, draw two arcs of radii OU and OV. Now develop by radial method as already explained.

(ii) Lune Method Fig. Development of a Sphere by Lune Method

In this, cut the sphere into a number of equal meridian sections named as lunes.  Divide the top view of the sphere into 12 equal sections.  There are 12 lunes. For the complete development of the sphere, develop each lune completely. The length of each lune is equal to half the circumference of the sphere. The width of each lune is equal to the arc length.

### DO THE DEVELOPMENT OF SURFACES

1.           Cubical solid