Slide 1

Ref. Descriptive Geometry Metric PARE/LOVING/HILL Fifth edition Slide 2 Descriptive Geometry Descriptive Geometry: is the science of graphic representation and solution and space problems By Arch. Areej Afeefy Slide 3 projections Two common types of projections: 1) perspective projections (used by architects or artists) 2) orthographic projections (perpendicular to the object) Slide 4 Perspective Projection Screen Human eye Slide 5 Orthographic Projection Screen Slide 6 Orthographic Projection Front Horizontal Profil Slide 7 Horizontal Front Profil Slide 8 Principal Views Slide 9 Draw the profile Slide 10 Steps to obtain a view 1) Establish the line of sight. 2) Introduce the folding line 3) Transfer distances to the new view 4) Determine visibility and complete the view Slide 11 Step 1: Establish the line of sight. 1 Primary Auxiliary Views Step 2: Introduce the folding line Step 3: transfer distances Step 4: determine visibility and complete view k1k1 H 1 y d,h a,e b,f c,g g,h y b,a c,d f,e d h b f c g a e y D1 D2 D1 D2 D Slide 12 All views projected from top view has the same height dimension Slide 13 Primary Auxiliary Views Slide 14 View 1 is an auxiliary view projected from the front View Slide 15 All the views projected from front view have the same depth dimension Slide 16 Slide 17 Edge View of a plane Slide 18 Slide 19 Slide 20 Slide 21 Slide 22 Slide 23 Slide 24 Slide 25 Slide 26 Slide 27 Slide 28 Frontal Line Slide 29 Slide 30 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. Slide 31 Level (Horizontal) Line Slide 32 Level Line Slide 33 Profile Line Slide 34 Slide 35 True Length of an Oblique Line Slide 36 Slide 37 Slide 38 Slide 39 Bearing, Slope, and Grade aHaH b 55 aHaH b S55 o E N N Bearing: a term used to describe the direction of a line on the earths surface Slide 40 aHaH 125 o N Azimuth Bearing b aHaH b N125 o Slide 41 problem A 160-m segment AB of a power line has a bearing of N 60 o and a downward slope of 20 o from the given point A. Complete the front and top views. ahah aFaF Slide 42 ahah aFaF N 60 o a1a1 20 o 160 m b b b D1 H F H 1 N Slide 43 Slide 44 Slide 45 Grade Grade: another way to describe the inclination of a line from the horizontal Plane Slide 46 Grade Slide 47 Slide 48 Slide 49 Planes Slide 50 Points and lines in Planes Slide 51 Locating a Point in a Plane Problem: 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 a F x m n oFoF n m oPoP Slide 52 Solution a F x m n oFoF n m oPoP X Y X Y aPxaPx Slide 53 Lines in Planes b c aFaF e b c g e aHaH Complete the front view Slide 54 Lines in Planes b c g e aHaH b c aFaF e x x g Slide 55 Principal Lines in Planes Slide 56 Frontal Line All frontal lines in the same plane are parallel unless the plane it self is frontal Slide 57 Horizontal or Level Lines Slide 58 All horizontal lines in the same plane are parallel unless the plane it self is horizontal Slide 59 Profile Line Slide 60 All profile lines in the same plane are parallel unless the plane it self is profile Slide 61 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. Slide 62 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 Slide 63 Solution c aHaH b aFaF b c h h h h f f f f K K 6 mm 5 mm Slide 64 Pictorial Intersection 2) If two planes are parallel, any lines on the planes in question are parallel. M K N H A B C E D Two principles to solve the problem: 1) Lines in a single plane must either be parallel or intersect. Slide 65 Pictorial Intersection Slide 66 Slide 67 Successive Auxiliary Views Slide 68 Construction of successive Auxiliary Views Step 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. Slide 69 Point View of a Line A 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. Slide 70 Point View of a Line ahah aFaF 1 b b H F Point View (P.V) T.L. b a2a2 a1,ba1,b 2 Slide 71 Problem I Find the true clearance between the point O and the line AB. ahah aFaF b b H F T.L. o o b ahah o 1 2 a2,ba2,b o Clearance Slide 72 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. Slide 73 Edge View of a Plane ahah aFaF 1 b b H F T.L. c c h h c b a E.V. Slide 74 Normal Views of a Plane A 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. Slide 75 Edge View of a Plane ahah aFaF 1 b b H F T.L. c c h h c b a E.V. 2 Normal View T.S. Slide 76 Uses of Auxiliary and additional Views Use Position of line of sight In spaceOn the drawing sheet 1) True length of line (TL)Perpendicular to line Perpendicular to any view of the line or directed to a point view of the line 2) Point view of lineParallel to lineParallel to the true length of the line 3) Edge view of plane (EV)Parallel to plane Parallel to true length of line in plane OR directed toward a true size view of plane 4) Normal or true size view of plane (TS) Perpendicular to plane Perpendicular to edge view of plane Slide 77 problem Find the front and top views of a 2.5m radius curve joining two intersecting lines BA & BC. Slide 78 a c b a c b f fTL c a b c b a Slide 79 a c b a c b f f c a b c b a 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 Slide 80 Piercing Points Slide 81 Piercing point The 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. Slide 82 Piercing point - Auxiliary View Method bHbH c a bFbF c a b 1,c a g e g e e g 1. p p p TL Slide 83 Piercing point- Two View Method A piercing point could be found using the given views as follows: ( see the following Fig.) 1) Any convenient cutting plane containing line EG is introduced, it appears EV in a principal view. 2) The line of intersection between the two planes is determined. 3) Since line EG and line 1 - 2 both lies in the cutting plane they intersect, locating point P. 4) Since line 1 2 also lies in Plane ABC, point P is the required Piercing Point. Slide 84 1 2 E G A B C Vertical cutting plane N P Piercing point- Two View Method Slide 85 bHbH c a bFbF c a g e g e p 1 2 1 2 p Vertical cutting plane N Slide 86 Intersection of Planes Slide 87 Any two 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. Slide 88 Intersection of Planes Auxiliary view Method bHbH c a g e x y bFbF c a J k g e J k f f b1b1 c a e k j g x y x y z z Slide 89 bHbH c a g e x y bFbF c a J k g e J k bHbH c a e k j g y z y z Slide 90 Intersection of Planes Two View - Piercing point Method b a cFcF d eFeF g d ePeP g b a cPcP x x y y Slide 91 b a cFcF d eFeF g d ePeP g b a cPcP E.V. 1 2 1 2 x x 3 4 3 4 yy L1 Slide 92 Intersection of Planes Two View - Piercing point Method b a cFcF d eFeF g d ePeP g b a cPcP Slide 93 Intersection of Planes Cutting Plane Method 1 2 3 4 5 6 7 8 H1 H2 P1 P2 Line of intersection b a c m o n Slide 94 Intersection of Planes Cutting Plane Method b a cHcH b a cFcF m o nHnH m o nHnH 1 2 3 4 EV of HI 1 2 3 4 P1 EV of H2 5 6 7 8 5 6 7 8 P2 LI P1 P2 LI Slide 95 Pictorial Intersection of Planes b a c n m k s e d o 2 3 Slide 96 Pictorial Intersection Of Planes b a c n m k 2 3 v Slide 97 Angle between Planes Slide 98 m n A B E.V. of m E.V. of n P.V. of line of intersection AB Line of sight Slide 99 Dihedral Angle Line of Intersection given eHeH LI A g eFeF g e1e1 g B TL LI B A E.V. of A E.V. of B e2ge2g Slide 100 Dihedral Angle Line of Intersection is NOT given bHbH a c bFbF a c o n m kHkH on m kFkF EV.1 EV.2 3 4 1 2 3 4 1 2 x y x y Slide 101 Dihedral Angle Line of Intersection is NOT given bHbH a c bFbF a c o n m kHkH on m kFkF x y x y b1b1 a c x y TL o n m k1k1 b2b2 c n m X,y Slide 102 Dihedral Angle Line of Intersection is NOT given Alternative solution: You can find the Edge View for both planes without resorting to find the line of intersection. See next slide Slide 103 Dihedral Angle Line of Intersection is NOT given bHbH a c bFbF a c o n m kHkH on m kFkF b2b2 c o n m k1k1 TL b 1,c a EV a o n m k2k2 TS TL Both Planes will Appear EV. 1 2 3 Slide 104 Angle between Oblique Plane and Principal Plane aHaH b c aFaF b c f f TL H F 1 a1a1 b c F ff EV of frontal plane Angle between plane and frontal plane Slide 105 Angle between Oblique Plane and Principal Plane aHaH b c aFaF b c TL H F EV of Profile plane c b aPaP P f f 1 a1a1 b c PP Angle between plane and Profile plane Slide 106 Angle between Oblique Plane and Principal Plane Angle 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. Slide 107 Angle between Oblique Plane and Principal Plane aHaH b c aFaF b c H F Angle between plane and horizontal plane f f 1 aHaH b c HH TL Slide 108 Parallelism Slide 109 Parallel Lines Oblique Lines that appears parallel in two or more principal views are parallel in space. Slide 110 Parallel Lines aHaH b d H F P c aFaF b d c b d c aPaP Slide 111 aHaH b d H F P c aFaF b d c b c d aPaP F Slide 112 Principal Line Two horizontal, two frontal, or two profile lines that appears to be parallel in two principal views may or may not be parallel in space. non intersecting, non parallel lines are called SKEW LINES. Slide 113 Parallel Lines aHaH X c H F P b aFaF b b aPaP F X a 1 b e c X X c P 1 Slide 114 Parallel Lines aHaH X c H F P b aFaF b b aPaP F X a 1 b e c X X c P 1 e X X e D1 D2 Slide 115 Parallel Planes mHmH o n mFmF o n aHaH c b aFaF c b f f TL 1 F H o m1m1 n b c a1a1 Slide 116 Parallel Planes If two 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. Slide 117 Lines parallel to planes Planes parallel to lines If two 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. Slide 118 Lines parallel to planes Planes parallel to lines x y x y m o r q p m o q p r Slide 119 Perpendicularity Slide 120 Perpendicular Lines If a line is perpendicular to a plane, it is perpendicular to every line in the Plane. x y g j e f 90 x1 y1 Perpendicular lines are not necessarily intersecting lines and they do not necessarily Lie in the same plane. Slide 121 Perpendicular Lines If two lines are perpendicular, they appear perpendicular in any view showing at least one of the lines in true length. If two 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. Slide 122 Perpendicular Lines m n o s o s m n m n o s H F H 1 TL Slide 123 Plane Perpendicular to Line Two-View Method A plane is perpendicular to a line if the plane contains two intersecting lines each of which is perpendicular to the given line. Slide 124 Plane Perpendicular to Line Two-View Method y z y z x h TL x h f f H F F 1 xf h z y EV TL Slide 125 Plane Perpendicular to Line Auxiliary-View Method y z y z x h x k H F F 1 x h z y EV TL k k h Slide 126 Line Perpendicular to Plane Two-View Method A line perpendicular to a plane is perpendicular to all lines in the plane. Slide 127 Line Perpendicular to Plane Two-View Method n o n o a a H F k m m h h TL k f f k Slide 128 Line Perpendicular to Plane Auxiliary-View Method n o n o a a H F k m m h h TL k a m o n EV k k TL Slide 129 Common Perpendicular Point View Method The shortest distance from a point to a line is measured along the perpendicular from the point to a line. The shortest distance between two skew lines is measured by a line perpendicular to each of them. Slide 130 Common Perpendicular Point View Method e a cb e c a b H F 1 a b e c TL 2 e c ab x Slide 131 Common Perpendicular Point View Method e a cb e c a b H F 1 a b e c TL 2 ab x e c TL x x y x y x y Slide 132 Common Perpendicular Plane Method Another method to find the shortest distance between skew lines, specially when the perpendicular view are not required. Slide 133 Common Perpendicular plane Method e a cb e c a b H F k k h h TL 1 x kh c e EV b a Shortest Distance Slide 134 Shortest line at specified Grade connecting Two Skew Lines e a c b e c a b H F p p h TL 1 x ph c e EV b a Shortest Horizontal Distance h h Slide 135 Shortest line at specified Grade connecting Two Skew Lines e a c b e c a b H F p p h TL 1 x ph c e EV b a h h 100 15 Slide 136 Projection of line on a Plane The projection of a point on a plane is the point in which a perpendicular from the point to the plane pierces the plane. Slide 137 Projection of line on a Plane n m o b a b a n m o F P h h TL 1 o m n ev a b ap bp TL ap bp ap bp Slide 138 X v b a a b 1 2 3 4 m n n m k o ok 1 2 3 4