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ENGINEERING
GRAPHICSCourse No. 1
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BIBLIOGRAFIE:
1. Petrescu L., s.a.GEOMETRIE DESCRIPTIVA SIGRFICINGINEREASC, Ed. BREN, Bucuresti, 1997.2. Petrescu L.ENGINEERING GRAPHICS,
Ed. BREN, Bucuresti, 2003.
3. Frederick E. Giesecke, Alva Mitchell s.a.TECHNICAL DRAWING, Mecmillan Publishing
Company, New York, 1986.4. Herbert W. YankeeENGINEERING GRAPHICS,PWS Engineering Publishers, Boston, 1985.
PETRESCU LIGIA confereniar doctor inginerDepartament
GRAFICINGINEREASC I DESIGN [email protected]
0742181465
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The engineering thinkingandcreationcombines spatial
imagination, spatial situations
analysis and synthesis, with theengineering art and with an own
language of communication.
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The representationof a real or an
imaginary object, of an idea thatexist in the mind of the engineer
or designer before becoming
reality, executed either on aclassical support (paper),or on amodern one (computers screen),
is realized in a graphic way.
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Although different languages are
spoken throughout the World, auniversal language existed from
ancient times, the graphiclanguage. This natural,elementary mean of idea
communication is limitlessboth inspace and time.
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The engineering graphicsis more
than a language, it is a wholeconception of space and of the
spatial object representation; it is
the solutions source of the spatialproblems and situations. Thats
why the eng ineer ing graphicsis
ascience.
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The components of this science
are:
Descriptive geometry
Technical drawing Computer graphics(computer
aided drawing).
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1.2.1 SHEETS (FORMATS) SR ISO 5457-94 (STAS 1-84). The support of the drawings isrectangular The sheet can be set vertically (Fig. 1.1-a), or
horizontally, meaning on the long side (Fig. 1.1-b), theirindexing being done as in the presented examples:
A(ab) A(ba)a). b).
Fig. 1.1
a
b
a
b
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Preferred sheets Exceptional sheets
A0 841 1189 A02 1189 1682 A1 594 841 A13 841 1793 A2 420 594 A23 594 1261 A3 297 420 A24 594 1682 A4 210 297 A25 594 2102
Special sheets A35 420 1482A36 420 1783
A33 420 891 A37 420 2080 A34 420 1189 A46 297 1261 A43 297 630 A47 297 1471
A44 297 841 A48 297 1682 A45 297 1051 A49 297 1892
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Fig. 1.2
20
10
Frame (border
line)
Title block
A(ba)
Zone for
binding in a
file
29
7
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1.2.2 LINES STAS 103-84. Taking intoaccount the destination, there are two
thicknesses of lines that can be used: Thick or heavy
(thickness=b);
thin or fine (b/3or b/2).The line thicknessdepends on the dimensions and
complexity of the parts to be drawn, as well on thepurpose and size of the drawing. For b there aregiven the values: 0,18; 0,25; 0,35; 0,5; 0,7;1; 1,4; 2; 2,5; 3,5; 5.
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The following types of lines are used as they
are needed:
continuous line
wavy line
zigzag line
dashed line
dash dot line
heavy open dash dot line two dots dash line
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1.2.3 LETTERING SR ISO 3098/1-93 (STAS 186-86). The character of lines and the lettering gives
the drawing what is known as technique,a phaseof drafting which is too often neglected. The heightof the capitals or of the figures (numbers), defines
the size of the lettering by h: 2,5; 3,5; 5; 7; 10;
14; 20. It is permitted the use like slant the verticalwritingor the inclined writingat 75 degrees, and
like shape, a normal one(10/10xhthe height ofcapitals, and the thickness of the writing line
h/10), or a longed one(14/14x
h, the thickness ofthe writing line h/14).
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1.2.4 TITLE BLOCK (INDICATOR) SR ISO 7200-94(STAS 282-87).
the identification zone : - the registration number oridentification of the
drawing;
- the name of the drawing;- the name of the legal owner
of the drawing.
the zone of supplementary information: - indicative;
- technical;- administrative.
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TITLE BLOCK
Name Sign.
(Material)
(Drawing No.)
(Student
No.)
Student
Professor(Mass)
(Fac. YearGroup)121 E
(Scale)
1:1 (Drawing Name)(Date) 08.10.13
170
20 25 15 25 15
20
10
5
5
A(b x a)
Fig. 1.3
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1.3 GENERAL NOTIONS ABOUTGRAPHIC REPRESENTATIONS
In the technical field the drawing is used asmeans of communication.
The shapeis best described through
projection, a procedure of getting an image byrays of observationor of sight. The direction ofthe rays can be parallel(when the observer islocated at an infinite distance from the object),
or conic(if the distance is a finite one), leadingto getparallel projections, orcentral(perspective) projections(Fig. 1.4 - a and b).
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parallel projection central (perspective)
projection
a). b).
Fig. 1.4
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SYSTEMS OF PROJECTIONS
A system of projection is compound by
four elements:
the observerseye;
the rays formed by lines of sight;the object to be projected;the plane of projection.
According to the space order of these four elements there
are two principal systems of projections:
European system (fig. 1.5)American system (fig. 1.6).
the observerseye
(at the )
the object
opaque
projection
plane
rays
Fig. 1.5
the observerseye(at the )
the object
transparent
projection
plane
rays
Fig. 1.6
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The graphic representations used in technique,impose a very good knowledgeof elementarygeometry (plane and spatial),of the descriptivegeometry, and of the technical drawing.
Descriptive Geometryestablishes laws which areto enable the representation of spatial objects andof spatial situations. These laws (rules) are coming
directly from the elementary geometry. Technical drawingrelies on orthogonal(orthographic) projection, which supplies the bestconditions for describing shape of an object, and itis best fitted to make dimensioning, which is the
second function of a technical drawing.
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1.3.2 COMPUTER GRAPHICS.Charles Babbage, anEnglish mathematician, developed the idea of a mechanicaldigital computer in the 1830s, and many of the principles
used in Babbages design are the basis of todayscomputers. The computer appears to be a mysteriousmachine, but it is nothing more than a toolthat justhappens to be a highly sophisticated electronic device. It iscapable of data storage, basic logical functions, and
mathematical calculations. Computer applications haveexpanded human capabilities to such an extent thatvirtually every type of business and industry utilizes acomputer, directly or indirectly.
The first demonstration with a computer, as a tool of
drawing and design, was made at the Institute ofTechnology of Massachusetts, in 1963, by Dr. Eng. IvanSutherland, with his system called Sketchpad.
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The CAD(Computer Aided Design or Drawing)techniques, using specialized programs led to the
increase of the qualityof realism contained in thedrawing realized by means of computer.
The computer is able to do many things, veryquickly, but it is still an electronic equipment,
without brains, at least for the moment. It cannotthink and cannot do anything more or anything less
than what it was told to do. A CAD system is notcreative, but it can help a lot the user to become
more productive, earn time. The creator is theman with his so-called limit of his incompetence.
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0x
b.
c.
x
0
[V]
[H]
[V]
[H]D ID II
D IVD IIID I
D II
D III
D IV
A
abc
B
C
[P]
a.
Fig. 2.1
THE SYSTEM OF PROJECTION
DIHEDRALS
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TRIHEDRALS
x
z
y
[V]
[H]
[L]
0
T1
T2
T3
T4
T5
T6
T8
[H] [V]= - abscises axis[H] [L]= - depth axis[V] [L]= - quotas axis;
Fig. 2.2
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x
z
y
[V]
[H]
[L]
0
A
a
xa
za
a
a
ya
T1
T2
T3
T4
T5
T6
T8
Fig. 2.4
abscisaxxAa
depthyyAa
quotazzAa
a
a
a
0"
0'
0
a horizontal projection
a - verticalprojection
a- lateral projection
T1 T2 T3 T4 T5 T6 T7 T8
x + + + + - - - -
y + - - + + - - +
z + + - - + + - -
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x
z
y
[V]
[H]
[L]
0
a
xa
za
a
a
y1a
ya
y1
ais defined by the coordinates pear (x,y);a- is defined by the coordinates pear(x,z);a- is defined by the coordinates pear(y1,z);
Fig. 2.5
EPURA
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za1
xa1
y1a1
a1a1
a1ya1
z
x 0
y1
y
a2
a2ya2
y1a2
za2
xa2
a2
z
x 0
y1
y
a. - A1(20, 40, 30) b. - A2(20, -40, 30)
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c.A3(20, - 40, -30)
xa4
y1a4
a4ya4
z
x 0
y1
y
za4a4 a4
d.A4(20, 40, -30)
a3
a3ya3
za3a3
xa3
z
x 0
y1
y
y1a3
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xa5
a5
a5
za5
y1a5
a5
ya5
z
x 0
y1
y
e.A5(-20, 40, 30)
ya6
a6za6
xa6
a6
a6
y1a6
z
x 0
y
y
f.A6(-20, - 40, 30)
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g.A7(-20, - 40, -30)
Y
0
z
za7
xa7
y1a7
a7a7
a7ya7
y1
x
h.A8(-20, 40, -30)
Fig. 2.6
a8za8 a8
y1a8
ya8
z
x 0
y1
y
a8
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x
z
y
[V]
[H]
[L]
0=k=m=n
H=h
K=k=k
v
M=m=m
l
L=l
h
v
N=n=n
V=v
l
h
Fig. 2.7
PARTICULAR POSITION OF A POINT
H(x , y, 0)
V(x, 0, z)
L (0, y, z)
K (x, 0, 0)
M(0, y, 0)
N(0, 0, z)
H [H]
V [V]L [L]
K[H] [V]M[H] [L]N[V] [L]
Gi h i A1(20 40 30) f A1 d A2
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Given the point A1(20; -40; 30), represent epuraof A1and A2, its symmetrical to the origin. Towhat trihedral these points belong? Solution:the coordinates of the point A2are obtained by
changing the sign of the point A1 all coordinates A2(-20; 40; -30). A1T2,and A2T8 (Fig.2.8)
ya1
za1
xa1y1a1
a1a1
a1
xa2
za2
ya2
y1a2
a2
a2a2
z
x 0
y1
y
Fig. 2.8
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3 STRAIGHT LINE IN DESCRIPTIVE GEOMETRY
y
x
z
[V]
[H]
[L]
0
H=h h
h v
d
D
d
V=v
L=l
v
l
d
l
Fig. 3.1
);;;0(;][
);;0;(;][
)0;;(;][
zyLLLD
zxVVVD
yxHHHD
32
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3.1 LINE TRACES.POINT LOCATED ON A STRAIGHT LINE.
;"d"m;'d'm
;dm
DM
y
x
z
[V]
[H]
[L]
0
m
xm
zm
m
m
ym1
ym
y1
L=l
V=v
l
v
l
vh
h
H=h
dd
d
y=0
x=0
x=0
z=0
y=0
z=0
Fig. 3.2
);;;0(;][
);;0;(;][
)0;;(;][
zyLLLD
zxVVVD
yxHHHD
33
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3.2 PARTICULAR POSITIONS OF A STRAIGHT LINE
They are two types of particular positions for a line:
Straight line parallel to a plane of projections;
Straight line parallel to two planes of projections,
that means perpendicular to the third.
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STRAIGHT LINE PARALLEL TO THE HORIZONTAL PLANE [H],
is named horizontal lineor level line and
it has all its points to the same distance from the plane [H]:
;y0||"n
;x0||'n
1
]H[||)"n;'n;n(N z = const.
Fig. 3.3
z
n v a bv la bl n
x v 0 y1
a
bl
n
y
sizetrue
sizetrue
yn
xn
ABab
;0||"
;0||'
1
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1. Given the point A(40; 30; 50),change the abscissa, depth
and quota of A, to make it belong to every eight trihedrals.
Represent these B, C, D, E, F, G, andI points in epura.
2. Given the point A(50; 20; -30)represent it in epura
together with the pointsBsymmetrical of Ato [H];C- symmetrical of Ato [V];
D- symmetrical of Ato [L];
E-symmetrical of Ato 0x;
F- symmetrical of Ato 0y;
G- symmetrical of Ato 0z.
HOME WORK HW- 01: POINTS PROJECTIONS
1 2
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LAB L- 01: POINTS AND STRAIGHT LINES
1. Represent in epura the points: H(40; 30; 0), V(20; 0; 40), L(0; 40;
25), K(30; 0; 0), M(0; 45; 0), N(0; 0; 50), T(0; 0; 0). Where belongs
every point ?2. They are given the points: A(70; 50; 35)and B(45; 15; 20).Obtain the
traces H and Vof the line define by the points Aand B.
3. They are given the points: A(10; 25; 40), B(35; 5; 10)and M(70; 50;
40).Construct the rhombus [ABCD],if one of its diagonals is located
on the line defined by the points Aand M.
1 3
2
POINTS S G S
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LAB L- 01: POINTS AND STRAIGHT LINESOnly for mechanics.
4. Construct the level line of z = 30, which intersects the straight lines defined
by the pair of points A(125; -45; 45),B(25; 50; 10), and K(65; 55; 15), L(10; -30; 55).
5. Given the points: A(25; 10; 25), B(45; 55; 60) and C(75; 15; 55), construct
the parallelogram [ABCD]. Find the intersection of this parallelogram with the
[V]plane. Draw with dashed line the hidden part of the parallelogram.
4 5