10b. Parallel Lines
• Parallel lines do not have any common point between them
• Parallel lines are seen as parallel in adjacent views, exception
to this when the lines are perpendicular to the FL, the lines
may or may not be parallel
10b. Parallel Lines
• To find out if the lines are parallel, even if the lines are
perpendicular to the FL, it is best to draw the 3rd view
• If it is required to get the lines parallel, then use one view,
draw the lines parallel and complete the 3rd view
10b. Parallel Lines
bH
jH
bH
jH
aH kH aH kH
H
F
H
F
kF
aF
aP
kF
aF
jF
bF
jF
bF
F P F P
kP
aP
kP
bP
jP
bP
jP
10c. Intersecting Lines
bH
• Intersecting lines
have one common
point between them
jH
bH
eH
aH kH
aH
• The projection of the
points must be
aligned in adjacent
views
gH
H H
• If they are, then the
F F
lines are intersecting
• If not, they are
skewed
gP
gF
aP
kF
aF
eF
aP
bP
aF
bF
F P
bF
jF
eP
10c. Intersecting Lines
• Intersecting lines
have one common
point between them
• The projection of the
points must be
aligned in adjacent
views
• If they are, then the
lines are intersecting
• If not, they are
skewed
bH
eH
aH
gH
H
F
gP
gF
aP
aF
eF
bP
bF
F P
eP
10c. Intersecting Lines
• Intersecting lines
have one common
point between them
• The projection of the
points must be
aligned in adjacent
views
• If they are, then the
lines are intersecting
• If not, they are
skewed
bH
eH
aH
gH
H
F
gP
gF
aP
aF
eF
bP
bF
F P
eP
10c. Coincident lines
bH
aH
H
F
aP
aF
bP
bF
F P
10c. Coincident lines
dH
bH
cH
aH
H
F
cP
aP
cF
aF
dF
bF
dP
bP
F P
11. Location of a line
Locate a line // to a given line passing through a point
bH
sH
aH
H
F
aF
sF
bF
11. Location of a line
Locate a line // to a given line passing through a point
jH
bH
sH
aH kH
H
F
kF
aF
sF
jF
bF
12. True distance between 2 // lines
bH
jH
HA
kA1=jA1
aA1=bA1
jA
aH kH
kA
H
F
bA
A A1
aA
Two auxiliary views
kF
aF
jF
bF
12. True distance between 2 // lines
HA
jH
bH
aH kH
Y
X’
H
F
x
x
bA
A A1
aA
X’ Y
Y’
kF
aF
jF
bF
kA
Y’
kA1=jA1
aA1=bA1
jA
Two auxiliary views
12. True distance between 2 // lines
bH
jH
HA
kA1=jA1
aA1=bA1
jA
aH kH
kA
H
F
bA
A A1
aA
kF
aF
jF
bF
Distance between the
two points gives the
true distance between
parallel lines
13. Perpendicular lines
bH
90°
cH
aH
H
F
• A 90° angle appears in
true size in any view
showing one leg in TL
provided the other leg
does not appear as point
view
• Two intersecting lines are
perpendicular if the TL
projection is making 90°
with the other line
aF
bF
cF
13. Perpendicular lines
Mechanical Engineering Drawing
MECH 211
LECTURE 5
The objectives of the lecture
• Continue to acquire knowledge in the Descriptive
Geometry – point and line concepts
• Distance form a point to a line
• Location of a perpendicular line at a give location on a
line
• Non-intersecting lines – skew lines
• Shortest distance between skew lines
• Location of a line through a given point and intersecting
two skew lines
The objectives of the lecture - Contd
• Continue to acquire knowledge in the Descriptive
Geometry – point and line and plane concepts
•
•
•
•
•
•
•
Representation of a plane surface
Relative position of a line versus a plane
Location of a line on a plane
Location of a point on a plane
True-length lines in a plane
Strike of a plane – bearing of the horizontal line in a plane
Edge view of a plane – planes that appear as edge view in the
principal views
• Slope of a plane – the angle the plane is doing with the horizontal
plane from T.E.V.)
Distance form a point to a line
Distance form a point to a line
Distance form a point to a line
Distance form a point to a line
Distance form a point to a line
Distance form a point to a line
Location of a perpendicular line
at a give location on a line
Location of a perpendicular line
at a give location on a line
Location of a perpendicular line
at a give location on a line
Location of a perpendicular line
at a give location on a line
Location of a perpendicular line
at a give location on a line
Location of a perpendicular line
at a give location on a line
Non-intersecting lines – skew lines
Non-intersecting lines – skew lines
Non-intersecting lines – skew lines
Non-intersecting lines – skew lines
Non-intersecting lines – skew lines
Shortest distance between skew lines
Shortest distance between skew lines
Shortest distance between skew lines
Shortest distance between skew lines
Shortest distance between skew lines
Shortest distance between skew lines
Shortest distance between skew lines
Location of a line
through a given point and intersecting two skew lines
Location of a line
through a given point and intersecting two skew lines
Location of a line
through a given point and intersecting two skew lines
Location of a line
through a given point and intersecting two skew lines
Location of a line
through a given point and intersecting two skew lines
Location of a line
through a given point and intersecting two skew lines
Representation of a plane surface
bH
mH
cH
nH
aH
cF
nF
A plane is defined by one of
the below:
1) Two parallel lines
2) Two intersecting lines
3) One line and a point
external to the line
4) Three point that are not
positioned along the same line
aF
mF
bF
Relative position of line Vs. plane
bH
cH
aH
cF
A line is located in a plane if
all the points of that line are
in that plane. However, is
sufficient to show that two
points that belong to the line
belong to the plane too.
aF
bF
Relative position of line Vs. plane
bH
mH
cH
nH
aH
cF
nF
aF
mF
bF
A line is located in a plane if
all the points of that line are
in that plane. However, is
sufficient to show that two
points that belong to the line
belong to the plane too.
Line MN is located in the
plane ABC since M is
simultaneously located in AB
and MN and N on AC and
MN.
Relative position of line Vs. plane
Line DE is parallel to the
plane ABC since is
parallel to a line (MN)
that is contained in that
plane
dH
bH
jH
mH
cH
eH
cF
eF
nH
aH
nF
aF
jF
mF
bF
dF
A line is located in a plane if
all the points of that line are
in that plane. However, is
sufficient to show that two
points that belong to the line
belong to the plane too.
Line MN is located in the
plane ABC since M is
simultaneously located in AB
and MN and N on AC and
MN.
Relative position of line Vs. plane
Line PQ is intersecting
the plane ABC in the
point I.
dH
bH
Line DE is parallel to the
plane ABC since is
parallel to a line (MN)
that is contained in that
plane
qH
jH
mH
iH
cH
eH
cF
eF
nH
aH
pH
nF
pF
aF
iF
jF
mF
bF
dF
A line is located in a plane if
all the points of that line are
in that plane. However, is
sufficient to show that two
points that belong to the line
belong to the plane too.
qF Line MN is located in the
plane ABC since M is
simultaneously located in AB
and MN and N on AC and
MN.
Relative position of line Vs. plane
Line PQ is intersecting
the plane ABC in the
point I.
dH
bH
Line DE is parallel to the
plane ABC since is
parallel to a line (MN)
that is contained in that
plane
qH
jH
mH
iH
cH
eH
cF
eF
nH
aH
pH
nF
pF
aF
Apart from the three
positions, there is no
other relative position on
a line with a plane.
iF
jF
mF
bF
dF
A line is located in a plane if
all the points of that line are
in that plane. However, is
sufficient to show that two
points that belong to the line
belong to the plane too.
qF Line MN is located in the
plane ABC since M is
simultaneously located in AB
and MN and N on AC and
MN.
Location of a line on a plane
bH
mH
cH
nH
aH
cF
nF
aF
mF
bF
A line is located in a plane if
all the points of that line are
in that plane. However, is
sufficient to show that two
points that belong to the line
belong to the plane too.
Line MN is located in the
plane ABC since M is
simultaneously located in AB
and MN and N on AC and
MN.
Location of a line on a plane
Can you locate the line 4-5 in the plane 1-2-3
Location of a point on a plane
bH
iH
cH
nH
aH
cF
nF
aF
iF
bF
Location of a point on a plane
bH
mH
iH
cH
nH
aH
cF
nF
aF
iF
mF
bF
A point I is located
on a plane if is
located on a line that
belongs to that plane.
Location of a point on a plane
Can you locate the point 4 in the plane 1-2-3
Using Parallelism
Location of a point on a plane
Locate a point which is 10mm above point 2 and 12mm behind
point 3
True Length line lies on the plane
Line MN is a horizontal
line. mHnH is the true
length of the line MN.
bH
nH
iH
jH
cH
mH
aH
cF
Line IJ is a front line.
jF iFjF is the true length of the
line IJ.
aF
nF
mF
iF
bF
Strike of a plane
N
bH
nH
mH
9°E
N5
Line MN is a horizontal
line. mHnH is the true
length of the line MN.
The bearing of this line
represents the strike of
the plane.
cH
aH
cF
aF
nF
mF
bF
Edge View of a plane
bH
cH
aH
cF
aF
bF
Edge View of a plane
bH
cH
aH
cF
aF
bF
Slope (dip) of a plane
E.V
.
Horizontal plane
bH
nH
cH
mH
Elevation
View
aH
cF
The Edge View (EV) of the plane is built in
an auxiliary view adjacent with the
Horizontal (Top) view. The angle of the EV
of the plane with the horizontal direction
represents the slope (dip ) of the plane
aF
nF
mF
bF
Shortest line from a point to plane
To find the shortest line from point
to plane
bH
cH
aH
cF
aF
bF
Shortest line from a point to plane
Find the EV of
plane
bA
aA
bH
nH
cA
TL
cH
mH
aH
cF
aF
nF
mF
bF
Shortest line from a point to plane
Find the EV of
plane
bA
Project point in
that view
aA
bH
eA
nH
cA
TL
cH
mH
aH
eH
cF
aF
nF
mF
bF
eF
Shortest line from a point to plane
Find the EV of plane
bA
Project point in that
view
aA
eA
bH
eA
nH
Draw perp from
point to EV
cA
TL
eH
mH
aH
cH
eH
Traceback with perp
from TL in the HV
cF
eF
For FV use distance
aF
nF
mF
bF
eF
Shortest grade line - point to plane
bA
rA
Horizontal direction
aA
eA
bH
eA
rH
nH
cA
TL
eH
mH
aH
cH
eH
cF
eF
aF
rF
mF
bF
nF
eF
Shortest grade line - point to plane
bH
cH
aH
cF
aF
bF
Shortest grade line - point to plane
bA
aA
bH
nH
cA
TL
cH
mH
aH
cF
aF
nF
mF
bF
Shortest grade line - point to plane
bA
aA
bH
eA
nH
cA
TL
cH
mH
aH
eH
cF
aF
nF
mF
bF
eF
Shortest grade line - point to plane
bA
aA
eA
bH
eA
nH
cA
TL
eH
mH
aH
cH
eH
cF
eF
aF
nF
mF
bF
eF
Shortest grade line - point to plane
bA
rA
Horizontal direction
aA
eA
bH
eA
rH
nH
cA
TL
eH
mH
aH
cH
eH
cF
eF
aF
rF
mF
bF
nF
eF
Shortest grade line - point to plane
bA
The slope could be
shown ONLY IN AN
ELEVATION VIEW
rA
qA aA
Horizontal direction
Line at 20° slope
eA
bH
eA
TL
rH
qH
mH
nH
cA
eH
aH
cH
eH
cF
eF
qF
aF
rF
mF
bF
nF
eF