devp surfaces

Chapter 12 Development of Surfaces

ENGINEERING GRAPHICS(TA C111)

4/2/2009 Development of Surfaces 2

Introduction

When the surfaces of an object are laid out over a single plane, the spread surface will take certain shape. The shape so obtained on the plane is the development of the surface for that particular object.

Every line on the development must represent ONLY the true length or dimensions of the corresponding edge on the surface.


The surface of polyhedra (such as prisms and pyramids), and single curved surfaces (cones and cylinders) can be accurately developed. In dealing with the development of these objects, the ends or bases are not generally considered but they can be incorporated if necessary.This development without incorporating the ends or bases is called the development of the lateral surface

Introduction


Methods of Development

Two principal methods of development:

• The parallel line development

• The radial line development


Parallel-line development:

Applicable to prisms and cylindersThe solid is rolled on a plane in a direction perpendicular to the axis of the object to get the developmentThe longer edges or generators of the object will be parallel to each other in the developmentThe total area of the development for one complete revolution of the object = (perimeter of the base) (height of the axis)

Rectangular ARRAY can be used to

develop the surfaces.


Development of curved surface of cylinder

H H

πdd


Development of lateral surfaces of a Hexagonal Prism

H H

w

w


Radial-line development

Applicable to pyramids and conesThe solid is rolled on a plane with the apex hinged at a point on itThe true length of the generator or slant edge is used as radiusFOR ONE COMPLETE REVOLUTION

The length of the arc = the circumference of the base of the solid

Polar ARRAY can be used to develop the

surfaces.


Development of single curved surface of a Cone

S

θ

r

360×=Srθ


Development of lateral (slant) surfaces of a hexagonal pyramid


Make use of MEASURE, DIVIDE, ARRAY (R & P) commands wherever possible.While drawing a development of surfaces of solids the starting point ‘S’ and opening direction (ccw or cw) is important.

Instructions


Examples


Examples

Draw the development of the lateral surface of a square pyramid with base edge 100mm and height 200mm

I III IVII


Example

Draw the development of the lateral surface of the hexagonal pyramid with base edge 100mm and height 250mm cut by

section planes as shown

I III IVII


V VIIVI


Examples


Announcement

There will be a Lecture class on Wednesday (08.04.09) during the tutorial hour.

Time: 9 a.m. – 10 a.m.Room: 5105

devp surfaces

Documents