60 Profile LineAll profile lines in the same plane are parallel unless the plane it self is profile
61 LocusThe 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 curveThe locus of a point moving in a plane with a specified distance from another point is circle.
62 LocusProblem: 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
64 Pictorial Intersection BHDNECKMTwo principles to solve the problem:1) Lines in a single plane must either be parallel or intersect.2) If two planes are parallel, any lines on the planes in question are parallel.
68 Construction of successive Auxiliary Views Step 1: Establish the line of sight.Step 2: Introduce the necessary foldinglines.Step 3: transfer distance to the new view.Step 4: Complete view.
69 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.
70 Point View of a Line2ba2ahbHa1,bFbT.L.PointView (P.V)aF1
71 Problem I Find the true clearance between the point O and the line AB. 1a2,bClearancebooahT.L.2HoFaFahbo
72 Edge View of a PlaneA 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.
74 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.
75 Edge View of a Plane c 2 c h E.V. ah b a H b F c h b T.L. 1 aF Normal ViewT.S.baHFbchbT.L.1aF
76 Uses of Auxiliary and additional Views Position of line of sightIn spaceOn the drawing sheet1) True length of line (TL)Perpendicular to linePerpendicular to any view of the line or directed to a point view of the line2) Point view of lineParallel to lineParallel to the true length of the line3) Edge view of plane (EV)Parallel to planeParallel to true length of line in plane OR directed toward a true size view of plane4) Normal or true size viewof plane (TS)Perpendicular to planePerpendicular to edge view of plane
77 problemFind the front and top views of a 2.5m radius curve joining two intersecting lines BA & BC.
81 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.
82 Piercing point - Auxiliary View Method 1.eb1,ccpeTLbHapggaaepgcbF
83 Piercing point- Two View Method A 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 two planes is determined.Since line EG and line 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.
84 Piercing point- Two View Method AVertical cutting plane N1EPGC2B
85 Piercing point- Two View Method ae1pcVertical cutting plane N2bHga1epgcbF2
86 Intersection of Planes Chapter 7Intersection of Planes
87 Intersection of Planes 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.
88 Intersection of Planes Auxiliary view Method bHexkzab1fykegJxcayjackgecxzyfJgbF
89 Intersection of Planes Auxiliary view Method bHekzabHykegJxcayjackcgezyJgbF
90 Intersection of Planes Two View - Piercing point Method bbddaaxxggyyeFePcFcP
91 Intersection of Planes Two View - Piercing point Method bE.V.bddL1L12a2axxE.V.11gg4yy433eFePcFcP
92 Intersection of Planes Two View - Piercing point Method bbddaaggeFePcFcP
93 Intersection of Planes Cutting Plane Method Line of intersectionmcH1P12314H267P25b8nao
94 Intersection of Planes Cutting Plane Method cHmP121346P278bnHLIo5acFm12EV of HIP143568EV of H2aP27obnHLI
98 Angle between Planes B θ m E.V. of m θ n E.V. of n A P.V. of line of intersection ABLine of sight
99 Dihedral Angle Line of Intersection given eHBe1ATL LIeFgBLIe2gE.V. of AE.V. of Bθg
100 Dihedral Angle Line of Intersection is NOT given 4ox32mkHybHc1aEV.1on34xbFEV.22ym1kFc
101 Dihedral Angle Line of Intersection is NOT given b2anoX,yxmcθkHnybHmcaxob1anTLonxyk1bFmymkFcc
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
103 Dihedral Angle Line of Intersection is NOT given Both Planes willAppear EV.ab2noaTSmkHobHcck2TLn3aonm2bFTLmkFncmok1EVab1,c1
104 Angle between Oblique Plane and Principal Plane EV of frontal planebaHfcHF1Fca1bθfcfTLbaFAngle between plane and frontal plane
105 Angle between Oblique Plane and Principal Plane aHcHFP1ccTLbbaFffbaPEV of Profile planeθPca1Angle between plane and Profile plane
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.
107 Angle between Oblique Plane and Principal Plane 1aHbbθHaHTLcfcHFcfbaFAngle between plane and horizontal plane
112 Principal LineTwo 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.
113 Parallel LinesaHX a1be c Xb1X cPHFFPaFaPX cX cbb
114 Parallel Lines aH X e X a1b e c X b D2 1 X c P D1 H F F P aF D1 D2 aP
116 Parallel PlanesIf 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.
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.
118 Lines parallel to planes Planes parallel to lines yrmxqpxqmoypr
120 Perpendicular LinesIf a line is perpendicular to a plane, it is perpendicular to every line in the Plane.ey1g9090yfjx1xPerpendicular lines are not necessarily intersecting lines and they do not necessarilyLie in the same plane.
121 Perpendicular LinesIf 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.
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.
124 Plane Perpendicular to Line Two-View Method yhTLzxfHFxhzTLzfyxfEVFhTL1y
125 Plane Perpendicular to Line Auxiliary-View Method kzxHhFxzkzyxEVFkhTL1y
126 Line Perpendicular to Plane Two-View Method A line perpendicular to a plane is perpendicular to all lines in the plane.
127 Line Perpendicular to Plane Two-View Method fTLomkHFoaTLkmhfkn
128 Line Perpendicular to Plane Auxiliary-View Method TLEVnmakhTLoomHkFoakmhkn
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.
130 Common Perpendicular Point View Method be12aeHeab xbFTLacaeccb
131 Common Perpendicular Point View Method bxe1y2aexTLHeab xxbFTLacyaxecycb
132 Common Perpendicular Plane Method Another method to find the shortest distance between skew lines, specially when the perpendicular view are not required.
133 Common Perpendicular plane Method 1cx khShortest DistancebkEVTLchbeeaHaFaehkcb
134 Shortest line at specified Grade connecting Two Skew Lines 1chTLpceEVbx phbaeHShortest Horizontal DistanceFbhachpae
135 Shortest line at specified Grade connecting Two Skew Lines 1chTLpceEVbx phba100eHFbhac15hpae
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.
137 Projection of line on a Plane mm1apapTLbbnnabpbphhbTLooevFPombpapn