10b. Parallel Lines H F F P H F F P. kf af

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...
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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