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 () 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 F & P 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 F & H 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 F 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 p

Oblique Lines To find each true angle () 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 earths 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 earths 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 (H)

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

Descriptive GeometryTrue Length (TL) of a linePrinciple Projection LinesPrinciple LinesPrinciple LinesOblique LinesOblique LinesOblique LinesOblique LinesBearingBearingBearingBearingSlope of a lineBearing, Slope & TLGrade of a lineGrade of a lineGrade of a linePoints on LinesPoints on LinesPoints on LinesIntersecting LinesExample: Intersection of LinesExample: Intersection of LinesExample: Intersection of LinesProblem 3a.