ME 111: Engineering Drawing - iitg.ac.in

1 me 111 : Engineering DrawingLecture Slides1 Link: 111: Engineering DrawingLecture 719-08-2011 Projection of Lines and2 Projection of Lines andProjection of PlanesIndian Institute of Technology GuwahatiGuwahati 781039 Projections of Lines3 Projections of LinesLine inclined to HP and VPApparent Inclinations:aaaaandbbbbApparent Lengths: ab, a b Line inclined to HP and projections of aline AB inclined to both HPand VP, whose true lengthandtrueinclinationsandlocations of one of the endpoints, say A are the line AB is inclinedatqqqqto HP andffffto VP itstopviewabandthe frontviewa b arenot intruelengths andtheyarealsonot inclinedat anglesqqqqtoHP andffffto inclined to HP and the lineABabout the endA,keepingqqqq, the inclination ofABwithHPconstant till it becomes paralleltoVP. This rotation of the line willbring the endBto the 1: Rotate the line AB to make it parallel to it is inclined atqqqqtoHPandparallel SinceAB1isparallel toVP,a b1 , theprojectionofAB1onVPis intruelength inclined atqqqqto theXYline,andab1, the projection ofAB1onHPis parallel to theXYline.

2 Nowtheline is rotatedbacktoits inclined to HP and 2: Rotate the line AB to make it parallel to the lineABabout the endAkeepingffffthe inclination ofABwithVPconstant, till it becomes parallel rotation of the line will bring theendBto the second new ,AB2isthenewpositionofthelineAB,whenit isinclinedatfffftoVPandparallel on HP and VP. SinceAB2is parallel toHP, ab2, the projection ofAB2on HPis in true length inclined atffffto XYline, anda b2 the projection ofAB2onVPis parallel toXYline. Nowthe line is rotatedback to its inclined to HP and 3: Locus of end B in the front viewWhen the line ABis swept around about theendAkeepingqqqq, the inclinationof the linewiththeHPconstant,byonecompleterotat ion, the end B will always be at the samevertical height above HP, and the locus of theend Bwill be a circle which appears in thefrontviewasahorizontallinepassingthro ugh b'.

3 As longas the line is inclinedatqqqqto HP,whatever may be the position of the line ( ,whatever may be the inclinationof the linewithVP) thelengthof thetopviewwillalways be equal to ab1 and in the front viewthe projection of the end Blies on the locusline passing through b1 .Thus ab1, the top viewof the line when it isinclined atqqqqto HP and parallel to VP will beequal to ab and b , the projection of the endBinthefrontviewwilllieonthelocuslineL ine inclined to HP and 4: Locus of end B in the top viewWhen the lineABis swept around about the endAkeepingffffthe inclinationof the line withtheVPconstant, by one complete rotation, the endBwillalways be at the same distance in front ofVPandthe locus of the endBwill be a circle which appearsinthe topviewas a line, parallel toXY, long as the line is inclined atfffftoVP, whatevermay be the position of the line ( , whatever maybe the inclination of the line withHP)

4 , the length ofthe front viewwill always be equal toa'b2'and inthe top viewthe projection of the endBlies on thelocus line passing b2 the front viewof the line whenit isinclined atfffftoVPand parallel toHP, will be equaltoa'b'and alsob, the projection of the endBin thetop view lies on the locus line passing inclined to HP and Fromthe above two cases of rotation itcan be said that(i)the length of the line AB in top and front viewswill be equal toab1anda'b2'respectively and(ii) the projections of the endB, ( ,bandb )shouldliealongthelocuslinepassingthroug hStep 5: To obtain the top and front views of ABshouldliealongthelocuslinepassingthrou ghb2andb1 respectively. With center a, and radius ab2drawanarc to intersect the locus line through b2at b. Connect ab the top view of the lineAB. Similarlywith centera', and radiusa'b2'drawanarc tointersect the locus linethroughb1'atb.

5 Connecta'b'the frontview of the inclined to HP and VPOrthographic the location of one of the end points( )with respect toHPandVP,isgiven, markaanda , the top and thefront views of the lineABis assumed to bemadeparalleltoVPandinclinedatqqqqtomad eparalleltoVPandinclinedatqqqqtoHP. The front viewof the line will beequal to the true length of the line andalso, the inclination of the line with HPis seeninthe front view. Drawa'b1'passing througha'atqqqqtoXYline andequal to the true length ofAB. a'b1' isprojected down to get ab1, the top viewparallel to the XY inclined to HP and lineABis assumed to be made paralleltoHPand inclined atfffftoVP. The top viewofthe line will be equal to the true length of theline and alsoffff, the inclination of the line withVPis seen in the top throughaatffffto theXYlineandequal tothe true lengthofAB.

6 Ab2, isprojecteduptogeta'b2',thefrontviewpara llelprojecteduptogeta'b2',thefrontviewpa rallelto the XY horizontal locus lines through b2, andb1'. centeraand radiusab1, drawan arc to cutthe locus line drawn throughb2atb. Connectab, the top view of the centera'and radiusa'b2 ,drawan arc tocut thelocus linedrawnthroughb1'atb'.Connecta'b', the front view of the Find True length and true inclinations of a line Given : The top and front views of a line are given This is of great importance since some of the Engineering problems may be solved by this principle. The problems may be solved by (i) Rotating line methodor (i) Rotating line methodor (ii) Rotating trapezoidal plane methodRotating trapezoidal plane method or (iii) Auxiliary plane method. Thetopandfront viewsof theobject canbedrawnfromthefollowingdata: (a)Distancebetweentheendprojectors, (b)Distance of one or both the end points fromHP and VPand(c)Apparent inclinations of the line.

7 The method of obtaining the topandfront views of a line, whenitstruelengthandtrueinclinations are given. When a viewof a line is parallelto the XY line, its other viewwillbeintruelengthandat line methodinclination. Byfollowingtheaboveprocedure, inthe reverse order,thetruelengthandtrueinclinationsof alinefromthegiven set of top and front viewscan be by Step and front views Draw the top view ab and the front view a'b' as given2. Rotation of the top view2. Rotation of the top view With centeraand radius ab rotate the top view to the new position ab1to make it parallel to the XY line. Since ab1is parallel to theXYline, its corresponding front view will be in true length and at true Rotation of the front viewSimilarly, with center a'and radius a'b' rotate the front view to the new position a'b2'parallel to the XY line.

8 Since a'b2'is parallel to the XYline, its corresponding top view will be in true length and at true this position, the line will be parallel to HPand inclined at ffffto VP. Through bdraw the locus of Bin the top view. Project b2'to get b2,in the top view. Connect ab2which will be in true length and true inclination ffffwhich the given line ABmakes of a line The trace of a line is defined as a point at which thegiven line, if produced, meets or intersects a plane. When a line meets HP, (or if necessary on the extendedportion-of HP), thepoint at whichthelinemeetsorintersectsthehorizont alplane,iscalledhorizontalintersectstheh orizontalplane,iscalledhorizontaltrace (HT)of the line and denoted by the letter H. When a line meets VP (or if necessary on the extendedportionof VP), the point at whichthe linemeetsorintersects the vertical plane, is called vertical trace (VT)of the line and denoted by the letter V.

9 When the line is parallel to both HP and VP, there will be no traces on the said planes. Therefore the traces of lines are determined in the following positions of the lines. Lines perpendicular to one plane and parallel to the other. Lines inclined to one plane and parallel to the other. Lines inclined to one plane and parallel to the other. Lines inclined to both the planes. Trace of a line perpendicular to one plane and parallel to the otherSince the line is perpendicular to one plane and parallel to the other, thetrace of the line is obtained only on the plane to which it is perpendicular,and no trace of the line is obtained on the other plane to which it is Perpendicular to VP and Parallel to HP:TRACE of the line perpendicular to the VP Traces of a line inclined to one plane and parallel to the otherWhen the line is inclined to one plane and parallel to the other, the trace of the line is obtained only on the plane to which it is inclined, and no trace is obtained on the plane to which it is inclined atqqqqtoHP and parallel toVPLine inclined at ffffto VP and parallel to HPLine inclined at qqqqto HP and jjjjto VP.

10 The line when extended intersects HP at H, the horizontal trace, but will never intersect the portion of VP above XY line, within the portion of the VP in the 1stquadrant. Therefore VP is extended below HP such that when the line AB is produced it will intersect in the extended portion of VP at V, the vertical this case both HT and VT of the line AB lie below XY of a line inclined to both the planesProjection of PlanesProjection of Planes28 IIT GUWAHATITERMS USED IN PROJECTIONS OF PLANES True ShapeThe actual shape of a plane is called itstrue shape. Inclination with the HP:It is the acute angle the plane makes with the HP. Inclination with the VPIt is the acute angle the plane makes with the VP. Traces of the PlaneThe traces of a plane are the lines of intersections ofthe plane with the RPs. A plane may have a horizontal trace or vertical trace or both.