MEL 110: GRAPHIC SCIENCE Harish Hirani Associate Professor Block II/354. Dept of Mech. Eng. I.I.T Delhi
2-0-4 Learn by Doing
Mon, Thurs Minor I, 3.0 Minor II, 2.0 Last two weeks no lecture
MEL 110: GRAPHIC SCIENCE r
C
r
R r P
R r P
GRAPHICS: Art or Science of drawing Systematic knowledge-base practice capable of resulting in predictable type of outcome.
GRAPHICS: Art or Science of drawing Systematic knowledge-base practice capable of resulting in predictable type of outcome.
Why to learn drawing when 3-D modeling is easier ? • Bi-directional associativity
Graphic images are more powerful than simple text A fixture, having overall length 150 mm, consists of a rectangular block 75mm high, 44mm long and 100mm wide. The rectangular block has a Vee shaped slot symmetrically through the top surface in a longitudinal direction. It is 38mm each side of the center at the top surface and is 45° to this surface. The bottom of the Vee slot is removed by a rectangular slot 19mm wide with its bottom face 10mm above the top face of the flange. It has a 25mm thick by 100mm wide flange protruding from the 100mm face of the block with the lower surfaces aligned. Conclusion: Technical drawing compared to Written Description, Theoffers free end the flange rounded with a farofbetter ideaisabout the Shape, Size & Appearance of any 50mm radius and at the center ofthat that radius machine/structure, too inisquite a less time. a hole 8mm diameter through the flange with a 20mm diameter counter bore 10mm deep in the top surface of the flange.
Importance of Text !!!!
Lettering
http://web.iitd.ac.in/~hirani/courses2.html
• Height of letter (2.5 to 20mm). • Width of letter • Spacing between letters • Gap between words • Gap between lines. ABC
72 points = 1 inch.. Condensed..Expanded
Sheet Size
210 * 297 297* 420
420* 594
A4 Tracing sheets for Sketching. A2 Sheets for Drawing
594* 841
Thick Lines Thin Lines
841 * 1189
Various Lines • Center • Hidden • Construction • Outline
• Outlines are made thicker than all other lines. • Center line represents the center of object.
Various Lines • Outline, Hidden, Center, Construction, – Dimension, Cutting plane, Phantom, break.
• Center line: – Where center lines cross, the short dashes should intersect symmetrically. – Center lines should not end at object lines.
• Line precedence: Outlines take precedence over all other lines, Hidden lines take precedence over centre lines.
How Do I Start • Learn Pro-E. • Think few simple shapes.
Simple Shapes
Systematic Procedure to Sketch
Systematic way to Sketch • Dimension smallest to largest length.
Two stage extrusion
Two stage extrusion
Primitive Shapes: basic shapes that can be used to make more complex structures. Extrusion Revolve
Prism
Primitive Shapes: basic shapes that can be used to make more complex structures.
Orthographic Projections
Y
X
Object in I quadrant = I angle Object in III quadrant = III angle Object in II or IV quadrant ??
Orthographic Projections
ORTHOGRAPHIC PROJECTIONS: DIFFERENT VIEWS of an OBJECT are PROJECTED on DIFFERENT REFERENCE PLANES OBSERVING PERPENDICULAR to RESPECTIVE REFERENCE PLANE
Reference Planes:
Different Views:
Horizontal/Top Plane (HP / TP) Vertical/Front Plane ( VP /VP ) Side Or Profile Plane ( SP / PP)
Front View (FV) Top View (TV) Side View (SV)
FV is a view projected on VP. TV is a view projected on HP. SV is a view projected on PP.
FV TV SV
HP VP PP
PATTERN OF PLANES & VIEWS (First Angle Method)
3 planes in one plane ???
PROCEDURE :TO MAKE All Plane VISIBLE, A) HP IS ROTATED 900 DOWNWARD B) PP, 900 IN RIGHT SIDE DIRECTION. THIS WAY BOTH PLANES ARE BROUGHT IN THE SAME PLANE CONTAINING VP. ACTUAL PATTERN OF PLANES & VIEWS OF ORTHOGRAPHIC PROJECTIONS DRAWN IN FIRST ANGLE METHOD OF PROJECTIONS
PP
VP
Y
FV
Y
X X
TV HP
HP IS ROTATED DOWNWARD 900 & BROUGHT IN THE PLANE OF VP.
PP IS ROTATED IN RIGHT SIDE 900 & BROUGHT IN THE PLANE OF VP.
LSV
Orthographic Projection • Greek word Æ Orthos (=Straight) + Graphe (=Drawing). • Technical method to represent 3D object in 2D (plane). – Parallel projection • All projection lines are orthogonal to the projection plane.
FOR T.V.
First Angle projection
ORTHOGRAPHIC PROJECTIONS
FRONT VIEW
L.H.SIDE VIEW
x
y
Pictorial Presentation IS GIVEN Once F.V. (principal view) chosen, other views need to be arranged w. r. t. FV.
TOP VIEW
I angle III angle
THIRD ANGLE PROJECTION OBJECT IS ASSUMED TO BE SITUATED IN THIRD QUADRANT ( BELOW HP & BEHIND OF VP. )
PLANES BEING TRANSPERENT AND IN BETWEEN OBSERVER & OBJECT.
TV
X
Y LSV
FV
ACTUAL PATTERN OF PLANES & VIEWS OF THIRD ANGLE PROJECTIONS
FOR T.V.
FIRST ANGLE PROJECTION
FOR T.V.
OBJECT IS ASSUMED TO BE SITUATED IN FIRST QUADRANT.
OBJECT IS IN BETWEEN OBSERVER & PLANE. PP
VP FV
LSV
Y
X TV HP ACTUAL PATTERN OF PLANES & VIEWS IN FIRST ANGLE METHOD OF PROJECTIONS
Summarizing methods of Drawing Orthographic Projections Rotate H.P. & P.P. in V.P.
First Angle Projections Method object placement
Third Angle Projections Method object placement
in 1st Quadrant
in 3rd Quadrant.
( Fv above X-y, Tv below X-y )
( Tv above X-y, Fv below X-y )
SYMBOLIC PRESENTATION OF BOTH METHODS WITH AN OBJECT STANDING ON HP/GROUND ON IT’S BASE.
FV
X TV
TV
Y
X
Y
FV G
L
Most informative view of an object shall be used as the front view.
First angle projection method View in direction above FV, is placed underneath FV. View in direction below FV, is placed above FV. View seen from the right of FV, is placed on the left of FV. View seen from the left of FV, is placed on the right of FV.
Third angle projection method
Selection of Views • Only those views that are necessary for a clear & complete description should be selected. – Simple objects such as cylinder, bushing, etc. require only two views (FV & SV/TV). • Avoid (unnecessary) repetition of detail.
• Choose view which provide desired explanation with minimum number of hidden lines. – Invisible lines are represented with short dashes. Such line always starts with a dash in contact with the object line from which it starts, unless it forms a continuation of a visible line.
Tracing sheet pad, one graph paper, HB/H pencils, eraser.
Books: 1. Fundamentals of Engineering Drawing by Luzadder & Duff. Prentice-Hall of India. 2. Engineering Drawing, N D Bhatt
ORTHOGRAPHIC PROJECTIONS OF POINTS & LINES.
OBJECT
POINT A
LINE AB
IT’S TOP VIEW
a (aT)
a b (aT bT)
IT’S FRONT VIEW
a’ (aF)
a’ b’ (aF bF)
IT’S SIDE VIEW
a” (asv)
a” b” (asv bsv)
31
PROJECTIONS OF A POINT IN FIRST QUADRANT.
POINT A ABOVE HP & INFRONT OF VP
POINT A ABOVE HP & IN VP For Tv
For Tv PICTORIAL PRESENTATION
a’
For Tv
a’
A
A
Y
Y
Y
X
POINT A IN HP & INFRONT OF VP
a’
a
a
X
X
a
A
ORTHOGRAPHIC PRESENTATIONS OF ALL ABOVE CASES.
VP
VP a’
X
VP a’
Y
X
a
Y
a’
X
a HP
Y
a HP
HP
32
PROJECTIONS OF A POINT IN FIRST QUADRANT.
POINT A ABOVE HP & INFRONT OF VP
POINT A ABOVE HP & IN VP For Tv
For Tv PICTORIAL PRESENTATION
aF
POINT A IN HP & INFRONT OF VP
For Tv
A
aF
A
Y
Y
Y
aF aT
X
aT
X
X
A
aT
ORTHOGRAPHIC PRESENTATIONS OF ALL ABOVE CASES.
aF
aF F
F
T
T
F
aT
aF
T
aT HP
aT HP
HP
33
PROJECTIONS OF A POINT IN SECOND QUADRANT.
VP 2nd Quad. A
A
1ST Quad.
a'
Y
a X Y
Observer HP
a X
3rd Quad.
4th Quad.
PROJECTIONS OF A POINT IN THIRD QUADRANT.
VP 2nd Quad.
1ST Quad.
Y
a
HP
a X Y A
Observer
X
A 3rd Quad.
a' 4th Quad.
POINT A IN ND 2 QUADRANT A
POINT A IN QUADRANT
VP a’
VP a’
1ST A
a HP HP
OBSERVER
OBSERVER
a
a HP
HP
A POINT A IN RD QUADRANT 3
OBSERVER
a’
a a’
VP
OBSERVER
A
VP
Projections of points in four quadrants
POINT A IN 4TH QUADRANT 36
PROJECTIONS (FV & TV) of straight lines. SIMPLE CASES 1. A vertical line ( LINE PERPENDICULAR TO HP & // TO VP) 2. Line parallel to both HP & VP. 3. Line inclined to HP & PARALLEL TO VP. 4. Line inclined to VP & PARALLEL TO HP. 5. Line inclined to both HP & VP (oblique line).
37
For Tv
(Pictorial Presentation)
Note: Fv is a vertical line Showing True Length & Tv is a point.
a’ A
1.
A Line perpendicular to Hp & // to Vp
FV b’
Y
V.P.
a’ Fv b’
X
Y
B TV a b X
Orthographic Pattern
(Pictorial Presentation)
For Tv
2. b’
A Line // to Hp & // to Vp
Tv a b
B
H.P. V.P.
Note: Fv & Tv both are // to xy & both show T. L.
a’
Fv
b’
a’ A
X
Y
b
Y a Tv
X
b
a
H.P.
38
3.
b’
A Line inclined to Hp and parallel to Vp
V.P.
Fv inclined to xy Tv parallel to xy.
b’
B
θ
a’
θ
Y
a’
X
Y
θ
(Pictorial presentation)
A
a
b
T.V.
b
X a
H.P. Orthographic Projections
Tv inclined to xy Fv parallel to xy.
4.
A Line inclined to Vp and parallel to Hp (Pictorial
V.P. a’
b’
Fv
b’
a’ A
Ø
B
X
Y a
presentation) Ø
a
Ø
Tv
b
H.P.
b 39
For Tv
For Tv 5.
b’
A Line inclined to both Hp and Vp
b’
(Pictorial presentation) B
B α
α
Y
On removal of object i.e. Line AB Fv as a image on Vp. Tv as a image on Hp,
a’ A X
β
a
a’ A X
T.V.
Y
b
β
a
T.V.
b
V.P. b’ FV a’
α
X
Oblique lines.
Y
a
β TV
H.P.
b
Note These Facts:Both Fv & Tv are inclined to xy. (No view is parallel to xy) Both Fv & Tv are reduced lengths. (No view shows True Length) 40
PROJECTION OF RECTANGLE SURFACE PARALLEL TO HP PICTORIAL PRESENTATION
ORTHOGRAPHIC TV-True Shape FV- Line // to xy VP
HP
SURFACE INCLINED TO HP PICTORIAL PRESENTATION
ORTHOGRAPHIC FV- Inclined to XY TV- Reduced Shape
Oblique plane ONE SMALL SIDE INCLINED TO VP PICTORIAL PRESENTATION
ORTHOGRAPHIC FV- Apparent Shape TV-Previous Shape VP
VP
d1’ a1’
a’ b’
d’ c’
a
d
a1
d1
b
c
b1
c1
HP
HP
b1’
c1 ’
FOR T.V.
ORTHOGRAPHIC PROJECTIONS
FRONT VIEW
L.H.SIDE VIEW
F T
TOP VIEW
PICTORIAL PRESENTATION IS GIVEN DRAW THREE VIEWS OF THIS OBJECT BY FIRST ANGLE PROJECTION METHOD
Mistakes ??
FOR T.V.
ORTHOGRAPHIC PROJECTIONS
FRONT VIEW
F T
TOP VIEW
PICTORIAL PRESENTATION IS GIVEN DRAW THREE VIEWS OF THIS OBJECT BY FIRST ANGLE PROJECTION METHOD
L.H.SIDE VIEW
FOR T.V.
ORTHOGRAPHIC PROJECTIONS
FRONT VIEW
Y
X
TOP VIEW
PICTORIAL PRESENTATION IS GIVEN DRAW THREE VIEWS OF THIS OBJECT BY FIRST ANGLE PROJECTION METHOD
L.H.SIDE VIEW
FRONT VIEW
F T
TOP VIEW
L.H.SIDE VIEW
FRONT VIEW
F T
TOP VIEW
L.H.SIDE VIEW
FOR T.V. ORTHOGRAPHIC PROJECTIONS
FRONT VIEW
F T
TOP VIEW
PICTORIAL PRESENTATION IS GIVEN DRAW THREE VIEWS OF THIS OBJECT BY FIRST ANGLE PROJECTION METHOD
L.H.SIDE VIEW
PICTORIAL PRESENTATION IS GIVEN DRAW THREE VIEWS OF THIS OBJECT BY FIRST ANGLE PROJECTION METHOD
FRONT VIEW
X
L.H.SIDE VIEW
Y
TOP VIEW
Block View
All orthographic views must fit on the same sheet.
Space for: FV: 90, 50 TV: 90, 40 Space between FV & TV SV: 40, 50 Space between FV & TV (90+10+40) * (50+10+40)
Y
x
Summarizing previous lectures • Block view • Fold line • Projection Æ Front, Top and side views
Dimensioning • Lines, numerals, symbols, notes: – Dimension line: Thin continuous line. Terminated by arrowheads. – Extension line: Thin continuous line. ⊥ to feature – Arrowhead: Closed/Open. Length = 3* Width. – Note: Specific info about feature. – Leader: Pointer connecting feature & note.
Dimensioning Symbols • • • • • •
φ : Diameter Sφ : Spherical diameter : Square R : Radius SR : Spherical radius ∩ : Arc length
Dimensioning of Chamfers & Multi-features
Pitch circle diameter
Dimensioning by Coordinates (Tabulation)
13.5 15.5 13.5 11.0 26.0
3 mm?
All dimensions in inches
Procedure:
¾ break part down into a series of geometric features (hole, projection, etc.) ¾ apply dimensions to size each of the features (Functional dimensions), ¾ apply dimensions to control the location of the features (Non-functional dimensions).
Common mistakes
Dimensions 25, 40, and φ12 are functional dimensions. Dimensions 20 and 12.5 are non-functional dimensions.
Common mistakes
Dimension lines should not end at object lines
Common mistakes
Each feature shall be dimensioned only once on a drawing. Each drawing shall use the same unit (i.e. mm) Centerline may be used in place of extension line.
Common mistakes
Ex. Of NOTE
Common mistakes Use φ for dia. Leaders × horizontal or vertical.
Placing dimensions • Aligned system • Unidirectional system
All dimensions in Inches
Use metric system.
Aligned
Dimension can be read from bottom edge/ right hand edge of drawing
Unidirectional
All dimensions can be read from bottom edge of drawing.
Scales
Scale shall be large enough to permit easy and clear interpretation of the information .
• Ratio of the linear dimension of an element of an object as represented in the drawing to the real linear dimension of the same element of the object itself. – Full size: 1:1 – Enlargement scale: 50:1; 20:1; 10:1; 5:1; 2:1. – Reduction scale: 1:2; 1:5; 1:10; 1:20; 1:50.
X: 1
1: X
FV 30
10
30
SV
30
10 30
x
PICTORIAL PRESENTATION IS GIVEN DRAW THREE VIEWS OF THIS OBJECT BY FIRST ANGLE PROJECTION METHOD
y
TV
ALL VIEWS IDENTICAL!!!
35
FV
35 10
x
20
10
30
10 40 70
TV
PICTORIAL PRESENTATION IS GIVEN DRAW FV AND TV OF THIS OBJECT BY FIRST ANGLE PROJECTION METHOD
Mistakes !!!!!
y
PICTORIAL PRESENTATION IS GIVEN DRAW FV AND TV OF THIS OBJECT BY FIRST ANGLE PROJECTION METHOD
ORTHOGRAPHIC PROJECTIONS
30
FV
R 10
50 35
30
R 15 10 X 10
10
35
50
R 30
10
R 10
TV
R 30 R 15 TOP VIEW
Y
LABORATORY 4: Draw Isometric Views
Q1:- of a pentagonal pyramid having a base with a 30 mm side and height 50 mm long, when its axis is vertical, and when the axis is horizontal. Q2:- A square pyramid rests centrally over a cylindrical block, which is resting centrally on top of a Square block (fig 1). Q3:- of solids shown in orthographic projections (fig 2,3,4,5 and 6).
2-D versus 3-D drawings • 2-D: A concept of displaying realworld objects on a flat surface showing only two dimensions (height and width; width and depth; height and depth). This system uses only the X and Y axes.
• 3-D: A way of displaying real-world object in a more natural way by adding depth to the height and width. This system uses the X Y and Z axes. – Isometric projections help to understand the essential features.
Axonometric projection Difference?
Plane Possibility of a number of axonometric
α
Axonometric Projection
β
• Dimetric: Angles between two of axes are same. Two scale factors. • Trimetric: Three scale factors. • Isometric: ISO MEANS SAME, SIMILAR OR EQUAL. X, Y, Z are projected on three dimensional axes maintained at equal inclinations with each other (120°). Size is reduced. Single scale factor.
γ
Isometric Planes
Grid Sheet
Isometric Scale a’
b’ d’
c’
0.707 Scale = = 0.816 0.866
h’ e’
f’
cos 45 Scale = cos 30
g’
d h
a
g c
e
Foreshortening is ignored ÆIsometric drawing. Æ Otherwise projection.
o
Angle cbp > angle obp Length bc > bo
f b
p
Importance of Isometric Drawing • Understand overall shape, size & appearance of an object prior to it’s production. Vertical + 30° to HP - 30° to HP
Isometric drawing combined with orthographic projections provide complete Description.
SOME IMPORTANT TERMS: ISOMETRIC AXES and LINES:
Three lines AL, AD and AH, meeting at point A and making 1200 angles with each other are termed Isometric Axes. Representation of three planes
A
H
Lines parallel to isometric axes are called Isometric Lines. Isometric graph
Lines for hidden edges are generally not shown.
Lines for hidden edges are generally not shown
FRONT VIEW of FIGURE requires H & L AXES. A
Vertical line will be drawn vertical, while horizontal line will be drawn inclined at 30° to horizontal. TOP VIEW of FIGURE require D & L.
H Isometric view if the Shape is F.V. or T.V.
SHAPE H
D
RECTANGLE A
D
D
A C
C A
B
C
B
B
Shapes containing Inclined lines cannot be drawn parallel to any isometric axes. Angle do not increase or decrease in any fixed proportion. Enclose in a rectangle… First draw isom. of that rectangle and then inscribe that shape as it is.
Inclined Lines ???? Isometric view if the Shape is F.V. or T.V.
SHAPE
B H TRIANGLE 1
B
3 B
3
1 A
3 2
A
A 1 2
2 4 H
PENTAGON E
1
4 D
A
E
1
D
4 D
E A
1 3 C
2
B
C
3
2
B
3 C
A B
2
Drawing circles ?? GIVEN: A circle in FV REQUIRED: Isometric view. FIRST ENCLOSE IT IN A SQUARE. USE H & L AXES.
Four-centre Method: Ends of Small diagonal provides two Centers. Locate two centers on longer Diagonal Easier for free hand sketching.
Ellipse is made of four arcs.
DRAW ISOMETRIC VIEW of the figure shown considering it first as FV and then TV. 25 R
50 MM
IF FRONT VIEW 100 MM
IF TOP VIEW
Summary on ISOMETRIC DRAWING OF PLANE FIGURES
SHAPE HEXAGON
CIRCLE
SEMI CIRCLE
IF F.V.
IF T.V.
Making Isometric Drawing of Rectangular Object
H
F.V. L
D
T.V. Concept of block views
Nonisometric Lines • Inclined lines (not parallel to isometric axes). – Distorted (cannot be measured directly) line. – Position & Projected length must be established by locating end points.
C
D TV
A FV
B
C A B
ISOMETRIC VIEW OF
HEXAGONAL PRISM STANDING ON H.P.
For hexagonal, angle is 120°
Edge a Length (0.5+1+0.5) a Height (0.866 + 0.866) a
CYLINDER, when Axis is Vertical
CYLINDER, When Axis is Horizontal
.
ISOMETRIC Drawing 60
FV
X
40
Draw isometric lines, then non-isometric
Y
20
TV
ISOMETRIC Drawing
60
FV
X
Y φ20
φ40
TV
10
First angle orthographic projections O
ISOMETRIC Drawing FV
30 10 30
φ 30
50
+
50
TV
F.V. & T.V. of an object are given. Draw it’s isometric view.
10
20 40
FV
40 X
Y
TV φ 50
φ 30
F T
O
F.V., T.V. and S.V.of an object are given. Draw it’s isometric view. ALL VIEWS IDENTICAL FV
SV
y
x 10
40
40 60
TV
60
F.V. & T.V. of an object are given. Draw it’s isometric view.
50
F T 20
25
25
20
F.V. & T.V. of an object are given. Draw it’s isometric view. Block of 60*10*30
40
20
30
F T
10
O
10
30 10
O Block of 80*40*10
30 80
F.V. & T.V. of an object are given. Draw it’s isometric view.
40
10
F T
φ 30 25 25
10
50
O
80
Block of 80*50*10 Block of 25*25*40 Four center method to draw ellipse
F.V. and S.V.of an object are given in I angle projection . Draw it’s isometric view.
SQ 30 10
40
20
50
20
10
O
30
F.V. O
60
S.V.
F.V. & T.V. of an object are given. Draw it’s isometric view.
40
FV
O
X
10
Y
100 10
30
10
10 25 25 30 R
O
R 10
TV
Cuboid of 100*50*10 Draw parallel lines at 30 mm Cuboid of 50*25*40
15
15
First angle projection O
F.V. and S.V.of an object are given in I angle projection. Draw it’s isometric view.
Mistake ??
F.V. Sq 20 20
O
30
40
40
20
10
O 100
30 50 60
40
40
ORTHOGRAPHIC PROJECTIONS 10
10
25
25
Y
X
O
15
FV
50
LSV
10
Oblique projection/view It is a method of drawing a 3-D view of an object (similar to isometric view)
Drawing an oblique projection y This face will have features with true shape
Cavalier projection Cabinet projection z
Full size, Half length.
Receding line α x
Receding angle
30, 45, 60.
α taken as 45o Oblique view of a cuboid
Draw essential contours (circles, curves etc.) on this face
Cavalier & Cabinet projections
Cavalier & Cabinet projections
R 25
Oblique view Features on the front face can be drawn with the actual dimensions and shape Receding axis is 45o to the horizontal
This image cannot currently be display ed.
Receding axis z
45o x Third Angle projection
Oblique Projection 40
T F
22 φ 10
Title Block
Within the drawing space. In the right hand corner.
Mandatory to make borders and the title block in Laboratory sheets 5,6, and 8-13. Name & entry number must be in ink by following standard lettering practice (One mark will be deducted from the total marks in case it is not made.)
Distance between borders and the edges of the sheet: 10 mm Size of title block: 170mm×60mm Object lines by H Guidelines in 2 H.
FV
X TV
NAME Y
ENTRY NO.
G.NO
LAB NO.
Sign with date
NAME ENTRY NO.
G.NO
LAB NO.
Sign with date
Mini-Drafter
Solids of Revolution The cylinder, cone and sphere are called ‘Solids of Revolution”. • Cylinder is obtained by rotation of a rectangle about axis. • Cone is obtained by rotation of a right angled triangle about axis • Sphere is obtained by rotation of a semicircle about axis.
Dimensional parameters of different solids. Square Prism
Corner of base
Cylinder
Slant Edge Base
Edge of Base
Base Edge of Base
Cone Apex
Apex
Top Rectangular Face Longer Edge
Square Pyramid
Triangular Base Face
Corner of base
Sections of solids( top & base not parallel)
Base
Generators Imaginary lines generating curved surface of cylinder & cone.
Frustum of cone & pyramids. ( top & base parallel to each other)
Problem. A square pyramid, 40 mm base sides and axis
60 mm long, has a triangular face on the ground and the plane containing the axis makes an angle of 450 with the VP. Draw its projections. Take apex nearer to VP.
1st. Angle oF a’1
F aFbF
cFdF
T
dT
aT
a1
o’1
a1 o1
o bT
c’1
d’1 d1
b’1
cT
c1
b1
(APEX NEARER TO V.P).
115
STEPS TO SOLVE PROBLEMS Related to Projection of SOLIDS STEP 1: Assume solid STANDING on the PLANE with which it is making INCLINATION. ( If INCLINED to HP, ASSUME it standing ON HP) ( If INCLINED to VP, ASSUME it standing on VP) STEP 2: CONSIDERING SOLID’S INCLINATION ( AXIS POSITION ), draw it’s FV & TV. STEP 3: IN LAST STEP, consider remaining inclination, DRAW IT’S FINAL FV & TV. GENERAL PATTERN ( THREE STEPS ) OF SOLUTION:
AXIS AXIS VERTICAL INCLINED HP
AXIS INCLINED VP
AXIS INCLINED HP
AXIS AXIS VERTICAL INCLINED HP
AXIS INCLINED VP
AXIS
er
TO VP
AXIS INCLINED VP
AXIS INCLINED HP
AXIS
er
TO VP
AXIS INCLINED VP
Hints • If axis of given solid is inclined to HP (VP) 1. Assume axis is perpendicular to HP (VP) •
Draw top view(FV) and then corresponding front view (TV) .
2. Change position of front view (TV)to the given inclination. • •
Draw corresponding new top view (FV) Change position of new top view (FV) if inclination with other principal plane is given.
.
Problem: A cone 40 mm diameter and 50 mm axis is resting on one generator on Hp which makes 300 inclination with Vp. Draw it’s projections. More number of generators Æ Better approximation. Replace a,b,.. With aT, bT…
o’
h’1 Drawing ellipse?
c’ g’
o’
f’ d’ e’ g1
g
T
h
f
f1
h1
f’1 c’1 d’ 1 e’1
o1
g1
o1
a
o
a1
e e1
a1
o1
b1
e1 b
d c
b1
d1 c1
30
h1
f1
Angle
b’1
g’1
F a’ h’b’
1st.
a’1
d1
c1
118
How to draw an Ellipse • Major and minor axes. – Arcs of circle method – Concentric circles method
Problem. Major axis AB & minor axis CD are 100 & 70mm long respectively. Draw ellipse. STEPS: 1.Draw two axes at 90°. Name ends & intersecting point. 2.Taking AO distance, i.e. half major axis, from C, mark F1 & F2 on AB (focus 1 and 2). 3.On line F1- O taking any distance, mark points 1,2,3, & 4 4.Taking F1 center, with distance A1 draw an arc above AB and taking F2 center, with B-1 distance cut this A arc. Name the point p1 5.Repeat this step with same centers but taking now A-2 & B-2 distances for drawing arcs. Name the point p2 6.Similarly get all other P points. With same steps positions of P can be located below AB. 7. Join all points by smooth curve to get an ellipse.
ARCS OF CIRCLE METHOD
As per the definition Ellipse is locus of point P moving in a plane such that the SUM of it’s distances from two fixed points (F1 & F2) remains constant and equals to the length of major axis AB.(Note A .1+ B .1=A . 2 + B. 2 = AB) p4
p3
C
p2 p1
F1
1
2
3
4
O
D
B F2
CONCENTRIC CIRCLE METHOD Problem :- Major axis 100 mm and minor axis 70 mm long. 3 2
4
Steps:
1. Draw two axes as ⊥ bisectors of each other. 2. Taking their intersecting point as a center, draw two concentric circles of 70 mm and 100 mm diameters. 3. Divide both circles in 12 equal parts. 4. From all points of outer circle draw vertical lines downwards and upwards respectively. 5.From all points of inner circle draw horizontal lines to intersect those vertical lines. 6. Mark all intersecting points. 7. Join all these points to get the required ellipse.
C 1 2
3
5 4
1
5
A
B 10 10
6 9 8 D
9
7
6
7 8
To divide a circle into 12 equal parts Draw the two diameters 1–7 and 4–10, perpendicular to each other. With 1 as a centre and radius = R (= radius of the circle), cut two arcs at 3 and 11 on the circle. Similarly, with 4, 7 and 10 as the centres and the same radius, cut arcs on the circle respectively at 2 and 6, 5 and 9, and 8 and 12. The points 1, 2, 3, etc., give 12 equal divisions of the circle.
PROBLEM: Line AB is 75 mm long and it is 300 & 400 Inclined to HP & VP respectively. End A is 12mm above Hp and 10 mm in front of VP. Draw projections. Line is in 1st quadrant.
bF
b’1
TL
θ F aF T aT
2 Front View LFV
1
Ø
TL Top View
bT
b1
PROBLEM: Line AB 75mm long makes 450 inclination with VP while it’s FV makes 550. End A is 10 mm above HP and 15 mm in front of VP. If line is in 1st quadrant draw it’s projections and find it’s inclination with HP. b’1 LOCUS OF b1’
bF
550
F T
aF
Front View
LFV
aT
1
Top View LOCUS OF b
bT
b1
Problem: A cylinder 40 mm diameter and 50 mm axis is resting on one point of a base circle on Vp while it’s axis makes 450 with Vp and Fv of the axis makes 350 with Hp. Draw 1st angle projections. 4’d’ 3’ c’ a’
1’ a’
F
d’
c’
2’ b’ a
bd
b’ c
4’
3’
1’
2’
350
450
c1
T
d1
b1
a1
3 4
1
24
3 1
2
Geometry with straight lines • • • • • •
Triangle Æ 180 Æ 60° Rectangle/Square Æ 360 Æ 90° Pentagon Æ 540 Æ 108° Hexagon Æ 720 Æ 120° Heptagon Æ 900 Æ 128.57° Octagon Æ 1080 Æ 135° α2 α1
α3
α1 + α 2 + α 3 = 180
α = 135o
Can we draw geometries without measuring angles ? With any point O as centre and radius = OA, draw a circle. B
From A draw a cord of length OA, which intersects circle at B. Length OB will be ????
C
D
Equilateral triangle???
O
Angle CAB = 120°
E
Method to make a hexagonal of side = AB. A
B
E is middle point of line DB.
How to locate point 5: Bisecting Line 4-6
8 7 6
P
5 4 4
E 5
6
A
B
Line 128
Problem: A cube of 50 mm long edges is so placed on Vp on one corner that a body diagonal is parallel to Vp and perpendicular to Hp. Draw it’s 3rd angle projections. Replace a,b,.. With aT, bT…
11 21
1
2,4
41
3
31
a
a1
Ta F
b1
b,d
b, d
c
d
d‘,4
a
' 1
c‘,3
a‘,1
' 1
' 1
1
c
' 1
' 1
c
b1'
21'
d1
a1'
4
' 1
3
b1' 21'
b‘,2
c1
d1'
11' c1'
41' 31'
Problem: A square pyramid 30 mm base side and 50 mm long axis is resting on it’s apex on Hp, such that it’s one slant edge is vertical and a triangular face through it is perpendicular to Vp. Draw it’s 1st angle projections.
a’
b’d’
F T
d
a
bo
a’1 d’1
c’
o’1
o’
b
d1 c ao1 1
c1 b1
b’1 c’1 Hidden lines in Projections of solid !
Summary of Topics
Hidden Lines
Treatment of Tangent Surfaces
FREELY SUSPENDED SOLIDS: Positions of CG, on axis, from base, for different solids are shown below.
CG
H/2
H CG
H/4 GROUP A SOLIDS ( Cylinder & Prisms)
GROUP B SOLIDS ( Cone & Pyramids)
Problem: A pentagonal pyramid 30 mm base sides & 60 mm long axis, is freely suspended from one corner of base so that a plane containing it’s axis remains parallel to Vp. Draw it’s orthographic projections. LINE
o’
d’g’ VERTICAL d’ c’e’
FOR SIDE VIEW
g’
H g’
IMPORTANT: When a solid is freely suspended from a corner, then line joining point of contact & C.G. remains vertical. ( Here axis shows inclination with Hp.) So in all such cases, assume solid standing on Hp initially.)
H/4
o’ c’ e’
a’ b’
a’b’ F
d’ e1
e
T a1
a do 1
o
d1
b
b1 c
c1
O
F.V. and S.V.of an object are given. Draw it’s isometric view.
30
10
20
20
10 15
O
15
15 15
X
O
Y 50
F.V.
30
LEFT S.V.
F.V., T.V. and S.V.of an object are given. Draw it’s isometric view.
ORTHOGRAPHIC PROJECTIONS
F. V.
L.H.S. 20 20
x
20
O
y
50
20 30
20
T. V.
20
20
O
Dimensioning Oblique Drawing • Dimension should be made to read from the bottom and right hand side of the sheet.
• As far as possible, the dimensions should be placed in the front face. • As far as possible, the dimensions should be placed outside the outlines of the.
50
• dimensions, Dimension lines, extension lines and arrowheads must lie in the same oblique plane to which they apply.
50
