10b. Parallel Linesnrskumar/Index_files/Mech211/Full... · •Parallel lines are seen as parallel...

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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

10c. Intersecting Lines

• Intersecting lines

have one common

point between them

• The projection of the

points must be

aligned in adjacent

• If they are, then the

lines are intersecting

• If not, they are

skewed

have one common

point between them

points must be

aligned in adjacent

skewed

have one common

point between them

points must be

aligned in adjacent

skewed

10c. Coincident lines

11. Location of a line

Locate a line // to a given line passing through a point

11. Location of a line

Locate a line // to a given line passing through a point

12. True distance between 2 // lines

Two auxiliary views

kA1=jA1

aA1=bA1

Two auxiliary views

kA1=jA1

aA1=bA1

kA1=jA1

aA1=bA1

Distance between the

two points gives the

true distance between

parallel lines

13. Perpendicular lines

90° • A 90° angle appears in

true size in any view

showing one leg in TL

provided the other leg

does not appear as point

• Two intersecting lines are

perpendicular if the TL

projection is making 90°

with the other line

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

• Non-intersecting lines – skew lines

• Shortest distance between skew lines

• Location of a line through a given point and intersecting

two skew lines

• 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.)

The objectives of the lecture - Contd

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

through a given point and intersecting two skew lines

Location of a line

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

Representation of a plane surface

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.

Relative position of line Vs. plane

Line MN is located in the

plane ABC since M is

simultaneously located in AB

and MN and N on AC and MN.

Line DE is parallel to the

plane ABC since is

parallel to a line (MN)

that is contained in that

plane ABC since is

Line PQ is intersecting

the plane ABC in the

point I.

plane ABC since is

Line PQ is intersecting

the plane ABC in the

point I.

Apart from the three

positions, there is no

other relative position on

a line with a plane.Line MN is located in the

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

A point I is located

on a plane if is

located on a line that

belongs to that plane.

Using Parallelism

Can you locate the point 4 in the plane 1-2-3

Locate a point which is 10mm above point 2 and 12mm behind

point 3

jFLine IJ is a front line.

iFjF is the true length of the

line IJ.

Line MN is a horizontal

line. mHnH is the true

length of the line MN.

True Length line lies on the plane

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.

N59°E

Strike of a plane

Edge View of a plane

cH Elevation

Horizontal plane

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 planenFmF

Slope (dip) of a plane

Shortest line from a point to plane

To find the shortest line from point

to plane

Find the EV of

Project point in

that view

Find the EV of plane

Project point in that

Draw perp from

point to EV

Traceback with perp

from TL in the HV

For FV use distance

Horizontal directionrA

Shortest grade line - point to plane

rAHorizontal direction

Line at 20° slopeqA

The slope could be

shown ONLY IN AN ELEVATION VIEW

Horizontal direction

Shortest grade line - point to plane

10b. Parallel Linesnrskumar/Index_files/Mech211/Full... · •Parallel lines are seen as parallel...

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