what is isometric view · isometric projection of solids 21 november 2018 dr.rgm, professor/...

What is Isometric view

The isometric view represents the overall appearance

of the object and makes it easy to understand some

details which may be difficult to understand in the

orthographic projections.

Isometric View:

The three dimensional view of an object obtained

on a plane of projection in which all the projectors are

parallel but inclined at an angle of 300 to the plane of

projection is known as Isometric View.

21 November 2018 2Dr.RGM, Professor/ Mechanical/ isometric projection /EG

Isometric Scale

Isometric scale:

The proportion by means of which the true distances

are reduced to isometric distance is known as

Isometric Scale. Construction Method of Isometric

Scale: To get accuracy in the Isometric projections, it

is necessary to get isometric lengths from the true

lengths.


Isometric Scale This can be done by constructing the Isometric Scale,

Construction steps are:

1. Draw a horizontal line AB

2. At point A, Draw a line AC at angle 450 as shown in the following figure

3. At point A, Draw another line AD at angle 300 as shown in the following

figure.

4. Now mark the true lengths such as 1, 2, 3, 4, 5, 6 cm etc on the line AC.

5. Project points 1, 2, 3, 4, 5, 6 etc on line AD so that projectors are

perpendicular to the line AB.

6. Corresponding points on line AD, represents isometric lengths 1, 2, 3, 4, 5, 6

cm etc from the point A.


Difference between Isometric view

and Isometric projection


S.No. Isometric View Isometric Projection

1 Drawn to actual scale Drawn to isometric scale

2 When lines are drawn parallel

to isometric axes, the true

lengths are laid off

When lines are drawn parallel to

isometric axes, the lengths are

foreshortened to 0.82 time the actual

lengths.

objective of IsometricObjectivesAt the end of this session, you will be able to:

1. Show the length, width and height of an object in a single view.

2. Create a three-dimensional effect of an object by means of an

isometric drawing.

Points to be remembered while drawing isometric

drawingsAt every visible corner of the object three lines must converge, of

these three lines, either all the three or any two lines may be

visible.

1. The hidden lines may not be shown, but it is advisable to

check every corner, so that no visible line is left out.

2. Two outlines will never cross each other.

3. If the axis of the solid is vertical, its end or ends will be

horizontal and if the axis of the solid is horizontal, its end or

ends will be vertical.21 November 2018 6Dr.RGM, Professor/ Mechanical/ isometric projection /EG

Method of Isometric Projection

Box method

The isometric projections of prisms, squares and

cylinders are generally drawn by the Box method.

Co - ordinate or offset method

The isometric projections of pyramids and cones

are generally drawn by Co-ordinate or offset

method.

21 November 2018

Dr.RGM, Professor/ Mechanical/ isometric

projection /EG 7

Isometric Projection of Planes

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projection /EG 8

Rectangle


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projection /EG 9

Square


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projection /EG 10

Pentagonal Plane


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projection /EG 11

Circular Plane

Isometric Projection of solids

21 November 2018 Dr.RGM, Professor/ Mechanical/ isometric projection /EG 12

1.Draw the isometric view of a square prism of side of

base 30mm and height 55mm when its axis is vertical.



2. Draw the isometric view of a hexagonal pyramid of

side of base 25 mm and height 60 mm, when it is resting

on the HP, such that an edge of the base is parallel to

the VP.



3 Draw the isometric view of a cylinder of 40 mm

diameter and 60 mm height when it rests with one of its

ends on the H.P.



4. Draw the isometric view of a cone of base 45 mm

diameter and height 65mm when it rests with its base on

the HP.



5. A hemisphere of 50mm diameter is nailed to the top face of the

frustum of a hexagonal pyramid. The edges of the top and bottom

faces of the frustum are 20mm and 35mm each respectively and

the height of the frustum is 55mm. The axes of both the solids

coincide. Draw the isometric view of the compound solid.



6.Draw the isometric view of a hexagonal prism of side

base 30 mm and height 70 mm when its rests with its

base on HP



7.Draw the isometric view of a hexagonal pyramid of

side base 30 mm and height 65 mm, when it is resting

on HP such that an edge of the base is parallel to VP.



8. A hexagonal prism of base side 30 mm and height 65

mm has a square hole of side 20 mm at the centre. The

axes of the square and hexagon coincide. One of the

faces of the square hole is parallel to a face of the

hexagon. Draw the isometric view of the square prism

with hole to full scale.



9. Draw the isometric view of a frustum of a hexagonal

pyramid when it is resting on its base on the HP with two

sides of the base parallel to the VP. The side of base is

20 mm and top 8 mm. The height of the frustum is 55

mm.



10.Draw the isometric view of a frustum of a square

pyramid .The side of base is 40 mm and top 20 mm. The

height of the frustum is 60 mm.



11. A square pyramid of base side 25 mm and height 50

mm has resting on HP with its base. It is cut by a cutting

plane inclined at 350 to HP and bisecting the axis. Draw

the isometric view.



12.A cylinder base diameter 35 mm and height 55 mm

resting on HP with its base. It is cut by a cutting plane

perpendicular to VP and inclined to HP at 450 and

meeting the axis at 15 mm from the top end. Draw the

isometric view of the truncated solid.



13. Draw the isometric view of a pentagonal pyramid 30 mm edge

of base and 65 mm height resting on HP such that an edge of the

base is parallel to VP and nearer to it and cut by a section plane

perpendicular to VP and inclined at 300 to HP passing through a

point on the axis at a height of 35 mm from the base.



14.Draw the isometric view of a pentagonal prism 30 mm edge of

base and 65 mm height resting on HP and one of it is base one of

the edges of base is perpendicular to VP. The prism is cut by a

plane perpendicular to VP and inclined at 300 to HP and intersect

the axis at 15 mm from the top.



15. A cone of the base diameter 40 mm and axis height

50 mm resting on HP with base. It is cut by section plane

inclined at 450 to HP and bisecting the axis. Draw the

isometric view.



16. The frustum of a pentagonal pyramid base 30 mm

side and top face 15 mm side has a height of 40 mm.

Draw its isometric view.



17.Draw its isometric view of a frustum of a cone base

60 mm side and top face 35 mm side has a height of 50

mm.



18.A cylinder of 50 mm and diameter and 60 mm height stands on

HP. A section plane perpendicular to VP inclined at 550to HP cuts

the cylinder and passing through a point on the axis at a height of

45 mm above the base. Draw the isometric view of the truncated

portion of the cylinder such that the cut surface is clearly visible to

the observer.



19.A dust bin is in the form of a frustum of a hollow square

pyramid with the base dimensions of 20 mm sides and the top

open surface of 45 mm sides. Draw the isometric view of the

hollow dust bin, if its height is 50 mm and the wall thickness of

negligible.



20.A waste paper bucket is in the form of a frustum of

hexagonal pyramid of side of base 180 mm and top 300 mm

side. Height is 400 mm. Draw the isometric view. Take

suitable scale.



21. A cone of base diameter 30 mm and height 40 mm rests

centrally over a frustum of a hexagonal pyramid of base side

40 mm top 25 mm and 60 mm height. Draw the isometric

view of the solid.



22. A square pyramid of side 30 mm axis length 50 mm is

centrally placed on top of a cube of side 50 mm. Draw the

isometric view of solid



23. A hexagonal shaped solid of base edge 20 mm and

height 40 mm lies centrally on a cylinder of 60 mm diameter

and 20 mm thick. Draw the isometric view of the solids if their

axes lie on the same line.



24. A square slab of 60 x 60 x 20 resting on HP with one of

its sides parallel to VP.A truncated cone of 50 mm bottom

base diameter 40 mm top face diameter and 50 mm height

placed centrally over the slab. A hemisphere of 30 mm radius

placed over the top face of the truncated cone centrally.

Draw the isometric view of the solids.



25. A circular slab of 60 mm diameter and 30 mm height

resting on HP with one of the base. A cube of 30 mm side is

placed over the circular slab centrally. A square pyramid of

base side 20 mm and axis height 20 mm placed centrally

over the cube. Draw the isometric view.



26. A frustum of a cone has its top and bottom diameters 35

mm and 50 mm respectively and altitude 53 mm. It rests on

the top face of the frustum of a square pyramid. The sides of

the top and bottom faces of the pyramid are 58 mm and 70

mm respectively. The height is 22 mm, Draw the isometric

view.



27. A frustum of the conical solid of the base diameter 50 mm

and top diameter 26 mm and 50 mm height is placed

centrally over a cylindrical block of 76 mm base diameter and

axis 25 mm long. The axes of the two solids as collinear.

Draw the isometric view of the combined solids.



28. A sphere of diameter 40 mm is kept centrally over a

square slab of 60 mm side and 25 mm height. Draw the

isometric projection of the solid.



29. A square pyramid rests centrally over a cylindrical block.

Draw the isometric projection of the arrangement. Consider a

pyramid has a base with 25 mm side and 40 mm long axis

whereas the cylindrical block has a base with 50 mm

diameter and 20 mm thickness.

Method of Isometric Projection

Box method

The isometric projections of prisms, squares and

cylinders are generally drawn by the Box method.

Co - ordinate or offset method

The isometric projections of pyramids and cones

are generally drawn by Co-ordinate or offset

method.

21 November 2018


projection /EG 41

Parallel-line DevelopmentsParallel-line developments are made from common

solids that are composed of parallel lateral edges or

elements. e.g. Prisms and cylinders

The cylinder is positioned such that one element lies

on the development plane. The cylinder is then

unrolled until it is flat on the development plane. The

base and top of the cylinder are circles, with a

circumference equal to the length of the development.

All elements of the cylinder are parallel and are

perpendicular to the base and the top.


Parallel-line Developments


Radial-line developments Radial-line developments are made from figures such as

cones and pyramids. In the development, all the

elements of the figure become radial lines that have the

vertex as their origin.

The cone is positioned such that one element lies on the

development plane. The cone is then unrolled until it is

flat on the development plane. One end of all the

elements is at the vertex of the cone. The other ends

describe a curved line.

The base of the cone is a circle, with a circumference

equal to the length of the curved line.


Radial-line developments


Triangulation developments


Triangulation developments are made from

polyhedrons, single curved surfaces, and wrapped

surfaces. The development involve subdividing any

ruled surface into a series of triangular areas. If each

side of every triangle is true length, any number of

triangles can be connected into a flat plane to form a

development Triangulation for single curved surfaces

increases in accuracy through the use of smaller and

more numerous triangles.

Triangulation developments of wrapped surfaces

produces only approximate of those surfaces.

Triangulation developments


.

Approximate developments


.Approximate developments are used for double

curved surfaces, such as spheres. Approximate

developments are constructed through the use of conical

sections of the object. Approximate developments the

material of the object is then stretched through various

machine applications to produce the development of the

object.

Development of surfaces – Prism Problems


1. A Square prism of base side 40 mm and axis length 50 mm is

resting on HP on one of its base with a side of base inclined at 350 to VP. It is cut by a plane inclined at 300 to HP and perpendicular

to VP and is bisecting the axis. Draw the development of the

remaining portion of the prism.



2. A pentagonal prism of base side 25 mm and height 55 mm is

cut by a plane perpendicular to VP and 300 to HP and passing

through the axis 30 mm above the base, draw the lateral surfaces

development in the lower portion of the solid.



3. A pentagonal prism of base side 25 mm and height 60 mm is

resting on the ground with one of its base edge parallel to VP .

Find graphically the shortest distance of the string which connect

one end of the lateral edge with the other end of the same edge,

covering all the lateral surfaces of the solid. Also trace the points

on the development.



4. A hexagonal prism of base side 30 mm and height 60 mm is

resting on the ground with one of its vertical faces perpendicular

to VP .It is cut by a plane inclined at 500 to HP and perpendicular

to VP and meets the axis of the prism at a distance of 10 mm

from the top end. Draw the development of the lateral surfaces.

Development of Surfaces – Cylinder Problems


5. Draw the development of the lateral surfaces of the lower

portion of a cylinder of diameter 45 mm and height 60 mm when

sectioned by a plane inclined at 400to HP and perpendicular to

VP and bisecting the axis.



6. A cylinder of diameter 50 mm and axis height 65 mm is cut by

a plane inclined at 600 to the HP and bisecting the axis. Draw

the development of the lateral surfaces



7. A cylinder of diameter 40 mm and axis height 75 mm is cut by

a plane perpendicular to VP inclined at 550 to HP meeting the

axis at the top face. Draw the development of the lateral

surfaces of solid.

Development of Surfaces – Pyramids Problems


8. A pentagonal pyramid of base 25 mm side and height 65 mm

stands with its base on the HP such that one of its base edges is

parallel to the VP. It is cut by a section plane perpendicular to the

VP and inclined at 300 to the HP, bisecting the axis. Draw the

development of the lateral surfaces of solid.



9.A pentagonal pyramid of base 25 mm side and height 60 mm

lying on the HP on its base such that one of its base edges is

parallel to and far away from the VP. It is cut by a section plane

one is perpendicular to the VP and inclined at 400 to the HP, and

meeting the axis at 14 mm from the base the other plane is

parallel to HP and perpendicular to VP meeting the axis distance

of 28 mm from the base. Draw the development of the lateral

surfaces of solid.



10. A square pyramid of base side 30 mm and altitude 65 mm is

resting on HP on its base with a side of the base inclined at 250

to VP. It is cut by a plane inclined 350 to HP and perpendicular to

VP and bisects the axis. Draw the development of the remaining

surfaces of solid.



11. A hexagonal pyramid of base 25 mm side and height 50 mm

rests on its base with one base edge parallel to VP.A string is

wound around the surfaces of the pyramid starting from the left

extreme point of the base and ending at the same. Find the

shortest length of the string required. Also trace the path of the

string in the projection.



12. A hexagonal pyramid of base side 25 mm and altitude 60

mm is resting vertically on its base on the ground with two of the

of the sides of the base perpendicular to the VP. It is cut by a

plane perpendicular to the VP and inclined at 450 to the HP. The

plane bisects the axis of the pyramid. Draw the development of

the lateral surfaces of solid.



13.A square pyramid of base side 30 mm and height 50 mm

rests on its base on the HP, with a base edge parallel to VP. It is

cut by a plane perpendicular to VP and inclined 500to HP

meeting the axis 30 mm above HP. Draw the development of the

lateral surfaces.



14. A pentagonal pyramid of base 30 mm side and height 60 mm

stands with its base on the HP on its base edges is

perpendicular to the VP. It is cut by a section plane

perpendicular to the VP and parallel to the HP, and meets the

axis at a distance of 25 mm from the vertex. Draw the

development of the lateral surfaces of solid.



15. A hexagonal pyramid of side of base 30mm and altitude 75

mm rests on its base on HP, such that a base edge is parallel to

VP. it is cut by two cutting planes perpendicular to VP. One of the

planes is inclined at 300 to HP and meeting the axis at a point 40

mm from the base. The other plane is curved of 30 mm radius

with the right corner of the base as centre. Draw the

development of the lateral surfaces.



16. A square pyramid of base side 35 mm and height 70 mm

rests on its base on the HP, such that two adjacent sides of the

base are equally inclined to VP. It is sectioned by a plane

perpendicular to VP, inclined 300to HP and passing through the

midpoint of the axis. Draw the development of the lateral

surfaces.



17. Draw the development of the lateral surfaces of a hexagonal

pyramid with a 40 mm base side and a 60 mm long axis ,which

is resting on the base in the HP such that an edge of the base is

perpendicular to VP when an auxiliary inclined plane whose VT

makes on angle 600 HP and bisecting the axis.

Development of surfaces – Cone Problems


18. A cone of base side 60mm and height 70 mm rests on its

base on the HP, It is sectioned by a plane perpendicular both HP

and VP, and 10 mm away from the axis. Draw the development

of the lateral surfaces.



19. A cone of base side 50 mm and height 65 mm rests on its

base on the HP, It is sectioned by a plane perpendicular VP and

inclined at 300 to HP bisect the axis of the cone. Draw the

development of the lateral surface.





inclined at 300 to HP bisect the axis of the cone. Draw the

development of the lateral surface.



20.A right circular cone of diameter 50 mm axis height 60 mm is

string on the ground with its base. Calculate the shortest length

of a string required to wound round the lateral surface of the

solid starting from one extreme point and ending at the same

point. Also trace the points on to the projections.





parallel to HP at a distance 20 mm from the vertex. It is also cut

by a plane inclined at 400to the base and meeting the axis at a

point 22 mm above the base. Draw the development of the

lateral surface.



22.A cone of base side 45 mm and height 70 mm rests on its

base on the HP, It is sectioned by a plane perpendicular VP

300to HP and bisecting the axis. Draw the development of the

lateral surfaces




base on the HP, It is sectioned by a plane perpendicular VP

,parallel to one of the generators and passing through a point on

the axis at a distance of 22 mm from the apex. Draw the

development of the lateral surfaces

Development of surfaces – Special Problems


24. Draw the development of the tray whose pictorial view as

shown in fig

Step:1Step:2



25. Draw the development of a duct as shown.



26. Draw the development of the three pipes forming a Y shape

as shown. All the pipes are diameters of 40 mm. The max.

Height of the vertical pipe is 50 mm. The angle between the

axes of the inclined pipes is 800.



27. An offset fitting is made up of three pipes of diameter 40 mm

each. The total length of the fitting is 90 mm and the offset is 55

mm. Draw the lateral surface of the pipes.



28. An elbow is made up of three pipes are diameter 40 mm

each fitted as shown. The shorter arm of both the vertical and

horizontal pipes has the same length of 20 mm. Draw the

development of pipes forming the elbow.



29. A funnel is made up of a truncated cone and a cut cylinder as

shown. The cone is of base diameter 60 mm and altitude 70

mm. They are fitted as shown. Draw the development of funnel

forming cone.

what is isometric view · isometric projection of solids 21 november 2018 dr.rgm, professor/...

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