10b. Parallel Lines • Parallel lines do not have any common point between them • Parallel lines are seen as parallel in adjacent views, exception to t...
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