Presentation on theme: "Projection of straight line"— Presentation transcript:
1Projection of straight line Line inclined to both HP & VPType-IGiven projections (FV & TV) of the line. To find True length & true inclination of the line with HP (θ) and with VP(Φ).PROBLEMEnd A of a line AB is 15mm above HP & 20mm in front of VP while its end B is 50mm above HP and 75mm in front of VP. The distance between end projectors of the line is 50mm. Draw projections of the line and find its true length and true inclination with the principal planes. Also mark its traces.
2θ: True inclination of the line with HP = 24º b1’b’θ: True inclination of the line with HP = 24ºTL50a’b2’α : Inclination of FV of the line with HP/XYαθHT15VT’XYvh’50Ø: True inclination of the line with VP = 41º20Φβb1aβ : Inclination of TV of the line with VP/XY75TLb2b
3Line inclined to both HP & VP Type –IIGiven (i) T.L., θ and Ø,(ii) T.L., F.V., T.V.to draw projections, find α, β,H.T. and V.T.PROBLEMA line AB, 70mm long, has its end A 15mm above HP and 20mm in front of VP. It is inclined at 30° to HP and 45°to VP. Draw its projections and mark its traces.
5Q The top view of a 75mm long line AB measures 65mm,while its front view measures 50mm. Its one end A is in HP and12mm in front of VP. Draw the projections of AB and determine its inclination with HP and VPTo draw FV &TV of the line ABTo find θ & ØGiven,TL=75mm,TV=65mm,FV=50mmA is in HP & 12mm→VPHint: Draw ab1=65mm // to XY. Because when TV is // to XY, FV gives TL.b’b1’Ans. θ=31º5075Ans. Ø=49ºa’XY31º1265b1a49º7565bb2
6Q10. 12 A line AB, 65mm long has its end A 20mm above H. P Q A line AB, 65mm long has its end A 20mm above H.P. and 25mm in front of VP. The end B is 40mm above H.P. and 65mm in front of V.P. Draw the projections of AB and show its inclination with H.P. and V.P.Given,TL=65mmA is 20mm ↑ HP & 25mm →V.P B is 40mm ↑ & 65mm → V.P.To draw FV &TV of the line ABTo find θ & ØHint1:Mark a’ 20mm above H.P & a 25mm below XYb’b1’Hint2:Draw locus of b’ 40mm above XY & locus of b 65 mm below XYa’65b2’4018º20XY25Ans. θ=18º38ºb1a65Ans. Ø=38º65bb2
7Q10. 13:The projectors of the ends of a line AB are 5cm apart Q10.13:The projectors of the ends of a line AB are 5cm apart. The end A is 2cm above the H.P and 3cm in front of V.P. The end B is1cm below H.P. and 4cm behind the V.P. Determine the true length and traces of AB, and its inclination with the two planesGiven,A0B0=50mm A is 20mm ↑ HP & 30mm →V.P B is 10mm ↓ & 40mm ← V.P.To find, True Length, θ,Ø, H.T. and V.T.bb2a’40HTb2’20VT’91XvY50h’103020ºb’Ans. θ=20ºa50ºb1Ans. Ø=50º
8Q10. 14:A line AB, 90mm long, is inclined at 45 to the H. P Q10.14:A line AB, 90mm long, is inclined at 45 to the H.P. and its top view makes an angle of 60 with the V.P. The end A is in the H.P. and 12mm in front of V.P. Draw its front view and find its true inclination with the V.P.b’Given,T.L.=90mm, θ=45º, β=60º A is in the H.P. & 12mm→V.P.b1’To find/draw,F.V.,T.V. & Ø90Ans. Ø = 38ºa’XY45º12b160º38ºa90b2b
9Q10. 16:The end A of a line AB is 25 mm behind the V. P Q10.16:The end A of a line AB is 25 mm behind the V.P. and is below the H.P. The end B is 12 mm in front of the VP and is above the HP The distance between the projectors is 65mm. The line is inclined at 40 to the HP and its HT is 20 mm behind the VP. Draw the projections of the line and determine its true length and the VTGiven,A0B0=65mm A is 25mm ←V.P.& is ↓H.P B is 12mm →V.P. & is above HP θ = 40ºTo find/draw,F.V., T.V., T.L., VT’b’b1’b2’VT’ab125HTb220Xh’Y40ºv12a’b65
1010. 17:A line AB, 90mm long, is inclined at 30 to the HP 10.17:A line AB, 90mm long, is inclined at 30 to the HP. Its end A is 12mm above the HP and 20mm in front of the VP. Its FV measures 65mm. Draw the TV of AB and determine its inclination with the VPb’b1’9065a’1230°XY20b144°aAns: Ø = 44º90bb2
11Q10.23:Two lines AB & AC make an angle of 120 between them in their FV & TV. AB is parallel to both the HP & VP. Determine the real angle between AB & AC.Cc1’c2’c’112°Ans. 112ºa’b’120°XYabc2c1120°c
12Q8:A line AB 65 mm long has its end A in the H. P Q8:A line AB 65 mm long has its end A in the H.P. & 15 mm infront of the V.P.The end B is in the third quadrant. The line is inclined at 30 to the H.P. and at 60 to the V.P. Draw its projections.
13Q10. 19 A line AB, inclined at 40º to the V. P Q10.19 A line AB, inclined at 40º to the V.P. has its end 50mm and 20mm above the H.P. the length of its front view is 65mm and its V.T. is 10mm above the H.P. determine .the true length of AB its inclination with the H.P. and its H.T.Given,Ø = 40º, A is 20mm↑HP, B is 50 mm ↑ HP, FV=65mm, VT is 10mm ↑ HPTo find,TL, θ & HTb1’b’8550a’b2’21ºHTVT’2010XYv40ºh’b1Ans,TL = 85 mm, θ = 21º & HT is 17 mm behind VPab2b
14Q6. The top view of a 75mm long line CD measures 50 mm Q6. The top view of a 75mm long line CD measures 50 mm. C is 50 mm in front of the VP & 15mm below the HP. D is 15 mm in front of the VP & is above the HP. Draw the FV of CD & find its inclinations with the HP and the VP. Show also its traces.Given,TL = 75 mm, FV =50 mm, C is 15mm ↓ HP & 50 mm → VP, D is 15 mm → VPTo draw,FV & to find θ & Ød1’d’Hint 1: Cut anarc of 50 mm from c on locus of DHint 2: Make TV (cd), // to XY so that FV will give TL75XY15d2Ans: Ø=48ºd50c’Locus of DØ=48ºAns: θ=28º50θ=28ºd1c
15Q10. 10 A line PQ 100 mm long is inclined at 30º to the H. P Q A line PQ 100 mm long is inclined at 30º to the H.P. and at 45º to the V.P. Its mid point is in the V.P. and 20 mm above the H.P. Draw its projections, if its end P is in the third quadrant and Q is in the first quadrant.Given,TL = 100, θ = 30º, Mid point M is 20mm↑HP & in the VP End P in third quadrant & End Q in first quadrantTo draw,FV & TVq’q1’p2p50p2’m’q2’5030º5020p1XYmp1’p’q250qq2