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Descrptive Geometry
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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