Descriptive Geometry
CH3 : Lines
True Length (TL) of a line
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… is shown in any plane (Frontal, Horizontal, Profile) when the line
is parallel to that plane.
Principle Projection Lines
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…Lines that are parallel
to a principal projection
plane (F,H,P)
A frontal line is in or
parallel to a frontal
projection plane
If the LOS is ┴ to the
line, it is shown TL
Check the angle of the
line by looking at an
adjacent view (the top
view of line ab is parallel
to the FL H/F)
Principle Lines
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The horizontal line lies in or
is parallel to a horizontal
plane
The TRUE ANGLE (θ)
between any line & any
plane appears in any view
that shows both the line in
TL & the plane in edge view
(i.e. as a FL)
Angles θF & θP are shown
as true angles since FLf &
FLp are in edge view
Principle Lines
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The profile line lies in or
parallel to a profile plane
Angles θF & θH are
shown as true angles
since FLf & FLh are in
edge view
Oblique Lines
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An Oblique line is one not parallel to any principal
projection plane
Views of the line are foreshortened in the principal views
(F, H, P)
Oblique Lines
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To show the TL of an oblique line the LOS must be
perpendicular to the line
A line is shown TL in a view when the adjacent view of the line
is parallel to the FL between the 2 views
True angle θF is also shown since the Frontal plane is an edge
view (i.e. a FL)
Oblique Lines
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The same can be done when drawing an auxiliary view from the
profile view to show θp
Oblique Lines
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To find each true angle (θ) of oblique line AB in relation to all 3
principal views (F,H,P) a 3 separate auxiliary views must be
constructed
Bearing
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In practice, the position of a line in space is often described by its
bearing & slope, or its bearing & grade.
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Bearing of a line is the angular relationship of the top view of the line
with respect to due north or south (N is assumed U.O.N.)
Bearing
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… the direction or course of a line on the earth’s surface (which is
conceptually thought of as a series of small planes)
Quadrant where arrow lies determine cardinal directions used
Bearing
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… the direction or course of a line on the earth’s surface (which is
conceptually thought of as a series of small planes)
Quadrant where arrow lies determine cardinal directions used
Bearing
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Azimuth Bearing – used in navigation & civil engineering
Measures the clockwise departure from a base direction (usually N)
Slope of a line
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... the angle in degrees that the line makes with a horizontal
plane (θH)
Bearing, Slope & TL
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The auxiliary view shows the TL & thus, true slope & D1
Point b can be located in the top view from the auxiliary
Grade of a line
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… another means of describing the inclination of a line in respect
to a horizontal plane
Grade of a line
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Always shown as a %
Frontal lines can show true slope
& grade
Grade of a line
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With an oblique line, an auxiliary view must be constructed to
measure & calculate the grade
The run must be measured parallel to the FL H/I
The rise must be measured ┴ to the FL H/I
Points on Lines
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… can usually be located in successive views by simple
projection
Points on Lines
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… may be determined by spatial relat ions
Points on Lines
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Points dividing a line segment in a given ratio will divide any
view of the line in the same ratio
So, division could be made without constructing an auxiliary
view
Intersecting Lines
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… contain a common point
a single projection line can connect the intersecting point between
any adjacent views
Example: Intersection
of Lines
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Complete the top view of the hoist frame...
Example: Intersection
of Lines
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Point E cannot be obtained from a front or top view so a profile
view is drawn...
Example: Intersection
of Lines
Problem 3a.
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Find the true lengths of the three members OA, OB, & OC.
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1. OC is shown TL in F
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2. An auxiliary view shows OA in TL
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3. Multiply x10 for scale