10Steps to obtain a view Establish the line of sight. Introduce the folding lineTransfer distances to the new viewDetermine visibility and complete the view
11Primary Auxiliary Views Step 1: Establish the line of sight.Primary Auxiliary ViewsStep 2: Introduce the folding lineStep 3: transfer distancesa,ed,hyb,fc,gH1Step 4: determine visibility andcomplete view1D2D1Dyhdgk1eD2cyfaf,eg,hD1bb,ac,d
12All views projected from top view has the same height dimension
60Profile LineAll profile lines in the same plane are parallel unless the plane it self is profile
61LocusThe 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.
62LocusProblem: 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
64Pictorial 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.
68Construction 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.
69Point 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.
70Point View of a Line2ba2ahbHa1,bFbT.L.PointView (P.V)aF1
71Problem I Find the true clearance between the point O and the line AB. 1a2,bClearancebooahT.L.2HoFaFahbo
72Edge 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.
74Normal 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.
75Edge 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
76Uses 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
77problemFind the front and top views of a 2.5m radius curve joining two intersecting lines BA & BC.
81Piercing 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.
82Piercing point - Auxiliary View Method 1.eb1,ccpeTLbHapggaaepgcbF
83Piercing 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.
84Piercing point- Two View Method AVertical cutting plane N1EPGC2B
85Piercing point- Two View Method ae1pcVertical cutting plane N2bHga1epgcbF2
86Intersection of Planes Chapter 7Intersection of Planes
87Intersection 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.
88Intersection of Planes Auxiliary view Method bHexkzab1fykegJxcayjackgecxzyfJgbF
89Intersection of Planes Auxiliary view Method bHekzabHykegJxcayjackcgezyJgbF
90Intersection of Planes Two View - Piercing point Method bbddaaxxggyyeFePcFcP
91Intersection of Planes Two View - Piercing point Method bE.V.bddL1L12a2axxE.V.11gg4yy433eFePcFcP
92Intersection of Planes Two View - Piercing point Method bbddaaggeFePcFcP
93Intersection of Planes Cutting Plane Method Line of intersectionmcH1P12314H267P25b8nao
94Intersection of Planes Cutting Plane Method cHmP121346P278bnHLIo5acFm12EV of HIP143568EV of H2aP27obnHLI
98Angle 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
99Dihedral Angle Line of Intersection given eHBe1ATL LIeFgBLIe2gE.V. of AE.V. of Bθg
100Dihedral Angle Line of Intersection is NOT given 4ox32mkHybHc1aEV.1on34xbFEV.22ym1kFc
101Dihedral Angle Line of Intersection is NOT given b2anoX,yxmcθkHnybHmcaxob1anTLonxyk1bFmymkFcc
102Dihedral 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
103Dihedral Angle Line of Intersection is NOT given Both Planes willAppear EV.ab2noaTSmkHobHcck2TLn3aonm2bFTLmkFncmok1EVab1,c1
104Angle between Oblique Plane and Principal Plane EV of frontal planebaHfcHF1Fca1bθfcfTLbaFAngle between plane and frontal plane
105Angle between Oblique Plane and Principal Plane aHcHFP1ccTLbbaFffbaPEV of Profile planeθPca1Angle between plane and Profile plane
106Angle 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.
107Angle between Oblique Plane and Principal Plane 1aHbbθHaHTLcfcHFcfbaFAngle between plane and horizontal plane
112Principal 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.
113Parallel LinesaHX a1be c Xb1X cPHFFPaFaPX cX cbb
114Parallel Lines aH X e X a1b e c X b D2 1 X c P D1 H F F P aF D1 D2 aP
116Parallel 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.
117Lines 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.
118Lines parallel to planes Planes parallel to lines yrmxqpxqmoypr
120Perpendicular 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.
121Perpendicular 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.
123Plane 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.
124Plane Perpendicular to Line Two-View Method yhTLzxfHFxhzTLzfyxfEVFhTL1y
125Plane Perpendicular to Line Auxiliary-View Method kzxHhFxzkzyxEVFkhTL1y
126Line Perpendicular to Plane Two-View Method A line perpendicular to a plane is perpendicular to all lines in the plane.
127Line Perpendicular to Plane Two-View Method fTLomkHFoaTLkmhfkn
128Line Perpendicular to Plane Auxiliary-View Method TLEVnmakhTLoomHkFoakmhkn
129Common 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.
130Common Perpendicular Point View Method be12aeHeab xbFTLacaeccb
131Common Perpendicular Point View Method bxe1y2aexTLHeab xxbFTLacyaxecycb
132Common Perpendicular Plane Method Another method to find the shortest distance between skew lines, specially when the perpendicular view are not required.