Descriptive Geometry

Eng. Areej Afeefy

Ref. Descriptive Geometry Metric PARE/LOVING/HILLFifth edition

Descriptive Geometry

Descriptive Geometry:

is the science of graphic representation and solution and space problems

projectionsTow common types of projections:

1) perspective projections (used by architects or artists) 2) orthographic projections (perpendicular to the object)

Principal Views

Draw the profile

Steps to obtain a viewEstablish the line of sight.Introduce the folding lineTransfer distances to the new viewDetermine visibility and complete the view

Step 1: Establish the line of sight.1Primary Auxiliary ViewsStep 2: Introduce the folding lineStep 3: transfer distancesStep 4: determine visibility and complete viewk1H1yd,ha,eb,fc,gg,hyb,ac,df,edhbfcgaeyD1D2D1D2D

All views projected from top view has the same height dimension

Primary Auxiliary Views

View 1 is an auxiliary view projected from the front View

All the views projected from front view have the same depth dimension

Edge View of a plane

Chapter 3: LINES

Frontal Line

Frontal Line

the true angel between a line and any projection plane appears in any view shows the line in true length and the projection plane in Edge View.

Level (Horizontal) Line

Level Line

Profile Line

Profile Line

True Length of an Oblique Line

True Length of an Oblique Line

Bearing , Slope, and GradeaHb55aHbS55oENNBearing: a term used to describe the direction of a line on the earths surface

aH125oNAzimuth BearingbaHbN125o

problemA 160-m segment AB of a power line has a bearing of N 60o and a downward slope of 20o from the given point A. Complete the front and top views.

ahaF

ahaFN 60oa120o160 mbbbHFH1N

GradeGrade: another way to describe the inclination of a line from the horizontal Plane

Grade

Chapter 4Planes

Points and lines in Planes

Locating a Point in a PlaneProblem: Given the front and side views of a plane MON and the front view of a point A in the plane. Determine the side view aF xmnoFnmoP

Solution aF xmnoFnmoPXYXYaPx

Lines in PlanesbcaFebcgeaHComplete the front view

Lines in PlanesbcgeaHbcaFexxg

Principal Lines in Planes

Frontal LineAll frontal lines in the same plane are parallel unless the plane it self is frontal

Horizontal or Level Lines

Horizontal or Level Lines All horizontal lines in the same plane are parallel unless the plane it self is horizontal

Profile Line

Profile LineAll profile lines in the same plane are parallel unless the plane it self is profile

Locus The Locus: is the path of a point, line or curve moving is some specified manner.

Or it is the assemblage of all possible positions of a moving point, line or curve

The locus of a point moving in a plane with a specified distance from another point is circle.

Locus Problem: in the given plane ABC locate a point K that lies 6 mm above horizontal line AB and 5 mm in front of frontal line AC. Scale: full size

Solution caHbaFbchhhhffffKK

Pictorial Intersection

2) If tow planes are parallel, any lines on the planes in question are parallel.

M KNHABCE D Tow principles to solve the problem: 1) Lines in a single plane must either be parallel or intersect.

Pictorial Intersection

Pictorial Intersection

Chapter 5Successive Auxiliary Views

Construction of successive Auxiliary ViewsStep 1: Establish the line of sight.

Step 2: Introduce the necessary folding lines.

Step 3: transfer distance to the new view.

Step 4: Complete view.

Point View of a LineA line will appear in point view if the line of sight is parallel to the line in space..

In the drawing sheet, the line of sight should be parallel to the true length of the line.

Point View of a LineahaF1bbHFPoint View (P.V)T.L.ba2a1,b2

Problem IFind the true clearance between the point O and the line AB. ahaFbbHFT.L.oobaho12a2,boClearance

Edge View of a Plane A plane will appear in edge view in any view for which the line of sight is parallel to the plane.

In the drawing sheet, a plane will appear in edge view in any view for which the line of sight is parallel to a true length line in the plane.

Edge View of a PlaneahaF1bbHFT.L.cchhcbaE.V.

Normal Views of a PlaneA normal view or TRUE SIZE and shape of a plane is obtained in any view for which the line of sight is perpendicular to the plane.

In the drawing sheet the line of sight appear perpendicular to the Edge View of the plane.

Edge View of a PlaneahaF1bbHFT.L.cchhcbaE.V.2Normal ViewT.S.

Uses of Auxiliary and additional Views

problemFind the front and top views of a 2.5m radius curve joining tow intersecting lines BA & BC.

acbacbffTLcabcba

acbacbffTLcabcba12345123451234512345

Chapter 6Piercing Points

Piercing pointThe intersection of a line with a plane is called Piercing Point.

If the line is not in or parallel to a plane, it must intersect the plane.

Piercing point - Auxiliary View MethodbHcabFcab1,cagegeeg1.pppTL

Piercing point- Tow View MethodA piercing point could be found using the given views as follows: (see the following Fig.) Any convenient cutting plane containing line EG is introduced, it appears EV in a principal view. The line of intersection between the tow planes is determined.Since line EG and line 1 - 2 both lies in the cutting plane they intersect, locating point P. Since line 1 2 also lies in Plane ABC, point P is the required Piercing Point.

12EGABCVertical cutting plane N PPiercing point- Tow View Method

Piercing point- Tow View MethodbHcabFcagegep1212pVertical cutting plane N

Chapter 7Intersection of Planes

Intersection of Planes Any tow planes either parallel or must intersect.

Even the intersection beyond the limits of planes.

The intersection of planes result a line common to both of them.

Intersection of Planes Auxiliary view MethodbHcagexybFcaJkgeJkffb1caekjgxyxyzz

Intersection of Planes Auxiliary view MethodbHcagexybFcaJkgeJkbHcaekjgyzyz

Intersection of Planes Tow View - Piercing point MethodbacFdeFgdePgbacPxxyy

Intersection of Planes Tow View - Piercing point MethodbacFdeFgdePgbacPE.V.1212xxE.V.3434yyL1L1

Intersection of Planes Tow View - Piercing point MethodbacFdeFgdePgbacP

Intersection of Planes Cutting Plane Method12345678H1H2P1P2Line of intersectionbacmon

Intersection of Planes Cutting Plane MethodbacHbacFmonHmonH1234EV of HI1234P1EV of H256785678P2LIP1P2LI

Pictorial Intersection Of Planesbacnmksedo23

Pictorial Intersection Of Planesbacnmk23v

Chapter 8Angle between Planes

Angle between PlanesmnABE.V. of mE.V. of nP.V. of line of intersection ABLine of sight

Dihedral Angle Line of Intersection given eHLIAgeFge1gB TL LIBAE.V. of AE.V. of Be2g

Dihedral Angle Line of Intersection is NOT givenbHacbFaconmkHonmkFEV.1EV.234123412xyxy

Dihedral Angle Line of Intersection is NOT givenbHacbFaconmkHonmkFxyxyb1acxyTLonmk1b2cnmX,y

Dihedral Angle Line of Intersection is NOT givenAlternative solution: You can find the Edge View for both planes without resorting to find the line of intersection.

See next slide

Dihedral Angle Line of Intersection is NOT givenbHacbFaconmkHonmkFb2conmk1TLb1,caEVaonmk2TSTLBoth Planes willAppear EV. 123

Angle between Oblique Plane and Principal PlaneaHbcaFbcffTLHF1a1bcFfEV of frontal planeAngle between plane and frontal plane

Angle between Oblique Plane and Principal PlaneaHbcaFbcTLHFEV of Profile planecbaPPff1a1bcPAngle between plane and Profile plane

Angle between Oblique Plane and Principal PlaneAngle between a plane and a horizontal plane can be measured in the similar fashion.

The angle between sloping plane and a horizontal plane is called DIP ANGLE.

Angle between Oblique Plane and Principal PlaneaHbcaFbcHFAngle between plane and horizontal planeff1aHbcHTL

Chapter 9Parallelism

Parallel Lines Oblique Lines that appears parallel in tow or more principal views are parallel in space.

Parallel LinesaHbdHFPcaFbdcbdcaP

Parallel LinesaHbdHFPcaFbdcbcdaPF

Principal LineTow horizontal, tow frontal, or tow profile lines that appears to be parallel in tow principal views may or may not be parallel in space.

non intersecting, non parallel lines are called SKEW LINES.

Parallel LinesaHX cHFPbaFbbaPFX cX a1be c X X cP1

Parallel LinesaHX cHFPbaFbbaPFX cX a1be c X X cP1e X X e X eD1D1D2D2

Parallel Planes mHonmFonaHcbaFcbffTL1FHom1nbca1

Parallel PlanesIf tow planes are parallel, any view showing one of the planes in edge view must also show the other plane as parallel edge view.

Parallel edge views prove that planes are parallel.

Lines parallel to planesPlanes parallel to lines If tow lines are parallel, any plane containing one of the lines is parallel to the other line.

A line may be drawn parallel to a plane by making it parallel to any line in the plane.

Lines parallel to planesPlanes parallel to linesxyxymorqpmoqpr

Chapter 10Perpendicularity

Perpendicular Lines If a line is perpendicular to a plane, it is perpendicular to every line in the Plane. xygjef9090x1y1Perpendicular lines are not necessarily intersecting lines and they do not necessarilyLie in the same plane.

Perpendicular Lines If tow lines are perpendicular, they appear perpendicular in any view showing at least one of the lines in true length.

If tow lines appear perpendicular in a view, they are actually perpendicular in space if at least one of the lines is true length in the same view.

Perpendicular Lines mnososmnmnosHFH1TL

Plane Perpendicular to LineTow-View Method A plane is perpendicular to a line if the plane contains tow intersecting lines each of which is perpendicular to the given line.

Plane Perpendicular to LineTow-View MethodyzyzxhTLxhfTLfHFF1xfhzyEVTL

Plane Perpendicular to LineAuxiliary-View MethodyzyzxhxkHFF1xhzyEVTLkkh

Line Perpendicular to PlaneTow-View MethodA line perpendicular to a plane is perpendicular to all lines in the plane.

Line Perpendicular to PlaneTow-View MethodnonoaaHFkmmhhTLkffTLk

Line Perpendicular to PlaneAuxiliary-View MethodnonoaaHFkmmhhTLkamonEVkkTL

Common Perpendicular Point View MethodThe shortest distance from a point to a line is measured along the perpendicular from the point to a line. The shortest distance between tow skew lines is measured by a line perpendicular to each of them.

Common Perpendicular Point View MethodeacbecabHF1abecTL2ecab x

Common Perpendicular Point View MethodeacbecabHF1abecTL2ab xecTLxxyxyxy

Common Perpendicular Plane MethodAnother method to find the shortest distance between skew lines, specially when the perpendicular view are not required.

Common Perpendicular plane MethodeacbecabHFkkhhTL1x khceEVbaShortest Distance

Shortest line at specified Grade connecting Tow Skew LineseacbecabHFpphTL1x phceEVbaShortest Horizontal Distancehh

Shortest line at specified Grade connecting Tow Skew LineseacbecabHFpphTL1x phceEVbahh10015

Projection of line on a PlaneThe projection of a point on a plane is the point in which a perpendicular from the point to the plane pierces the plane.

Projection of line on a PlanenmobabanmoFPhhTL1omnevabapbpTLapbpapbp

12EGABCPSecond exam Solution

X vX vbaab1234mnnmkook1234