Skew Lines
Topic Integration
DESIGN AND COMMUNICATION GRAPHICS
Solutions to problems should be taught with….
“an explanation as to how the construction was derived ”
Draft Guidelines for Teachers (page 14)
Two key concepts of plane and descriptive geometry
relating to skew lines are
parallel lines
the parallel plane
Understanding the Why rather than knowing the How
PROPERTIES AND PROJECTIONS OF SKEW LINES
“Define the concept of skew lines and their use in solving practical problems”
page 17 of syllabus
 Clearances between cables, pipes and braces
 Shortest connecting tunnel between two mine tunnels
 Shortest connection between two oblique sewer lines or pipelines
Skew lines are lines which are non-intersecting and non-parallel.
Skew lines are
non-coplanar
If you look at a bridge over a river, you are looking at an example of skew lines.
An overpass is an excellent example of skew lines. The roadway represents one
line and the pedestrian bridge represents another line. The “lines” do not intersect
because they are on different planes.
Which set of lines is skew?
Intersecting Lines
Skew Lines
When two lines intersect, the point of
intersection will align in elevation and
plan, and any other view.
Skew lines do not intersect. Their
apparent point of intersection will not
align in elevation, plan or any other view.
C1
A1
A1
D1
B1
A
C1
B1
D1
D
B
C
D
C
B
Find the vertical distance between the two skew lines?
A
THE CONCEPT OF A PARALLEL PLANE
PARALLEL LINES REMAIN PARALLEL IN EVERY VIEW
Lines which are parallel in space will appear parallel in all views
e D
Parallel Lines
r a
w i n g s
C o n t r o l
PARALLEL LINES REMAIN PARALLEL IN EVERY VIEW
Lines which are parallel in space will appear parallel in all views
except
in the views in which they appear as points
or
where one line is behind the other
PARALLEL PLANE
If a line is parallel to any line in a plane, it is parallel to the plane
The projections of two skew lines AB and CD are shown.
(a)
Find a plane containing the line CD and parallel to the line AB.
(b)
Prove that the plane is parallel to the line.
C
A
D
B
C
B
A
D
e D
Parallel Plane 1
r a
w i n g s
C o n t r o l
C
M
A
D
B
C
true length (strike)
true length (strike)
A
D
M
B
A
D
C
B
SHORTEST DISTANCE BETWEEN
TWO SKEW LINES
What types of applications of skew lines are around us?
The directions of two parachute jumpers landing are represented by the skew lines AB and CD.
(a)
(b)
Determine the shortest distance between the two skew lines.
Determine the projections of this shortest distance.
D1
B1
A1
C1
A
B
D
C
e D
Shortest Distance
r a
w i n g s
C o n t r o l
B2
D1
D3
B1
D2
A2
B3
A1
A3
C1
A
C2
B
D
C3
datum line
C
SHORTEST HORIZONTAL DISTANCE
BETWEEN TWO SKEW LINES
The directions of two javelins are represented by the skew lines AB and CD.
Determine the projections of the shortest horizontal distance between the two skew lines.
D1
B1
A1
C1
A
B
D
C
e D
Shortest Horizontal
r a
w i n g s
C o n t r o l
B2
D1
B1
D2
A2
A1
D3
C1
A
C2
B
D
A3
B3
C3
datum line
C
V
D1
B1
A1
T
C1
A
B
D
Where is the other
plane director?
traces of plane
director
C
H
e D
r a
Hyperbolic Paraboloid
w i n g s
C o n t r o l
MINING GEOMETRY
headwall
Earth’s surface
footwall
Skew boreholes
Line on headwall
Line on footwall