skew lines
TRANSCRIPT
Skew LinesTopic 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
“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
PROPERTIES AND PROJECTIONS OF SKEW LINES
If you look at a bridge over a river, you are looking at an example of skew lines.
Skew lines are lines which are non-intersecting and non-parallel.
Skew lines are non-coplanar
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.
C1
D
B
AC
A1
D1 B1
C1
A
C
DB
A1
D1 B1
Skew Lines
Skew lines do not intersect. Their apparent point of intersection will not
align in elevation, plan or any other view.
Intersecting Lines
When two lines intersect, the point of intersection will align in elevation and
plan, and any other view.
Find the vertical distance between the two skew lines?
Which set of lines is skew?
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
Parallel Lines
eDrawings Control
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 PLANEIf a line is parallel to any line in a plane, it is parallel to the plane
C
BA
D
BD
CA
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.
Parallel Plane 1
eDrawings Control
CB
A
D
BD
CA
CD
B
A
M
M
true length (strike)true length (strike)
SHORTEST DISTANCE BETWEEN TWO SKEW LINES
What types of applications of skew lines are around us?
A B
C
D
A1
B1
C1
D1
The directions of two parachute jumpers landing are represented by the skew lines AB and CD.
(a) Determine the shortest distance between the two skew lines.(b) Determine the projections of this shortest distance.
Shortest Distance
eDrawings Control
AB
C
D
A1
B1
C1
D1
A2
B2
C2
D2
datum line
A3
B3
C3
D3
SHORTEST HORIZONTAL DISTANCE BETWEEN TWO SKEW LINES
A B
C
D
A1
B1
C1
D1
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.
Shortest Horizontal
eDrawings Control
AB
C
D
A1
B1
C1
D1
A2
B2
C2
D2
datum line
A3
B3
C3
D3
AB
C
D
A1
B1
C1
D1
T
H
V
traces of plane director
Where is the other plane director?
Hyperbolic Paraboloid
eDrawings Control
MINING GEOMETRY
Earth’s surface
headwall
footwall
Skew boreholes
Line on headwall
Line on footwall