Projection of Solids - Complete

SOLIDS

SOLIDS

• Solids are figures having the three dimensions of length, width, and depth bounded by plane surfaces. Solids may also be known as polyhedra. The plane surfaces of polyhedra are called faces and if the faces are regular polygons, the solids are regular polyhedra.

SOLIDS

SOLIDS

Platonic solid

• Any of the five regular polyhedrons – solids with regular polygon faces and the same number of faces meeting at each corner – that are possible in three dimensions. They are the tetrahedron (a pyramid with triangular faces), the octahedron (an eight-sided figure with triangular faces), the dodecahedron (a 12-sided figure with pentagonal faces), the icosahedron (a 20-sided figure with triangular faces), and the hexahedron or cube. They are named after Plato who described them in one of his books, though it was Euclid who proved that there are only five regular polyhedra. A regular solid with hexagonal faces cannot exist because if it did, the sum of the angles of any three hexagonal corners that meet would already equal 360°, so such an object would be planar.

Platonic solid

Platonic solid

• Each of these solids possesses an inscribed and a circumscribed sphere, which has the same center O. Further, the mid-points of all the edges of a Platonic solid also lie on a sphere again with center O. If we construct the inscribed sphere of a Platonic solid and join neighboring points of contact of the sphere with the faces of the polyhedron, there results within the sphere another regular polyhedron, which has the same number of vertices as the original solid has faces, and the same number of edges as the original solid. The cube yields an octahedron, the icosahedron a dodecahedron, and the tetrahedron another tetrahedron.

PRISMS

• A prism is a solid with two bases (top and bottom) that are equal regular polygons and three or more lateral faces that are parallelograms. If the bases are also parallelograms, the prism is a parallelepiped. A right prism has faces and lateral edges that are perpendicular to the bases. Oblique prisms have faces and lateral edges oblique to the bases.

PRISMS

PRISMS

PYRAMIDS

• Pyramids have polygons for a base and triangular lateral faces that intersect at the vertex or top of the pyramid. A centerline from the vertex to the center of the base is known as the axis and its height is called the altitude. If the axis is perpendicular to the base, the pyramid is a right pyramid. All other pyramids are oblique pyramids. A pyramid that has been cut off near the vertex oblique to the base is said to be truncated; if the pyramid is cut off parallel to the base, the cut plane is known as a frustum

PYRAMIDS

PYRAMIDS

SOLIDS OF REVOLUTION

CYLINDERS

• Cylinders are two parallel bases formed by a fixed curve or directrix revolving around a straight line or generatrix at the center. The generatrix at the center of the cylinder is also called an axis. The height of the cylinder is called the altitude. Any point along the edges of the cylinder is referred to as an element. Right circular cylinders have lateral edges perpendicular to the bases and oblique circular cylinders have lateral edges oblique to the bases. Moving a point around and along the surface of a cylinder with uniform angular velocity to the axis and with a uniform linear velocity in the direction of the axis produces a helix. You may construct a helix using a cylinder or cone

CYLINDERS

CONES• Cones have a generatrix that terminates in a fixed point at a vertex

around which revolves a directrix or closed curve base. The generatrix is also known as the axis whose height is referred to as altitude. Any point around the cone from the base to the vertex is called an element. A cone whose axis is perpendicular to its base is a right cone.

• Planes intersecting a cone will make the cone appear truncated or frustum. Planes intersecting a right cone produce conic sections. Conic sections appear as curves.

• A conic section perpendicular to the axis appears as a circle at the plane of intersection. A conic section with a cutting plane oblique to the axis but making a greater angle with the axis than the elements appears as an ellipse.

• When the plane of intersection is oblique to the axis and at the same angle to the axis as the elements, the curves is referred to as a parabola. An oblique plane of intersection that makes a smaller angle to the axis than the elements is known as a hyperbola. Cones may also be used to construct helixes.

CONES

SPHERES

• Spheres are formed by a circle revolving around its diameter. The diameter of the circle then becomes the axis and the ends of the axis are known as poles

PROJECTION OF SOLIDS

Tips for projection of solids• When the axis of the solid inclined any of the projection plane,• First assume the axis is perpendicular to that plane. • Draw the projection in simple position

– Top view first if the axis is perpendicular to HPFront view first if the axis is perpendicular to VP

• Change position of the view to the given inclination – Tilt the front view, if the axis inclined to the HP

Tilt the top view, if the axis inclined to the VP

• Project from this view to get the final view – Project from the front view, to get the top view if the axis inclined to the HP

Project from the top view, to get the front view if the axis inclined to the VP

• Ensure all the points are named in an appropriate manner – Lower case letters with a (‘)dash for the front views – Lower case letters alone for the top views

SINGLE POINT PERSPECTIVE

Single-point perspective is just about the simplest form of perspective projection it is possible to have. It is called single-point perspective because it involves only a single vanishing point.

The vanishing point is a technique in perspective drawing. The simplest use of the vanishing point is the one point perspective

Perspective is a realistic way of drawing objects in 3D.

SINGLE POINT PERSPECTIVE - VANISHING POINTS

Altering the position of the VP changes the view of the object being drawn. For example, to look down at the top of the object the vanishing point must be above.

SINGLE POINT PERSPECTIVE -

VANISHING POINTS

However, to look up at the object the vanishing point must be below .

SINGLE POINT PERSPECTIVE -

VANISHING POINTSMoving the VP to the left or right of the object will allow the sides to be seen. If the VP is placed directly behind the object then only the front will be seen.

SINGLE POINT PERSPECTIVE DRAWING - EXERCISE

Draw your name in a decorative / imaginative style. Place a single vanishing point above, in the centre. Apply appropriate colour and shade. See the example below

DRAWING A TABLE IN SINGLE POINT PERSPECTIVE

A three dimensional view of a traditional wood kitchen table is seen below. Draw the table or a similar one in single point perspective.


1. Draw a side of the table and the position of the vanishing point. Positioning the vanishing point high on the left or right hand side means that one side of the table will be seen when the drawing of the table is completed.


2. Starting with the table top, project guidelines back to the vanishing point and complete drawing the top.

Then project more guidelines for each of the front legs, adding thickness to each one.


The most difficult part is ensuring that the back legs line up with the front legs. One way of ensuring that this happens is to project faint lines as shown on the drawing below.


Add suitable color /shade using a colored pencils.

Include wood grain to the top of the table.

TWO POINT PERSPECTIVE

A graphical technique in which a three-dimensional object is represented in two

dimensions, and in which parallel lines in two of its dimensions are shown to converge towards

two vanishing points


The cube apposite is drawn with two vanishing points and as a result the sides look as if they are slowly fading away into the distance. Two vanishing points gives this 'feel' to a drawing.


Mark two vanishing points on the paper and faintly draw a line between them - this is called the horizon line. Then draw one side/edge of the cube beneath the horizon line and in the centre between the vanishing points.


Draw faint lines from the ends of the edge of the cube to the vanishing points


Draw two more edges of the cube so that two sides of the cube can be clearly seen.


Draw faint guidelines from the ends of these lines to either vanishing point.


Use a fine black pen to draw over the outline of the cube. Add shade.


Complete the following two perspective drawing of the 'L' shape.

In this example a simple kitchen table is drawn in two point perspective. This is much more difficult compared to the single point perspective shown earlier. This time it is very important to project guidelines towards both vanishing points.



Mark both vanishing points and start drawing faintly - the table top.


Add thickness to the table top remembering to project all lines to the vanishing points. Add the front legs.


Add one of the back legs.


Add the final leg and any other detail such as shade/colour.

EXAMPLE - EXTERNAL VIEW OF BUNGALOW -1

Below is an example of a bungalow drawn in two point perspective. Appropriate colour and shade have been added. Hint - Always make your drawing / design a little different. In the drawing below clothes are hanging on a washing line and a door is open giving a view inside. Use your imagination and make your design stand out by adding individual touches.

EXAMPLE - EXTERNAL VIEW OF BUNGALOW - 2

Below is an example of a bungalow drawn in two point perspective. Appropriate colour and shade have been added. Hint - Always make your drawing / design a little different. In the drawing below a pond has been added and a range of plants and trees. Plus, other houses are drawn in the distance.. Use your imagination and make your design stand out by adding individual touches.

EXAMPLE - EXTERNAL VIEW OF BUNGALOW - 3

Below is an example of a bungalow drawn in two point perspective. Appropriate colour and shade have been added. Hint - Always make your drawing / design a little different. In the drawing below the interior of rooms can be seen through the windows. Also, a neat garden has been drawn at the front of the house. Use your imagination and make your design stand out by adding individual touches.

ESTIMATED PERSPECTIVESometimes, in order to produce a realistic drawing the vanishing points need to be positioned beyond the edge of the paper. This is estimated perspective. When drawing, the guidelines they are projected back to imaginary vanishing points. Estimated perspective allows objects to be drawn close up and yet still look as if drawn in perspective.

OBLIQUE PROJECTION

Oblique projection is a method of drawing objects in 3 dimensions. It is quite a simple technique compared to isometric or even perspective drawing. However, to draw accurately in oblique projection traditional drawing equipment is needed (see diagram below).

OBLIQUE PROJECTION

The technique for drawing a cube in oblique projection is outlined below, stage by stage. To draw it correctly in oblique projection three main rules must be followed:1. Draw the front or side view of the object.2. All measurements drawn backwards are half the original measurement.3. 45 degrees is the angle for all lines drawn backwards

OBLIQUE PROJECTION

Draw the front view. Remember to use a T-square and 45 degree set square.

OBLIQUE PROJECTION

Draw 45 degree lines from each corner of the square. The distance of any lines drawn back at 45 degrees should be halved. For example, a cube may have sides of 100mm but they must be drawn 50mm in length. This should mean that the cube will look more realistic and in proportion.

OBLIQUE PROJECTION

Draw 45 degree lines from each corner of the square. The distance of any lines drawn back at 45 degrees should be halved. For example, a cube may have sides of 100mm but they must be drawn 50mm in length. This should mean that the cube will look more realistic and in proportion.

STEPS TO SOLVE PROBLEMS IN SOLIDS Problem is solved in three steps:STEP 1: ASSUME SOLID STANDING ON THE PLANE WITH WHICH IT IS MAKING INCLINATION. ( IF IT IS INCLINED TO HP, ASSUME IT STANDING ON HP) ( IF IT IS INCLINED TO VP, ASSUME IT STANDING ON VP)

IF STANDING ON HP - IT’S TV WILL BE TRUE SHAPE OF IT’S BASE OR TOP: IF STANDING ON VP - IT’S FV WILL BE TRUE SHAPE OF IT’S BASE OR TOP.

BEGIN WITH THIS VIEW: IT’S OTHER VIEW WILL BE A RECTANGLE ( IF SOLID IS CYLINDER OR ONE OF THE PRISMS): IT’S OTHER VIEW WILL BE A TRIANGLE ( IF SOLID IS CONE OR ONE OF THE PYRAMIDS):

DRAW FV & TV OF THAT SOLID IN STANDING POSITION:STEP 2: CONSIDERING SOLID’S INCLINATION ( AXIS POSITION ) DRAW IT’S FV & TV.STEP 3: IN LAST STEP, CONSIDERING REMAINING INCLINATION, DRAW IT’S FINAL FV & TV.

AXIS VERTICAL

AXIS INCLINED HP

AXIS INCLINED VP

AXIS VERTICAL

AXIS INCLINED HP

AXIS INCLINED VP

AXIS TO VPer

AXIS INCLINED

VP

AXIS INCLINED HP

AXIS TO VPer AXIS

INCLINED VP

AXIS INCLINED HP

GENERAL PATTERN ( THREE STEPS ) OF SOLUTION:

GROUP B SOLID.CONE

GROUP A SOLID.CYLINDER

GROUP B SOLID.CONE

GROUP A SOLID.CYLINDER

Three stepsIf solid is inclined to Hp

Three stepsIf solid is inclined to Hp

Three stepsIf solid is inclined to Vp

Study Next Problems and Practice them separately !!

Three stepsIf solid is inclined to Vp

PROBLEM

• A right regular pentagonal pyramid, side of base 25mm and height 50 mm, lies on HP on one of its slant edges and has its axis parallel to V.P. Draw its projections.

PROBLEM

• A right circular cone, diameter of base 50mm and axis 62mm long, rests on its base rim on HP with its axis parallel to VP and one of the elements perpendicular to HP. Draw the projections of cone.

PROBLEM

• A right circular cone, diameter of base 50mm and height 62mm, lies on HP on one of its elements, with its axis parallel to VP. Draw the projections of cone.

PROBLEM

• A right circular cone, diameter of base 35mm and height 40mm, rests on an auxiliary horizontal plane on its base rim, such that its axis is parallel to the V.P and inclined at 45 degrees to the HP. Draw its projections using third angle projection method.

PROBLEM

• A right circular cylinder, diameter of base 50mm and height 70mm, rests on ground plane such that its axis is parallel to VP and inclined to HP at 45 degrees. Draw its projections.

PROBLEM

• A right circular cylinder, diameter of base 40mm and height 60mm, is resting in HP on its base rim such that its axis is parallel to VP, inclined at 30 degrees to th eHP and is 40mm away from the VP. Draw its projections when it is in first quadrant,

(i) by change of position of the reference line (ii) by change of position of cylinder

PROBLEM

• An ash tray, made of thin sheet of steel, is spherical in shape with flat, circular top of 68mm diameter and bottom of 52mm diameter and parallel to each other. The greatest diameter of it is 100mm. Draw the projections of the ash tray when its axis is parallel to VP and (i) makes an angle of 60 degrees with the HP (ii) its base is inclined at 30 degrees to the HP.

DEVELOPMENT OF SOLIDS

DEVELOPMENT OF SURFACES OF SOLIDS.DEVELOPMENT OF SURFACES OF SOLIDS.

MEANING:-MEANING:-ASSUME OBJECT HOLLOW AND MADE-UP OF THIN SHEET. CUT OPEN IT FROM ONE SIDE AND ASSUME OBJECT HOLLOW AND MADE-UP OF THIN SHEET. CUT OPEN IT FROM ONE SIDE AND UNFOLD THE SHEET COMPLETELY. THEN THE UNFOLD THE SHEET COMPLETELY. THEN THE SHAPE OF THAT UNFOLDED SHEET IS CALLEDSHAPE OF THAT UNFOLDED SHEET IS CALLED DEVELOPMENT OF LATERLAL SUEFACESDEVELOPMENT OF LATERLAL SUEFACES OF THAT OBJECT OR SOLID. OF THAT OBJECT OR SOLID.

LATERLAL SURFACELATERLAL SURFACE IS THE SURFACE EXCLUDING SOLID’S TOP & BASE. IS THE SURFACE EXCLUDING SOLID’S TOP & BASE.

ENGINEERING APLICATIONENGINEERING APLICATION::THERE ARE SO MANY PRODUCTS OR OBJECTS WHICH ARE DIFFICULT TO MANUFACTURE BY THERE ARE SO MANY PRODUCTS OR OBJECTS WHICH ARE DIFFICULT TO MANUFACTURE BY CONVENTIONAL MANUFACTURING PROCESSES, BECAUSE OF THEIR SHAPES AND SIZES. CONVENTIONAL MANUFACTURING PROCESSES, BECAUSE OF THEIR SHAPES AND SIZES. THOSE ARE FABRICATED IN SHEET METAL INDUSTRY BY USING THOSE ARE FABRICATED IN SHEET METAL INDUSTRY BY USING DEVELOPMENT TECHNIQUE. THERE IS A VAST RANGE OF SUCH OBJECTS. DEVELOPMENT TECHNIQUE. THERE IS A VAST RANGE OF SUCH OBJECTS.

EXAMPLES:-EXAMPLES:-Boiler Shells & chimneys, Pressure Vessels, Shovels, Trays, Boxes & Cartons, Feeding Hoppers,Boiler Shells & chimneys, Pressure Vessels, Shovels, Trays, Boxes & Cartons, Feeding Hoppers,Large Pipe sections, Body & Parts of automotives, Ships, Aeroplanes and many more.Large Pipe sections, Body & Parts of automotives, Ships, Aeroplanes and many more.

WHAT IS WHAT IS OUR OBJECTIVE OUR OBJECTIVE IN THIS TOPIC ?IN THIS TOPIC ?

To learn methods of development of surfaces ofTo learn methods of development of surfaces ofdifferent solids, their sections and frustumsdifferent solids, their sections and frustums..

1. Development is different drawing than PROJECTIONS.1. Development is different drawing than PROJECTIONS.2. It is a shape showing AREA, means it’s a 2-D plain drawing.2. It is a shape showing AREA, means it’s a 2-D plain drawing.3. Hence all dimensions of it must be TRUE dimensions.3. Hence all dimensions of it must be TRUE dimensions.4. As it is representing shape of an un-folded sheet, no edges can remain hidden4. As it is representing shape of an un-folded sheet, no edges can remain hidden And hence DOTTED LINES are never shown on development.And hence DOTTED LINES are never shown on development.

But before going ahead,But before going ahead,note following note following

ImportantImportant points points..

Study illustrations given on next slides carefully.Study illustrations given on next slides carefully.

D

H

D

SS

H

L

= RL

+ 3600

R=Base circle radius.L=Slant height.

L= Slant edge.S = Edge of base

L

S

S

H= Height S = Edge of base

H= Height D= base diameter

Development of lateral surfaces of different solids.(Lateral surface is the surface excluding top & base)

Prisms: No.of Rectangles

Cylinder: A RectangleCone: (Sector of circle) Pyramids: (No.of triangles)

Tetrahedron: Four Equilateral Triangles

All sides equal in length

Cube: Six Squares.

DEVELOPMENT OF PRISM

DEVELOPMENT OF PYRAMID

DEVELOPMENT OF A CYLINDER

DEVELOPMENT OF A CONE

X Y

X1

Y1

a’

b’ e’

c’

d’

A

B

C

E

D

a

e

d

b

c

TRUE SHAPE

A B C D E A

DEVELOPMENT

a”

b”

c”d”

e”

Problem 1:Problem 1: A pentagonal prism , 30 mm base side & 50 mm axis A pentagonal prism , 30 mm base side & 50 mm axis is standing on Hp on it’s base whose one side is perpendicular to Vp.is standing on Hp on it’s base whose one side is perpendicular to Vp.It is cut by a section plane 45It is cut by a section plane 450 0 inclined to Hp, through mid point of axis.inclined to Hp, through mid point of axis.Draw Fv, sec.Tv & sec. Side view. Also draw true shape of section and Draw Fv, sec.Tv & sec. Side view. Also draw true shape of section and Development of surface of remaining solid.Development of surface of remaining solid.

Solution Steps:Solution Steps:for sectional views:for sectional views: Draw three views of standing prism.Draw three views of standing prism.Locate sec.plane in Fv as described.Locate sec.plane in Fv as described.Project points where edges are getting Project points where edges are getting Cut on Tv & Sv as shown in illustration.Cut on Tv & Sv as shown in illustration.Join those points in sequence and showJoin those points in sequence and showSection lines in it.Section lines in it.Make remaining part of solid dark.Make remaining part of solid dark.

For True Shape:For True Shape:Draw xDraw x11yy11 // to sec. plane // to sec. plane

Draw projectors on it from Draw projectors on it from cut points.cut points.Mark distances of points Mark distances of points of Sectioned part from Tv, of Sectioned part from Tv, on above projectors from on above projectors from xx11yy11 and join in sequence. and join in sequence.

Draw section lines in it.Draw section lines in it.It is required true shape.It is required true shape.

For Development:For Development: Draw development of entire solid. Name from Draw development of entire solid. Name from cut-open edge I.e. A. in sequence as shown.cut-open edge I.e. A. in sequence as shown.Mark the cut points on respective edges. Mark the cut points on respective edges. Join them in sequence in st. lines.Join them in sequence in st. lines.Make existing parts dev.dark.Make existing parts dev.dark.

PROBLEM

• Develop the lateral surface of a right regular hexagonal prism of 20mm base edge and 50mm height.

PROBLEM

• A right regular pentagonal prism, edge of base 20mm and height 50mm, rests on its base with one of its base edges perpendicular to VP. An AIP inclined to HP at 30 degrees and perpendicular to th eVP cuts its axis at a distance of 30mm from the base. Develop the lateral surface of the truncated prism.

PROBLEM

• A right regular pentagonal prism, edge of base 30mm and height 75mm, resting on its base on HP, is cut by a section plane inclined to HP at 45 degrees and meeting the axis at a distance of 18mm from its top end. Develop the outside surface of the cut prism.

PROBLEM

• A right regular pentagonal prism, edge of base 30mm and height 75mm, rests on its base on HP. It is truncated from both of its ends by section planes develop the lateral surface of the truncated prism.

INTERSECTION OF SOLIDS

INTERSECTION OF SOLIDSWHEN ONE SOLID PENETRATES ANOTHER SOLID THEN THEIR SURFACES INTERSECT

AND AT THE JUNCTION OF INTERSECTION A TYPICAL CURVE IS FORMED,

WHICH REMAINS COMMON TO BOTH SOLIDS.

THIS CURVE IS CALLED CURVE OF INTERSECTIONAND

IT IS A RESULT OF INTERPENETRATION OF SOLIDS.

PURPOSE OF DRAWING THESE CURVES:-WHEN TWO OBJECTS ARE TO BE JOINED TOGATHER, MAXIMUM SURFACE CONTACT BETWEEN BOTH

BECOMES A BASIC REQUIREMENT FOR STRONGEST & LEAK-PROOF JOINT.Curves of Intersections being common to both Intersecting solids,

show exact & maximum surface contact of both solids.

Study Following Illustrations Carefully.Study Following Illustrations Carefully.

Square Pipes. Circular Pipes. Square Pipes. Circular Pipes.

Minimum Surface Contact.( Point Contact) (Maximum Surface Contact)

Lines of Intersections. Curves of Intersections.

A machine component having two intersecting cylindrical surfaces with the axis at acute angle to each other.

Intersection of a Cylindrical main and Branch Pipe.

Pump lid having shape of a hexagonal Prism and

Hemi-sphere intersecting each other.

Forged End of a Connecting Rod.

A Feeding HopperIn industry.

An Industrial Dust collector.Intersection of two cylinders.

Two Cylindrical surfaces.

SOME ACTUAL OBJECTS ARE SHOWN, SHOWING CURVES OF INTERSECTIONS. BY WHITE ARROWS.

REFFER ILLUSTRATIONS AND

NOTE THE COMMON CONSTRUCTION

FOR ALL THE CASES

1.CYLINDER TO CYLINDER2.

2.SQ.PRISM TO CYLINDER

3.CONE TO CYLINDER

4.TRIANGULAR PRISM TO CYLNDER

5.SQ.PRISM TO SQ.PRISM

6.SQ.PRISM TO SQ.PRISM ( SKEW POSITION)7.SQARE PRISM TO CONE ( from top )

8.CYLINDER TO CONE

COMMON SOLUTION STEPSOne solid will be standing on HPOther will penetrate horizontally. Draw three views of standing solid.Name views as per the illustrations.Beginning with side view draw threeViews of penetrating solids also.On it’s S.V. mark number of pointsAnd name those(either letters or nos.)The points which are on standardgenerators or edges of standing solid,( in S.V.) can be marked on respectivegenerators in Fv and Tv. And other points from SV should be brought to Tv first and then projecting upwardTo Fv.Dark and dotted line’s decision shouldbe taken by observing side view from it’s right side as shown by arrow.Accordingly those should be joined by curvature or straight lines.

Note: Incase cone is penetrating solid Side view is not necessary.Similarly in case of penetration from top it is not required.

X Y

1

2

3

4

a”

g” c”

e”

b”

f” d”

h”

4” 1”3” 2”1’ 2’4’ 3’

a’

b ’h’

c’g’

d’f’

a’

CASE 1. CYLINDER STANDING

& CYLINDER PENETRATING

Problem: A cylinder 50mm dia.and 70mm axis is completely penetrated by another of 40 mm dia.and 70 mm axis horizontally Both axes intersect & bisect each other. Draw projections showing curves of intersections.

X Y

a”

d” b”

c”

4” 1”3” 2”1’ 2’4’ 3’

1

2

3

4

a’

d’ b’

c’

a’

c’

d’b’


& SQ.PRISM PENETRATING

Problem: A cylinder 50mm dia.and 70mm axis is completely penetrated by a square prism of 25 mm sides.and 70 mm axis, horizontally. Both axes Intersect & bisect each other. All faces of prism are equally inclined to Hp.Draw projections showing curves of intersections.

X Y


& CONE PENETRATING

Problem: A cylinder of 80 mm diameter and 100 mm axis is completely penetrated by a cone of 80 mm diameter and 120 mm long axis horizontally.Both axes intersect & bisect each other. Draw projections showing curve of intersections.

1

2 8

3 7

4 6

5

7’

6’ 8’

1’ 5’

2’ 4’

3’

X Y

a”

d” b”

c”

a’

c’

a’

d’b’

c’

d’b’

1

2

3

4

1’ 2’4’ 3’ 4” 1”3” 2”

CASE 4. SQ.PRISM STANDING


Problem: A sq.prism 30 mm base sides.and 70mm axis is completely penetrated by another square prism of 25 mm sides.and 70 mm axis, horizontally. Both axes Intersects & bisect each other. All faces of prisms are equally inclined to Vp.Draw projections showing curves of intersections.

X Y

1

2

3

4

4” 1”3” 2”1’ 2’4’ 3’

b

e

a

c

d

f

bbc

de e

aa

f f

CASE 5. CYLINDER STANDING & TRIANGULAR PRISM PENETRATING

Problem: A cylinder 50mm dia.and 70mm axis is completely penetrated by a triangular prism of 45 mm sides.and 70 mm axis, horizontally. One flat face of prism is parallel to Vp and Contains axis of cylinder. Draw projections showing curves of intersections.

X Y

a”

e”

b”

d”

1

2

3

4

1’ 2’4’ 3’ 4” 1”3” 2”

300

c”

f”a’

f’

c’

d’

b’

e’

CASE 6. SQ.PRISM STANDING


(300 SKEW POSITION)

Problem: A sq.prism 30 mm base sides.and 70mm axis is completely penetrated by another square prism of 25 mm sides.and 70 mm axis, horizontally. Both axes Intersect & bisect each other.Two faces of penetrating prism are 300 inclined to Hp.Draw projections showing curves of intersections.

X Y

h

a

b

c

d

e

g

f

1

23

4

5

610

9

8

7

a’ b’h’ c’g’ d’f’ e’

5 mm OFF-SET

1’

2’

5’

4’

3’

6’

CASE 7. CONE STANDING & SQ.PRISM PENETRATING

(BOTH AXES VERTICAL)

Problem: A cone70 mm base diameter and 90 mm axis is completely penetrated by a square prism from top with it’s axis // to cone’s axis and 5 mm away from it.a vertical plane containing both axes is parallel to Vp.Take all faces of sq.prism equally inclined to Vp.Base Side of prism is 0 mm and axis is 100 mm long.Draw projections showing curves of intersections.

CASE 8. CONE STANDING

& CYLINDER PENETRATING

h

a

b

c

d

e

g

f

a’ b’h’ c’g’ d’f’ e’ g” g”h” a”e” b”d” c”

12

3

45

6

7

8

X Y

o”o’

11

33

5 56

7,

8,22

4 4

Problem: A vertical cone, base diameter 75 mm and axis 100 mm long, is completely penetrated by a cylinder of 45 mm diameter. The axis of thecylinder is parallel to Hp and Vp and intersects axis of the cone at a point 28 mm above the base. Draw projections showing curves of intersection.

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Projection of Solids - Complete