Descriptive Geometry. Spatial Relations on Lines

Size: px

Start display at page:

Download "Descriptive Geometry. Spatial Relations on Lines"

Ada Leonard
6 years ago
Views:

1 48-75 escriptive Geometry Spatial Relations on Lines

2 line is parallel to a plane if it has no common point with the plane. To test whether a given line and plane are parallel: simply, construct an edge view of the plane and project the line into the same view; if the line appears in point view or parallel to the edge view, then it cannot meet the plane in a point, and is therefore parallel to the plane This fact can be used to construct a plane parallel to a given line or a line parallel to a given plane. Lines parallel to a plane

3 3 M Two possible lines parallel to plane through point O O N O M N Line through O parallel to the edge view of plane 2 N How do we locate points M and N? O M line parallel through a point parallel to a plane

4 How do we determine if two planes are parallel? by constructing an auxiliary view that shows one plane in edge view; if the other plane is E also seen in edge view then the two planes are parallel F 2 F parallel planes E

5 parallel planes onstructing an auxiliary view that shows one plane in edge view; if the other plane is also seen in edge view then the two planes are parallel 3 2 E E F F parallel edge views indicate parallel planes 3 2 E E F F F E

6 line is perpendicular to a plane if every line in the plane that passes through L N Q M the point of intersection of P O the given line and the plane makes a right angle with the Lines LM, NO, PQ all lie in the plane given line Line is perpendicular to the plane line perpendicular to plane (normal)

7 p N M P, Q p is a plane Line is a normal to it Lines LM, NO and PQ lie in the plane L O 2 L,P 90º M,Q L,O 90º M,N 2 3 perpendicular line to plane (normal)

8 direction of the normal in view # 3 normal is perpendicular to the edge view of plane TL 90º 2 direction of the normal in view #2 direction of the normal to a plane

9 direction of the normal in view # TL 90º Two-view method to find direction (bearing) 2 90º TL direction of the normal to a plane direction of the normal in view #2

10 P 2 P quiz: perpendicular to the plane at point P

11 O Shortest line (OP) from point O to plane E Lines and EF lie in the plane P F Observer's line of sight plane is seen as an edge and true length of OP appears shortest distance from a point and a plane

12 3 True length of the shortest line from M to the plane M P h M Edge view of plane P 2 P lies on the perpendicular from M to the true length line in view # M h P P is located by using the transfer distance from view #3 or by tracing a line on the plane through P

13 how do we determine if a plane is perpendicular to a given plane? this requires finding edge views of the plane and seeing if they are perpendicular to each other which we will consider it later when we consider lines of intersection perpendicular planes

14 revisiting an old problem shortest distance to a line

15 s line is in true length, the constructed perpendicular from to produces point Y 4 3 True length of the shortest distance TL Y,Y Point view of line 3 Y Project back from view #3 to get Y 2 Y Project back from view # to get Y constructing shortest distance to a line (line method)

16 3 4 3 Edge view of True shape of Project back from view #4 to get Y Y is the shortest distance from to 2 defines a plane Project back from view # to get Y constructing shortest distance to a line (plane method)

17 90 Line Y is the shortest distance between skew lines and as it is perpendicular to both lines 90 Y shortest distance between skew lines

18 2 shortest distance between skew lines

19 Y, True length of shortest line Y is seen in view #4 is in true length in view #3 3 2 Y 90 Y ommon perpendicula between skew lines in view # shortest distance between skew lines (line method) ommon perpendicular Y between skew lines and in view #2 Y

20 Y W 2 HL W shortest distance between skew lines (plane method)

21 R,S 4 3 3, Y Y is parallel to in view # and passes through W Shortest distance RS between skew lines and R, S Plane Y seen in edge view in view #3 Y is parallel to in view #2 and meets at W Y is parallel to folding line 2 R shortest distance between skew lines (plane method) 2 S R S W W Y HL Y Y is a plane

22 Horizontal projection plane parallel Y Shortest horizontal distance between the two skew lines Y shortest horizontal distance between skew lines

23 2 shortest horizontal distance between skew lines

24 M LM is parallel to in view # Y is parallel to the edge view of the horizontal plane Y is also the true length of the shortest horizontal line M L TL L is in true length is parallel to the edge view of plane LM in view #3,L 2 View #3 is an elevation L HL M LM is parallel to in view #2 shortest horizontal distance between skew lines

25 ,Y 3 Y is parallel to the edge view of the horizontal plane Y is also the true length of the shortest horizontal line 4 3 is parallel to the edge view of plane LM in view #3 Y M,L L Y TL M LM is parallel to in view # L is in true length 2 View #3 is an elevation L HL M LM is parallel to in view #2 shortest horizontal distance between skew lines Y

26 ,Y Y is also the true length of the shortest upward 5 grade line Y M O 4 5,L N 4 L Y TL M LM is parallel to in view # L is in true length 2 View #3 is an elevation L HL M LM is parallel to in view #2 Y shortest grade distance between skew lines

27 % grade Y M LM is parallel to in view # Y M L TL L is in true length Y is also the true length of the shortest downward 20%grade line,l 2 View #3 is an elevation L HL M LM is parallel to in view #2 Y which grade distance?

28 Observers line of sight in which line is above line visibility

29 quiz: find a point on a line equidistant to two points l l f t l l l f t l l TL l Project back from top view to get Project back from view # to get t f t midpoint l l TL l t f t midpoint

30 quiz: locating a line between two skew lines through a point

31 Lines and specify centerlines of two existing sewers as shown in the figure. The sewer pipes are to be connected by a branch pipe having a downward grade of 2:7 from the higher to the lower pipe. Given that point is 20' North of point, the problem is to determine the true length and bearing of the branch pipe and show this pipe in all views. Line (in plan) measures 20'. quiz: construct a line at a certain grade

32 20' Y t f Y

33 2, TL = 30'-8" 2:7 grade 20',Y bearing = S 5.5 E t Y

34 20' bearing = S 5.5 E Y t f Y

35 quiz: construct a line at a certain grade

36 '-0" 5'-0" 4'-0" 45 3'-6" '-6" quiz: shortest distance from to nearest face

37 a t f

38 t a t f edge view of face a

39 Y is not on face p need to find point on face a nearest Y in the same plane t p Y t f Y is the foot of the perpendicular from to the plane of face p Y edge view of face p

40 p t Z is projected back from view # Z Y t f,y Z Y Z Z is projected back from view #2 true length of 2 Z is perpendicular from Y to in view #2

41 Z = 2'-" true shortest distance between and Z is given in view #3 p 3 t t Z Y Y t f,y Z Z 2

42 Three equal legs of a surveyor s tripod are located in their relationship to the plumb line. Leg bears N30 W and has a slope of 30 Leg is 3-3 due east of the plumb line and at the same elevation as the plumb line Leg bears S45 W and has a slope of 45 The plumb bob touches the bench mark at a vertical distance of 4 below the top of the line etermine TL of legs, and? What is the angle makes with plumb line? Show legs in front and top views. Problem

43 Step

44 Step 2

46 Two sewer lines and converge at manhole is 35 north 0 east of and 30 above is 20 north 60 west of and 5 above new line is located in the plane of at a point 30 due west of Using only two views locate What is the TL of each sewer line? What is the angle of the plane Problem

47 Step

48 Step 2

49 Step 3

50 Problem is parallel to plane. omplete the view.

51 Step

52 Problem Planes and EF are parallel. omplete the view

53 Step

54 What is the shortest length between nonintersecting diagonals of adjacent faces of a cube?

56 Given two partial pipelines construct the shortest level pipeline to connect them. These pipelines may be extended Problem

57 Step

58 Step 2

59 Step 3

60 onstruct the pyramid with base (2, 2, 5), (3.5,.5, 6), (4.75, 2, 6) (3.25, 2.5, 5) height 2.5 ll measurements in inches omplete top and front views with proper visibility ie., visible lines are solid and not visible lines shown dashed. Problem involving perpendicular lines

63 What is the clearance between a pipe and the ball?

TA101 : Engineering Graphics Review of Lines. Dr. Ashish Dutta Professor Dept. of Mechanical Engineering IIT Kanpur Kanpur, INDIA

TA101 : Engineering Graphics Review of Lines Dr. Ashish Dutta Professor Dept. of Mechanical Engineering IIT Kanpur Kanpur, INDIA Projection of a point in space A point is behind the frontal plane by d