lect 6. development

Development of Surfaces

SURFACE DEVELOPMENT

Development of Surfaces

The development of surface of an object means the unrolling and unfolding of all surfaces of the object on a plane

If the surface of a solid is laid out on a plain surface, the shape thus obtained is called the development of that solid

The development of a solid is the shape of a plain sheet that by proper folding could be converted into the shape of the concerned solid.

Importance of Surface Development

Knowledge of development is very useful in sheet metal work, construction of storage vessels, chemical vessels, boilers, chimneys etc.

Such vessels are manufactured from plates/sheets that are cut according to these developments and then properly bend into desired shaped and the joints are welded or riveted.

Principles of Surface Development

Every line on the development should show the true length of the corresponding line on the surface which is developed.

Methods of Development of Surface

Methods of Surface Development are:

1. Parallel line development

2. Radial line development

3. Triangulation development

4. Approximate development


uses parallel lines to construct the expanded pattern of each three-dimensional shape. The method divides the surface into a series of parallel lines to determine the shape of a pattern

Example: Prism, Cylinder.



Radial line development uses lines radiating from a central point to construct the expanded pattern of each three-dimensional shape.

Example: Cone, Pyramid.


3. Triangulation developments

Are made from polyhedrons, single-curved surfaces, and wrapped surfaces.

It is used for developing transition pieces

This is done by assuming the surface to be made from a series of triangular surfaces laid side-by-side to form the development

Example: Tetrahedron and other polyhedrons.



In approximate development,

the shape obtained is only approximate. After joining, the part is stretched or distorted to obtain the final shape.

Example: Sphere


Development of a Cylinder

Draw the plan & elevation of the cylinder

Divide the plan in to equal parts (i.e. 8, 12)

Draw horizontal lines A-A and A1-A1 from the side of the elevation

The length of these lines is πD (circumference of the cylinder)

Divide the stretch-out line into the equal number of same parts as the plan (i.e. 8, 12)

The rectangle (A- A; A1- A1), gives the development of the cylinder.

Side view

Development of a Truncated Cone

Draw the (truncated) cone elevation and plan views as shown.

Divide the plan view into equal parts/segments (i.e. 12)

Transfer these points to the elevation.


Development of a Pyramid

Draw the front and plan view of the square pyramid

Find the true length of the slant edge 0’ – 1’1

Take radius = length 0’ - 1’1 with any centre o, draw an arc of a circle.

Choose any point 1 on the arc and join it to point o (centre of the arc).

On the plan view, use length 1-2, 2-3, 3-4, 4-1 to mark off four division along the arc as 1, 2, 3, 4 etc. Join 1, 2, 3 and 4 along with 01. Join 1 to 2, 2 to 3, 3 to 4 and 4 to 1 with straight lines.

Use radius = the base side of the pyramid (i.e. 50 mm) mark four divisions on theThe 4 isosceles triangles represent the lateral development of the pyramid.

Development of a Truncated Pyramid

Draw the front and plan view of theDraw the front and top views of the truncated pyramid

On the plan, draw the diagonal 1-3, 2-4 to meet at 0. Numbered the plan and project to the front as shownExtend centre 0 horizontally. 0-1 as radius, draw an arc to meet 11

Project 11 vertically to meet elevation at 11’. Join 11’ to 0’ (equals the true length of the slanting side)

Drop off the cutting points a’ b’ c’ d’ on the elevation to meet the plan at d, c, b and a respectively


0’-11’ as radius with centre 0, draw an arc. Join any point 1 to centre 0 of the arc

From the plan use length 1-2, 2-3, 3-4 etc to cut points along the arc and number the points as 1, 2, 4, 1. Join these points to centre 0.0’-a’ as radius, with centre 0, draw an inner (smaller) arc.

Use length a-b, b-c, c-d and d-a, from the plan, locate 5 points A, B, C, D and A on the inner arc.

Join all the points on the big and smaller arc to form the development of the truncated pyramid


..Truncated Pyramid cont.


Transition pieces are the sheet metal used for connectingpipes or openings either of different shapes of cross sections or of same cross sections but not arranged in identical positions.

In this method, the lateral surfaces of the transition pieces are divided in to a number of triangles

By finding the true lengths of the sides of each triangle

the development is drawn by laying each one of the

triangles in their true shapes adjoining each other.


Triangulation method

PLAN

ELEVATION


Draw the elevation and the plan view as shown

The semicircle in the plan view is divided into eight equal parts 1,2,3,4,etc.

Join pts 1,2,3,4 and 5 to pt. a. and 5, 6, 7, 8, 9 to pt b.


The transition piece consists of 4 plane triangles 1da, 5ab, 9bc, and 13cd and

4 curved triangles 1a5, 5b9, 9c13 and 13d1

Project points 1,2,3,etc to the front view to meet 1’,2’,3’. etc.

Connect 1’, 2’, 3’ etc to a’ and 5’,6’, 7’, 8’ 9’ to b’.


Draw vertical line XY. The first triangle to be drawn is 1pa (from plan)

The true length of sides 1pand 1a are found from the true length diagram.


To get true length of sides 1p & 1a

step off the distances 1p and 1a on the horizontal drawn through X to get the point 1P’and 1A’.

Connect these two points to Y. The length Y-1P’ and Y-1A’are the true lengths of the sides 1p and 1a respectively.



DEVELOPMENT

Draw line 1₁P = Y-1P’

Draw an arc with center 1₁and radius Y-1A’.

P as center & radius pa,(from plan view) draw an arc to cut the line 1₁-A at A.

With A as center and radius equal to true length of the line 2a (i.e. Y-2A’), draw an arc.

With 1₁ as center & radius 1-2 (T.V), draw another arc intersecting the pervious arc at 2₁.



Similarly determine the points 3₁, 4 ₁ and 5₁.A -1₁ -2₁ -3₁ - 4₁ - 5₁ is the development of the curved triangle 1-a-5.AB is the true length of the plain triangle a-5-b.

Similar procedure is repeated for the other three curved trianglesand plain triangles.

A as center & radius = true length of the line 2a (i.e. Y-2A’), draw an arc.

With 11 as center & radius = 1-2 (T.V), draw another arcintersecting the pervious arc at 2₁.


In the same way, determine points 31, 41 and 51.

A -11-21-31- 41- 51 is the development of the curved triangle 1-a-5.AB is the true length of the plain triangle a-5-b.

Similar procedure is repeated for the other three curved trianglesand plain triangles.


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lect 6. development

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