PROJECTIONS OF PLANES

Transcription

1 PROJECTIONS OF PLANES A plne is two imensionl ojet hving length n reth only. Its thikness is lwys neglete. Vrious shpes of plne figures re onsiere suh s squre, retngle, irle, pentgon, hexgon, et.

2 PROJECTIONS OF PLANES In this topi vrious plne figures re the ojets. Wht is usully ske in the prolem? To rw their projetions mens F.V, T.V. & S.V. Wht will e given in the prolem? 1. Desription of the plne figure. 2. It s position with HP n VP. In whih mnner it s position with HP & VP will e esrie? 1.Inlintion of it s SURFACE with one of the referene plnes will e given. 2. Inlintion of one of it s EDGES with other referene plne will e given (Hene this will e se of n ojet inline to oth referene Plnes.) Stuy the illustrtion showing surfe & sie inlintion given on next pge.

3 CASE OF A RECTANGLE OBSERVE AND NOTE ALL STEPS. SURFACE PARALLEL TO HP PICTORIAL PRESENTATION SURFACE INCLINED TO HP PICTORIAL PRESENTATION ONE SMALL SIDE INCLINED TO VP PICTORIAL PRESENTATION VP ORTHOGRAPHIC TV-True Shpe FV- Line // to xy VP ORTHOGRAPHIC FV- Inline to TV- Reue Shpe ORTHOGRAPHIC FV- Apprent Shpe TV-Previous Shpe VP HP 1 1 A HP B C HP

4 Prolem 1: Retngle 30mm n 50mm sies is resting on HP on one smll sie whih is 30 0 inline to VP,while the surfe of the plne mkes 45 0 inlintion with HP. Drw it s projetions. Re prolem n nswer following questions 1. Surfe inline to whih plne? HP 2. Assumption for initil position? // to HP 3. So whih view will show True shpe? --- TV 4. Whih sie will e vertil? ---One smll sie. Hene egin with TV, rw retngle elow - rwing one smll sie vertil. Surfe // to Hp Surfe inline to Hp Sie Inline to Vp 1 1

5 Prolem 2: A set squre of longest sie 100 mm long, is in VP n 30 0 inline to HP while it s surfe is 45 0 inline to VP.Drw it s projetions (Surfe & Sie inlintions iretly given) 1 Re prolem n nswer following questions 1.Surfe inline to whih plne? VP 2. Assumption for initil position? // to VP 3. So whih view will show True shpe? --- FV 4. Whih sie will e vertil? longest sie. Hene egin with FV, rw tringle ove - keeping longest sie vertil. 1 sie inline to Hp Surfe // to Vp Surfe inline to Vp

6 Prolem 3: A set squre of longest sie 100 mm long is in VP n it s surfe 45 0 inline to VP. One en of longest sie is 10 mm n other en is 35 mm ove HP. Drw it s projetions (Surfe inlintion iretly given. Sie inlintion iniretly given) Re prolem n nswer following questions 1.Surfe inline to whih plne? VP 2. Assumption for initil position? // to VP 3. So whih view will show True shpe? --- FV 4. Whih sie will e vertil? longest sie. Hene egin with FV, rw tringle ove - keeping longest sie vertil. 1 1 First TWO steps re similr to previous prolem. Note the mnner in whih sie inlintion is given. En A 35 mm ove Hp & En B is 10 mm ove Hp. So rerw 2 n Fv s finl Fv pling these ens s si

7 Prolem 4: A regulr pentgon of 30 mm sies is resting on HP on one of it s sies with it s surfe 45 0 inline to HP. Drw it s projetions when the sie in HP mkes 30 0 ngle with VP SURFACE AND SIDE INCLINATIONS ARE DIRECTL GIVEN. Re prolem n nswer following questions 1. Surfe inline to whih plne? HP 2. Assumption for initil position? // to HP 3. So whih view will show True shpe? --- TV 4. Whih sie will e vertil? ny sie. Hene egin with TV,rw pentgon elow e - line, tking one sie vertil. 1 e 1 1 e e 45 0 e e

8 Prolem 5: A regulr pentgon of 30 mm sies is resting on HP on one of it s sies while it s opposite vertex (orner) is 30 mm ove HP. Drw projetions when sie in HP is 30 0 inline to VP. SURFACE INCLINATION INDIRECTL GIVEN SIDE INCLINATION DIRECTL GIVEN: Re prolem n nswer following questions 1. Surfe inline to whih plne? HP 2. Assumption for initil position? // to HP 3. So whih view will show True shpe? --- TV 4. Whih sie will e vertil? ny sie. Hene egin with TV,rw pentgon elow - line, tking one sie vertil. ONL CHANGE is the mnner in whih surfe inlintion is esrie: One sie on Hp & it s opposite orner 30 mm ove Hp. Hene rerw 1 st Fv s 2 n Fv mking ove rrngement. Keep on xy & 30 mm ove xy. 30 e 1 e 1 1 e 1 1 e 1 e 1 e

9 Prolem 8: A irle of 50 mm imeter is resting on Hp on en A of it s imeter AC whih is 30 0 inline to Hp while it s Tv is 45 0 inline to Vp.Drw it s projetions Re prolem n nswer following questions 1. Surfe inline to whih plne? HP 2. Assumption for initil position? // to HP 3. So whih view will show True shpe? --- TV 4. Whih imeter horizontl? AC Hene egin with TV,rw rhomus elow - line, tking longer igonl // to - Prolem 9: A irle of 50 mm imeter is resting on Hp on en A of it s imeter AC whih is 30 0 inline to Hp while it mkes 45 0 inline to Vp. Drw it s projetions. Note the ifferene in onstrution of 3 r step in oth solutions The ifferene in these two prolems is in step 3 only. In prolem no.8 inlintion of Tv of tht AC is given,it oul e rwn iretly s shown in 3 r step. While in no.9 ngle of AC itself i.e. it s TL, is given. Hene here ngle of TL is tken,lous of 1 Is rwn n then LTV I.e. 1 1 is mrke n finl TV ws omplete.stuy illustrtion refully

10 Prolem 10: En A of imeter AB of irle is in HP n en B is in VP.Dimeter AB, 50 mm long is 30 0 & 60 0 inline to HP & VP respetively. Drw projetions of irle. Re prolem n nswer following questions 1. Surfe inline to whih plne? HP 2. Assumption for initil position? // to HP 3. So whih view will show True shpe? --- TV 4. Whih imeter horizontl? AB Hene egin with TV,rw CIRCLE elow - line, tking DIA. AB // to - The prolem is similr to previous prolem of irle no.9. But in the 3 r step there is one more hnge. Like 9 th prolem True Length inlintion of i.ab is efinitely expete ut if you refully note - the the SUM of it s inlintions with HP & VP is Mens Line AB lies in Profile Plne. Hene it s oth Tv & Fv must rrive on one single projetor. So o the onstrution oringly AND note the se refully SOLVE SEPARATEL ON DRAWING SHEET GIVING NAMES TO VARIOUS POINTS AS USUAL, AS THE CASE IS IMPORTANT

11 Prolem 11: A hexgonl lmin hs its one sie in HP n Its pposite prllel sie is 25mm ove Hp n In Vp. Drw it s projetions. Tke sie of hexgon 30 mm long. ONL CHANGE is the mnner in whih surfe inlintion is esrie: One sie on Hp & it s opposite sie 25 mm ove Hp. Hene rerw 1 st Fv s 2 n Fv mking ove rrngement. Keep on xy & e 25 mm ove xy. Re prolem n nswer following questions 1. Surfe inline to whih plne? HP 2. Assumption for initil position? // to HP 3. So whih view will show True shpe? --- TV 4. Whih imeter horizontl? AC Hene egin with TV,rw rhomus elow - line, tking longer igonl // to - e 1 1 f f e e 25 1 f 1 e 1 f 1 f 1 1 e As 3 r step rerw 2 n Tv keeping sie DE on xy line. Beuse it is in VP s si in prolem.

12 FREEL SUSPENDED CASES. Prolem 12: An isoseles tringle of 40 mm long se sie, 60 mm long ltitue Is freely suspene from one orner of Bse sie.it s plne is 45 0 inline to Vp. Drw it s projetions. IMPORTANT POINTS 1.In this se the plne of the figure lwys remins perpeniulr to Hp. 2.It my remin prllel or inline to Vp. 3.Hene TV in this se will e lwys LINE view. 4.Assuming surfe // to Vp, rw true shpe in suspene position s FV. (Here keep line joining point of ontt & entroi of fig. vertil ) 5.Alwys egin with FV s True Shpe ut in suspene position. AS shown in 1 st FV. C 1 g 1 g 1 H H/3 G 1 A B First rw given tringle With given imensions, Lote it s entroi position An join it with point of suspension.,g 45 0 Similrly solve next prolem of Semi-irle

13 Prolem 13 :A semiirle of 100 mm imeter is suspene from point on its stright ege 30 mm from the mipoint of tht ege so tht the surfe mkes n ngle of 45 0 with VP. Drw its projetions. IMPORTANT POINTS 1.In this se the plne of the figure lwys remins perpeniulr to Hp. 2.It my remin prllel or inline to Vp. 3.Hene TV in this se will e lwys LINE view. 4.Assuming surfe // to Vp, rw true shpe in suspene position s FV. (Here keep line joining point of ontt & entroi of fig. vertil ) 5.Alwys egin with FV s True Shpe ut in suspene position. AS shown in 1 st FV. P A 20 mm p G CG g e First rw given semiirle With given imeter, Lote it s entroi position An join it with point of suspension. p,g e

14 To etermine true shpe of plne figure when it s projetions re given. B USING AUILIAR PLANE METHOD Follow the elow given steps: 1. Drw the given Fv & Tv s per the given informtion in prolem. 2. Then mong ll lines of Fv & Tv selet line showing True Length (T.L.) (It s other view must e // to xy) 3. Drw x 1 -y 1 perpeniulr to this line showing T.L. 4. Projet view on x 1 -y 1 ( it must e line view) 5. Drw x 2 -y 2 // to this line view & projet new view on it. It will e the require nswer i.e. True Shpe. WHAT WILL BE THE PROBLEM? Desription of finl Fv & Tv will e given. ou re suppose to etermine true shpe of tht plne figure. The fts you must know:- If you refully stuy n oserve the solutions of ll previous prolems, ou will fin IF ONE VIEW IS A LINE VIEW & THAT TOO PARALLEL TO LINE, THEN AND THEN IT S OTHER VIEW WILL SHOW TRUE SHAPE: NOW FINAL VIEWS ARE ALWAS SOME SHAPE, NOT LINE VIEWS: SO APPLING ABOVE METHOD: WE FIRST CONVERT ONE VIEW IN INCLINED LINE VIEW.(By using x1y1 ux.plne) THEN B MAKING IT // TO 2-2 WE GET TRUE SHAPE. Stuy Next Four Cses

15 Prolem 14 Tv is tringle. A is 50 mm long, ngle is 300 n ngle is 650. is Fv. is 25 mm, is 40 mm n is 10 mm ove Hp respetively. Drw projetions of tht figure n fin it s true shpe. As per the proeure- 1.First rw Fv & Tv s per the t. 2.In Tv line is // to xy hene it s other view is TL. So rw x 1 y 1 perpeniulr to it. 3.Projet view on x1y1. ) First rw projetors from & on x 1 y 1. ) from xy tke istnes of, & ( Tv) mrk on these projetors from x 1 y 1. Nme points 11 & 1. ) This line view is n Aux.Tv. Drw x 2 y 2 // to this line view n projet Aux. Fv on it. for tht from x 1 y 1 tke istnes of & n mrk from x 2 y= on new projetors. 4.Nme points 1 1 & 1 n join them. This will e the require true shpe C 1 C mm ALWAS FOR NEW FV TAKE DISTANCES OF PREVIOUS FV AND FOR NEW TV, DISTANCES OF PREVIOUS TV REMEMBER!!

16 PROBLEM 15: Fv & Tv oth re irles of 50 mm imeter. Determine true shpe of n elliptil plte. ADOPT SAME PROCEDURE. is onsiere s line // to xy. Then eomes TL for the purpose. Using steps properly true shpe n e Esily etermine. Stuy the illustrtion. 50D TL y y ALWAS, FOR NEW FV TAKE DISTANCES OF PREVIOUS FV AND FOR NEW TV, DISTANCES OF PREVIOUS TV REMEMBER!! 50 D. 1 TRUE SHAPE 1

17 Prolem 16 : Drw regulr pentgon of 30 mm sies with one sie 30 0 inline to xy. This figure is Tv of some plne whose Fv is A line 45 0 inline to xy. Determine it s true shpe. 1 1 IN THIS CASE ALSO TRUE LENGTH IS NOT AVAILABLE IN AN VIEW. 1 1 BUT ACTUALL WE DONOT REQUIRE TL TO FIND IT S TRUE SHAPE, AS ONE VIEW (FV) IS ALREAD A LINE VIEW. SO JUST B DRAWING 11 // TO THIS VIEW WE CAN PROJECT VIEW ON IT AND GET TRUE SHAPE: STUD THE ILLUSTRATION e e e ALWAS FOR NEW FV TAKE DISTANCES OF PREVIOUS FV AND FOR NEW TV, DISTANCES OF PREVIOUS TV REMEMBER!!