Development of Surfaces

Chapter-14

M. S. Dasgupta, BITS Pilani

What is development?

Learning Objectives

2. Applications of development.

1. To learn the theory and principals of development.

Theory of Development

Any solid can be enclosed in a wrapper of thin material. If this wrapper is opened out at folding edges and laid on a flat plane, the flattened out sheet metal is the development of complete surfaces of the solid. The development includes the lateral surfaces as well as base surfaces. Thus, when surfaces of a solid are laid out on a plane, the successive surfaces of the object are called its development.

Important Points about Development

• Every line on the development must be the true

length of the corresponding edge on the surface.

• The flat surface of prisms and pyramids, and single

curved surfaces like cones and cylinders can be

accurately developed. However, double curved

surfaces like the surface of the sphere cannot be

accurately developed. A sphere can be approximately

developed by dividing it into number of parts.

• Usually, only the lateral surfaces of the solids are

developed and the ends or bases are omitted from

the developments. The bases can be easily

incorporated whenever required.

Methods of Development

1) Parallel Line Development

2) Radial Line Development

Example: Parallel Line Development

CYLINDER

Example: Parallel Line Development

HEXAGONAL PRISM

Example: Radial Line Development

CONE

Example: Radial Line Development

HEXAGONAL PYRAMID

‘OD’ is true length as ‘od’ is parallel to XY

Model Solution-1 (Step-1)

A Pentagonal prism having base-edge 100 mm and height 175 mm is standing on its base on the ground with one face perpendicular to VP. It is cut by an AIP 30o to the ground and cutting the perpendicular surface at a point 50 mm below the top base in the FV. Draw development of

lateral surfaces of the remaining solid.

Model Solution-1 (Step-2)

“AA” as starting location and developed counterclockwise (CCW) so that outer surface is visible

Model Solution-1 (Various other possibilities)

Case-1 Starting point A, CW opening direction Case-2 Starting point B, CCW opening direction Case-3 Starting point C, CCW opening direction Case-4 Starting point D, CCW opening direction

2, 3, 4 are all correct solution if starting point is not specified in question

x

Model Solution-2

A cone having base-diameter 200 mm and height 175 mm is standing on its base on the ground. It is cut by an AIP 30o to the ground and passing through a point on the axis 100 mm below apex. Draw development of the remaining solid.

Model Solution-2 (Stepwise solution)

Development of Lateral Surfaces

Figure shows a hollow crucible as well as its orthographic views (TV, FV and RSV). Draw a development of lateral as well as base surfaces.

Development of Lateral Surfaces

Continued