Descriptive Geometry CH3 : Lines

True Length (TL) of a line • … is shown in any plane (Frontal, Horizontal, Profile) when the line

is parallel to that plane.

• …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 Projection Lines

• 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

Principle Lines

• 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 • 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 • 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 • The same can be done when drawing an auxiliary view from the

profile view to show θp

Oblique Lines • 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 • In practice, the position of a line in space is often described by its

bearing & slope, or its bearing & grade.

• 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 • … 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 • … 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 • Azimuth Bearing – used in navigation & civil engineering • Measures the clockwise departure from a base direction (usually N)

Slope of a line • ... the angle in degrees that the line makes with a horizontal

plane (θH)

Bearing, Slope & TL • 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 • … another means of describing the inclination of a line in respect

to a horizontal plane

• Always shown as a % • Frontal lines can show true slope

& grade

Grade of a line

Grade of a line • 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 • … can usually be located in successive views by simple

projection

Points on Lines • … may be determined by spatial relat ions

Points on Lines • 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 • … contain a common point • a single projection line can connect the intersecting point between

any adjacent views

Example: Intersection of Lines

• Complete the top view of the hoist frame...

Example: Intersection of Lines

• Point E cannot be obtained from a front or top view so a profile view is drawn...

Example: Intersection of Lines

Problem 3a. • Find the true lengths of the three members OA, OB, & OC.

• 1. OC is shown TL in F

• 2. An auxiliary view shows OA in TL

• 3. Multiply x10 for scale