TA101 : Engineering Graphics

Review of Lines

Dr. Ashish Dutta

Professor

Dept. of Mechanical Engineering

IIT Kanpur

Kanpur , INDIA

Projection of a point in space

A point is behind the frontal plane by ‘d’ units

and below the horizontal plane by ‘h’ units.

HORIZONTAL

FRONTAL

PLANE

HORIZONTAL

PLANE

Line positions

• Line lying on two principal planes of projection will

appear normal / true length (TL) in two views.

• A line lying in one principal plane will appear normal

in one view.

Find normal view of a lineMethod 1 (using auxiliary plane).

1. Determine the desired line of sight.

2. Establish a new projection plane perpendicular to

line of sight.

3. Project all points into the new view.

4. Locate points A and B along the projections in

plane.

Auxiliary plane method

Method 2 : Rotation method

1. Make the line parallel to one of the

Principal planes in any view by rotation.

2. Take projections on the other

view to get normal view of line.view to get normal view of line.

Why does it work?

Slope and Grade of a line

� Relationship of a line to the horizontal plane

• Line in TL (normal view)

• Slope =

• θ is the slope angle of a line.

θtanRun

Rise==

X

Y

• θ is the slope angle of a line.

Bearing

• Bearing of a line can be, measured only in horizontal

view.

• Examples are N60°W, S45°W etc.

Azimuth

Azimuth is measured clockwise from the north arrow

and only uses ‘N’ along with the angle.

Parallel lines:

Two lines are parallel if they lie on the same

plane and do not intersect or touch at a point.

Parallel lines appear parallel in all views.

CASE 1

Lines that appear normal in H and F planes may

not be parallel: Check for P view

CASE 2

Perpendicular lines:

Two lines are perpendicular if there is a 90o angle

between them if at least one line is in true length

Cases :

A : Perpendicular (both lines in TL)

B: Perpendicular (only one line in TL)

C: Not perpendicularC: Not perpendicular

Shortest distance from a point to a line is a

perpendicular from the point to a line.

• Shortest distance shows true length (TL) when

original line is a point view. ?

• Const.:

Draw a line O-P perpendicular Draw a line O-P perpendicular

to line 1-2 at ‘P’.

Similarly in F view,

Join point ‘O’ and point view of line.

• Point view of line 1-2 is given in F view. Hence

OP is in TL.

• Line OP is parallel to H plane.

Line not in point view• Point view required for line 3-4.

• Construct auxiliary view H/A to get point view of line

3-4

• Point P must lie along a line from ‘O’ parallel to H/A

folding line.

• Hence OP is in TL in• Hence OP is in TL in

view A.

• Once point P is found in H view, drop it to the F view

on line 3-4.

Given line not in true length• The shortest distance is seem as TL when line is

made a point view.

• In view 1 line A B is made TL.

• In view 2 AB is made point view.

• Distances from view H are transferred into view 2.

• View 2 TL of OP connector is made.

• Line OP is returned to other views.

• Line OP in view 1 is made parallel to the 1/2 fold

line to get P, such that OP is in TL in view 2.

Shortest distance from a line to a line

in case one line is in point view • Two lines that are not parallel and do not intersect

(skew lines).

• The shortest connector between two skew lines is

the connector perpendicular to each line.

• Connector shows TL as one line 1-2 is in point view in

F view.

• Hence OP is made TL in F view by constructing

perpendicular to line 3-4.

• OP is found in H view by projecting P on to 3-4 line.

• Run it parallel to H/F fold line.

Distance between Skew lines when

neither are in point view

• A line AB is mode in point view. (TL then point view)

In view 2 the shortest distance OP is added as a TL

connector.

• Connector makes 900 angle to line CD.

• Line AB is first made TL, and then point view.

• CD is carried along from view to view.

• In view 2 the shortest distance is found by

constructing a perpendicular to get point P.

• OP is projected

back.back.

Main Points to rememberNormal Line:

• A line lying in one principal plane will appear

normal in one view.

• A line lying on two principal planes will appear

normal in two views

Shortest distance:

• Shortest distance from a point to a line is a

perpendicular from the point to a line.

• Shortest distance shows true length (TL)

when original line is a point view. ?