Lab 06. Sectional views. Objects with hidden details

Transcription

1 Lab 06 Sectional views Objects with hidden details

2 what we need 1. Cutting plane 2. Part, assembly, any 3-D view. Sectional Views Cross section Section Required to add information of surfaces that are represented by hidden lines in standard FV, TV, and SV. 2

3 Section (thin parallel) lined areas are those portions that came in actual contact with cutting plane. Visible parts behind the cutting plane are shown, but not hatched.

4 Hatching Pattern Continuous thin lines at convenient angle (preferably 45 ) to the principal outlines.

5 Spacing between the hatching lines should be chosen in proportion to the size of the hatched areas, provided that the requirement for minimum spacing are maintained. Common Mistakes

6 Full section view

7 NOTES Sectional views are always viewed in the direction defined by cutting plane arrows. Any hidden surface that is behind cutting plane is not included in sectional view. Hatch lines represent location of cutting plane passing through solid material. 7

8 Full & Half section views

9 Example: Sectional Orthographic Views A A Mistakes in dimensioning? Representation of cutting plane? 9

10 Section B-B a b c Rib not sectioned Common mistake is to omit back edge Section A-A 10

11 Sectional view of Ribs Ribs add strength and rigidity to an object. Usually narrow. 11

12 Pg. 167 Luzadder book Keyway Front view a) Although the spoke is in line with the front view, it can give the impression that it is a stunted spoke b) Sectioned spoke can indicate that it is a continuous web c) The full length of spoke is shown to indicate the structure. It should be shown along with front view to indicate the number of spokes and angles between them 12

13 Revolved sections Cutting plane Section rotated 90 o so that exact shape can be viewed 13

14 Examples of Revolved Sections Revolved sections examples show the shape of an object s cross-section superimposed on a longitudinal view

15 Removed Sections Removed sections are like revolved sections but moved aside. Section A-A Section B-B B A A B Section C-C C C

16 Offset Sections Cutting plane lines need not be drawn as straight lines Stepped line Include as many features as possible without causing confusion Offset full section 16

17 Countersunk hole 17

18 Choosing Full/Half/Broken sectional view Half & Partial sectional views --- allow showing outer and inner features on the same figure. Normal half/partial orthographic projection may include hidden lines. Broken line is a freehand line. 18

19 Sectional view of Ribs Ribs add strength and rigidity to an object. Usually narrow. 19

20 Cutting Plane Lines Phantom line 20

21 Section B-B Section A-A

22 ALIGNED SECTIONS To include, in a section, certain angled elements, cutting plane may be bent so as to pass through those features. Plane & feature are aligned into original plane. 22

23 Summary When a part is cut fully in half, the resulting view is called a full section. A line called the cutting-plane line shows where the object was cut and from which direction the section is viewed. The arrows point toward the section being viewed. In the section view, the areas that would have been in actual contact with the cutting plane are show with section lining. The visible edges of the object behind the cutting plane are generally shown because they are now visible but they are not cross-hatched. Section views can replace the normal top, front, side, or any other standard orthographic view.

24 Summary Labeling!! When a cutting plane coincides with a center line, the cutting plane line takes precedence. Omit hidden lines in section views. A section-lined area is always completely bounded by a visible outline

25 Summary To avoid a false impression of thickness and solidity, ribs/webs, gear teeth, and other similar features are not hatched with section lining even though the cutting plane slices them. Sectional views are important for assemblies.

26 Sheet 7

27 PROBLEM: A room is of size L=6.5m, D=5m, H=3.5m. An electric bulb hangs 1m below the center of ceiling. A switch is placed in one of the corners of the room, 1.5m above the flooring. Draw the projections and determine real distance between the bulb & switch. PROBLEM:- A picture frame 2 m wide and 1 m tall is resting on horizontal wall railing makes 35 0 inclination with wall. It is attached to a hook in the wall by two strings. The hook is 1.5 m above wall railing. Determine length of each chain and true angle between them 27

28 3.5 x 1.5 a a b b 1 y PROBLEM: L=6.5m, D=5m, H=3.5m. An electric bulb hangs 1m below the center of ceiling. A switch is placed in one of the corners of the room, 1.5m above the flooring. Draw the projections and determine real distance between the bulb and switch. 5 b Answer: a b 1 All Dimensions in m.

29 a b h (chains) 1.5 m PROBLEM- A picture frame 2 m wide & 1 m tall is resting on horizontal wall railing makes 35 0 inclination with wall. It is attached to a hook in the wall by two strings. The hook is 1.5 m above the wall railing. 1m c d (wall railing) DETERMINE LENGTH OF EACH CHAIN AND TRUE ANGLE BETWEEN THEM X a 1 a d Y (frame) h b 1 b c (chains) Answers: Length of each chain= hb 1 True angle between chains =

30 F T Rectangular lamina parallel to V.P. F T F T Pentagonal lamina parallel to V.P. Pentagonal lamina parallel to H.P. FV shall replace TV & TV shall replace FV

31 Problem. A square pyramid, 40 mm base sides and axis 60 mm long, has a triangular face on the ground. Draw its projections. 1 st. Angle o F F a F b F c F d F T at d T d 1 a 1 o o 1 b T c T c 1 b 1 31

32 Ex: A line AB, 50 mm long, is inclined at 30 to the H.P. Draw its projections. a F b F T F a T b T

33 PROBLEM:- Two mangos on a tree A & B are 1.5 m and 3.0 m above ground and those are 1.2 m & 1.5 m from a 0.3 m thick wall but on opposite sides of it. If the distance measured between them along the ground and parallel to wall is 2.6 m, Then find real distance between them by drawing their projections. TV B A 0.3M THICK 33

34 1.5 a b 3.0 PROBLEM:- Two mangos on a tree A & B are 1.5 m and 3.00 m above ground and those are 1.2 m & 1.5 m from a 0.3 m thick wall but on opposite sides of it. If the distance measured between them along the ground and parallel to wall is 2.6 m, Then find real distance between them by drawing their projections. 2.6 b B a All dimensions in m.

35 PROBLEM:-Flower A is 1.5 m & 1 m from walls Q (parallel to reference line) & P (perpendicular to reference line) respectively. Flower is 1.5 m above the ground. Orange B is 3.5m & 5.5m from walls Q & P respectively. Drawing projection, find distance between them If orange is 3.5 m above ground. b b a Ground x 1.5 y Wall Q B 1.5 a Wall P 5.5 b All dimensions in m. 35

36 PROBLEM :- An object contains three rods OA, OB and OC whose ends A,B & C are on ground and end O is 100mm above ground. The top view of object contains three lines oa, ob & oc having length equal to 25mm, 45mm and 65mm respectively. These three lines are equally inclined and the shortest line is vertical. Draw their projections and find length of each rod. Tv O A C Fv B

37 PROBLEM :- A top view of object (three rods OA, OB and OC whose ends A,B & C are on ground and end O is 100mm above ground) contains three lines oa, ob & oc having length equal to 25mm, 45mm and 65mm respectively. These three lines are equally inclined and the shortest line is vertical. Draw their projections and find length of each rod. o TL 2 TL 1 x b 1 b a a 1 c c 1 y a b o Answers: TL 1 TL 2 & TL 3 c

38 PROBLEM:- A pipeline from point A has a downward gradient 1:5 and it runs due South - East. Another Point B is 12 m from A and due East of A and in same level of A. Pipe line from B runs 15 0 Due East of South and meets pipeline from A at point C. Draw projections and find length of pipe line from B and it s inclination with ground. 5 1 A 12 M B E C

39 PROBLEM:- A pipe line from point A has a downward gradient 1:5 and it runs due South - East. Another Point B is 12 m from A and due East of A and in same level of A. Pipe line from B runs 15 0 Due East of South and meets pipe line from A at point C. Draw projections and find length of pipe line from B and it s inclination with ground. 12m a 5 1 b F c c 1 c 2 T N W a 45 0 b EAST 15 0 c = Inclination of pipe line BC SOUTH

40 PROBLEM: A person observes two objects, A & B, on the ground, from a tower, 15 M high, at the angles of depression 30 0 & 45 0 respectively. Object A is due North-West direction of observer and object B is due West direction. Draw projections of situation and find distance of objects from observer and from tower also. O A W B S

41 a 1 a b a o N 15M PROBLEM: A person observes two objects, A & B, on the ground, from a tower, 15 M high, at the angles of depression 30 0 & Object A is due North-West direction of observer and object B is due West direction. Draw projections of situation and find distance of objects from observer and from tower also. W b Answers: Distances of objects from observe o a 1 & o b From tower oa & ob S o E Dimensions in m

42 b 1 a 2, b 2 Point view of line Shortest distance a 2 p 2 a 1 p 1 p 2 Point a T p b Auxiliary plane method. Find point view of line. Draw reference line parallel to line and obtain true length. F a p SHORTEST distance between POINT & LINE b

43 Shortest Distance between 2 skew Lines (AB & CD) Distance between intersecting (or //) lines???? Skew (oblique) lines Lines that are not parallel & do not intersect c Distance measured along Shortest to both. b Find T.L. of one of the lines and project its point view using auxiliary plane method a a c d b d T F Project the other line also in each view. Shortest distance between skew lines can be measured along the one line perpendicular to both. Common perpendicular!! 43

44 c Primary auxiliary view TL d d, c Secondary auxiliary view Required distance c a b a d b T F d a b B P A a c d q dp is to ab In mines, this method might be used to locate a connecting tunnel.

45 Piercing Point Intersection between a line and plane Point Piercing point. True angle between line and plane?? 45

46 Piercing point of a line with a plane Edge view of the plane Mistake? Line T F True length of principal line f d f' d' Principal line b T p A1 f 1 a 1 p 1 p Plane b' a' e' Part of the line hidden by the plane should be shown dotted a e c c' c 1 d 1 e 1 In a view showing the plane as an edge, the piercing point appears where the line intersects the edge view. Draw auxiliary view to get EDGE VIEW. How to find angle between a line and a given plane?

47 Concept of Principal lines of a plane C All the points lie on a straight line representing the edge of the plane Point view T B A TL T A1 F A B C Principal line Principle lines: Lines on the boundary or within the surface, parallel to the principle planes of projection

48 To obtain the edge view of a plane True length T F a a c c b b Horizontal line (parallel to top plane) l l c 1 a 1 b 1 -Draw a principle line in one principle view and project the true length line in the other principle view -With the reference line perpendicular to the true length line, draw a primary auxiliary view of the plane, to obtain the edge view Distances: Edge view of the plane a 1, b 1, c 1 from TA = a, b, c from FT

49 Find the shortest distance of point P from the body diagonal AB of the cube of side 50 mm as shown b1 a1 a 1, b 1 p1 10 Required distance p 1 d g 10 p b, e Draw an auxiliary view to get the true length of the line 50 Draw an auxiliary view to get the point view of the diagonal Project the point P in these views to get the required distance F, A f,d p c, d c,b a,g d,e

50 True Angle between 2 Skew Lines (AB & CD) Measure angle in view that Shows both lines in true length x T F c a a d d b c b y Draw P.A. V. such that one line (AB) shows its True Length Draw S.A.V. view with reference line perpendicular to the True Length of the line (AB) to get the point view of the line Draw a tertiary auxiliary view with reference line parallel to the other line in order to get its True Length Since the secondary auxiliary view had the point view of the first line, the tertiary auxiliary view will have the True Length of the first line also. 50

51 ANGLE BETWEEN TWO LINES Parallel c3 a3 TERTIARY AUXILIARY VIEW TRUE LENGTH OF BOTH LINES PRIMARY AUXILIARY VIEW c2 a2,b2 b3 d3 True Angle between the two lines True length c1 a1 b1 d1 d2 Point view of one line SECONDARY AUXILIARY VIEW x T F c a a d d b Parallel y Angle between two nonintersecting lines is measurable in a view that shows both lines in true shape. c b

52 Angle between 2 planes a T F a e d d e b b f c c f Obtain an auxiliary view such that the reference line is perpendicular to the True Length of the line of intersection of the planes In this case, the intersection line is parallel to both principle planes and hence is in True Length in both front and top views Both planes will be seen as edge views in the auxiliary view. The angle between the edge views is the angle between the planes

53 Line of intersection of the 2 planes (here it is True Length) e f x1 f1, e1 PRIMARY AUXILIARY VIEW x a T F a d b b c y1 b1, a1 y c1, d1 d c e f

54 Third angle projection method Auxiliary Views

55 First angle projection method Auxiliary Views

56 Problem: TV is a triangle abc. ab is 50 mm long, angle cab is 30 and angle cba is 65. a b c is a FV. a is 25 mm, b is 40 mm and c is 10 mm above Hp respectively. Draw projections of that figure and find it s true shape. a A1 b A1 15 a b b A F T c c Y c A1 A 1 A 2 c A2 a A2 a mm b DISTANCES FOR NEW FV come from PREVIOUS FV AND FOR NEW TV, DISTANCES OF PREVIOUS TV are accounted. 56

57 Problem Fv & Tv of a triangular plate are shown. Determine it s true shape c a b F 15 T a c 40 1 c 1 DISTANCES FOR NEW FV come from PREVIOUS FV AND FOR NEW TV, DISTANCES from PREVIOUS TV are accounted. b b 1 A 1A2 b 1 a 1 c 1 a 1

58 Angle between a line and a plane Edge view of the plane Line T F True length of principal line f d f' d' Principal line b T p A1 f 1 a 1 p 1 p Plane b' a' e' Part of the line hidden by the plane should be shown dotted a e c c' c 1 d 1 e 1 A2 A3 A1 A2 a 2 f 2 d 2 c 2 e 2

59 Projection of point P on A.I.P. ( to VP and inclined at β to HP) Draw FA such that it makes an angle β with FT Project P A on AIP by drawing a line P F P A such that P F P A is to FA and O P T = O P A. 59

60 Space curve Helix Draw a helix of one convolution, upon a cylinder. Given 80 mm pitch and 50 mm diameter of a cylinder. FV & TV specify helix completely. Widely employed on screw threads, helical springs, conical spring, screw conveyors, staircases, etc.

61 PROBLEM: Draw a helix of one convolution, upon a cylinder. Given 80 mm pitch and 50 mm diameter of a cylinder. 8 P 8 HELIX (UPON A CYLINDER) 7 P 7 6 P 6 Pitch: Axial advance during one complete revolution P 5 P 2 P 3 P 4 1 P P 1 6 F T 7 5 P

62 PROBLEM: Draw a helix of one convolution, upon a cone, diameter of base 70 mm, axis 90 mm and 90 mm pitch. P 8 P 7 P 6 HELIX (UPON A CONE) P 5 P 4 P 3 P 2 X P P 1 Y P 6 P 5 P P 7 P 4 4 P8 P 1 P P 2 3

63 Problem: Draw a spiral of one convolution. Take distance PO 40 mm. SPIRAL IMPORTANT APPROACH FOR CONSTRUCTION! FIND TOTAL ANGULAR AND TOTAL LINEAR DISPLACEMENT AND DIVIDE BOTH IN TO SAME NUMBER OF EQUAL PARTS. 2 3 P 2 P 1 1 P 3 4 P 4 O P P 7 P 5 P

64 Problem: Point P is 80 mm from point O. It starts moving towards O and reaches it in two revolutions around. It Draw locus of point P (To draw a Spiral of TWO convolutions). SPIRAL of two convolutions P 2 2,10 3,11 P 1 1,9 P 3 P 10 P 9 P 11 4,12 P 4 P P P 8 8,16 P 15 P 13 P 14 P 7 P 5 5,13 P 6 7,15 6,14

65 Problem: A link 60 mm long, swings on a point O from its vertical position of the rest to the left through 60 and returns to its initial position at uniform velocity. During that period a point P moves at uniform speed along the center line of the link from O at reaches the end of link. Draw the locus of P. O, P N M

66 Necessity of Auxiliary view 66

67 Ex: A line AB, 50 mm long, is inclined at 30 to the H.P. and its top view makes an angle of 60 with the V.P. Draw its projections. a F b F T F a T b T

68 Draw A.V. of a plane ABC (A(50,10,30), B(10,40,0), C(10,30,50)) on a plane which is to frontal plane and inclined at an angle of 45 o to top plane. Draw another A.V. on a plane which is perpendicular to the top plane and inclined at an angle 60 o to the frontal plane. USE III rd ANGLE X O Y T b b F a x 2 a b 1 a 1 c 60 o c 45 o c 1 c 1 y 2 y 1 b 1 a 1 Z Distance of a 1 from FA = distance of a from OZ Distance of b 1 from FA = distance of b from OZ Distance of c 1 from FA = distance of c from OZ Distance of a 1 from TA = distance of a from OZ Distance of b 1 from TA = distance of b from OZ Distance of c 1 from TA = distance of c from OZ x 1 68

69 Problem: A right circular cone, 40 mm base diameter and 60 mm long axis is resting on Hp on one point of base circle such that it s axis makes 45 0 inclination with Hp. Draw it s projections in I angle projection method. o F a h b c g f d e T h g f 45 0 g 1 h 1 f 1 a o e a 1 1 e 1 o 1 b d b 1 d 1 c c 1

70 Projection of Solids using Auxiliary Plane Method Projections of solids, whose axes are inclined to H.P./V.P. can be drawn using Primary Auxiliary Plane method. In this method, instead of changing the position of views w.r.t. fold line, we change the position of fold line.

71 Secondary auxiliary view of a cube Direction of view is perpendicular to the fold line h 1 g 1, d 1 P.A.V. e 1 c 1 f 1, a 1 e,h f, g 45 o b 1 Distances: e 1, f 1, a 1, b 1 from TA = e, f, a, b from FT T a, d b, c h 1, g 1, d 1, c 1 from TA = h, g, d, c from FT F a, e b, f d, h c, g

72 S.A.V. of a cube Distances e, f, a, b from TA 1 = e 2, f 2, a 2, b 2 from A 1 A 2 h, g, d, c from TA 1 = h 2, g 2, d 2, c 2 from A 1 A 2 h 1 g 1, d 1 e 1 c 1 e,h f, g f 1, a 1 b 1 45 o T F a, d b, c a, e b, f 60 o f 2 g 2 Fold line c 2 SECONDARY AUXILIARY VIEW e 2 b 2 h 2 d, h c, g d 2 a 2

73 Problem: A frustum of regular pentagonal pyramid is standing on it s larger base on Hp with one base side perpendicular to Vp. Draw it s Fv & Tv. Project it s Aux. Tv on an AIP parallel to one of the slant edges showing TL. Base side is 50 mm long, top side is 30 mm long and 50 mm is height of frustum AIP // to slant edge Showing true length i.e. a F T a b e c d e d 5 4 a c F A 1 e 1 d 1 a 1 c 1 Aux.Tv b 1 b 1. Attendance & Marks & attendance.pdf 2. Lab sheets (

74 Problem: A square pyramid 30 mm base side and 50 mm long axis is resting on it s apex on Hp, such that it s one slant edge is vertical and a triangular face through it is perpendicular to Vp. Draw it s 1 st angle projections. a b d c F T d o Hidden lines in Projections of solid! a bo c b

75 F T a a b d c o d bo c b a 1 o 1 d 1 b 1 c 1 Problem: A square pyramid 30 mm base side and 50 mm long axis is resting on it s apex on Hp, such that it s one slant edge is vertical and a triangular face through it is perpendicular to Vp. Draw it s 1 st angle projections.

76 Auxiliary Views Mistake??? Projection lines should be thin continuous lines.