TA101 : Engineering Graphics Review of Lines. Dr. Ashish Dutta Professor Dept. of Mechanical Engineering IIT Kanpur Kanpur, INDIA
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1 TA101 : Engineering Graphics Review of Lines Dr. Ashish Dutta Professor Dept. of Mechanical Engineering IIT Kanpur Kanpur, INDIA
2 Projection of a point in space A point is behind the frontal plane by d units and below the horizontal plane by h units. HORIZONTAL PLANE FRONTAL PLANE
3 Line positions Line lying on two principal planes of projection will appear normal / true length (TL) in two views.
4 A line lying in one principal plane will appear normal in one view.
5 Find normal view of a line Method 1 (using auxiliary plane). 1. Determine the desired line of sight. 2. Establish a new projection plane perpendicular to line of sight.
6 3. Project all points into the new view. 4. Locate points A and B along the projections in plane.
7 Auxiliary plane method
8 Method 2 : Rotation method 1. Make the line parallel to one of the Principal planes in any view by rotation. 2. Take projections on the other view to get normal view of line. Why does it work?
9 Slope and Grade of a line Relationship of a line to the horizontal plane Line in TL (normal view) Slope = Rise Y = = tan θ Run X θ is the slope angle of a line.
10 Bearing Bearing of a line can be, measured only in horizontal view. Examples are N60 W, S45 W etc.
11 Azimuth Azimuth is measured clockwise from the north arrow and only uses N along with the angle.
12 Parallel lines: Two lines are parallel if they lie on the same plane and do not intersect or touch at a point. Parallel lines appear parallel in all views. CASE 1
13 Lines that appear normal in H and F planes may not be parallel: Check for P view CASE 2
14 Perpendicular lines: Two lines are perpendicular if there is a 90 o angle between them if at least one line is in true length Cases : A : Perpendicular (both lines in TL) B: Perpendicular (only one line in TL) C: Not perpendicular
15 Shortest distance from a point to a line is a perpendicular from the point to a line. Shortest distance shows true length (TL) when original line is a point view.? Const.: Draw a line O-P perpendicular to line 1-2 at P. Similarly in F view, Join point O and point view of line.
16 Point view of line 1-2 is given in F view. Hence OP is in TL. Line OP is parallel to H plane.
17 Line not in point view Point view required for line 3-4. Construct auxiliary view H/A to get point view of line 3-4 Point P must lie along a line from O parallel to H/A folding line. Hence OP is in TL in view A.
18 Once point P is found in H view, drop it to the F view on line 3-4.
19 Given line not in true length The shortest distance is seem as TL when line is made a point view. In view 1 line A B is made TL. In view 2 AB is made point view. Distances from view H are transferred into view 2.
20 View 2 TL of OP connector is made. Line OP is returned to other views. Line OP in view 1 is made parallel to the 1/2 fold line to get P, such that OP is in TL in view 2.
21 Shortest distance from a line to a line in case one line is in point view Two lines that are not parallel and do not intersect (skew lines). The shortest connector between two skew lines is the connector perpendicular to each line.
22 Connector shows TL as one line 1-2 is in point view in F view. Hence OP is made TL in F view by constructing perpendicular to line 3-4. OP is found in H view by projecting P on to 3-4 line. Run it parallel to H/F fold line.
23 Distance between Skew lines when neither are in point view A line AB is mode in point view. (TL then point view) In view 2 the shortest distance OP is added as a TL connector. Connector makes 90 0 angle to line CD.
24 Line AB is first made TL, and then point view. CD is carried along from view to view. In view 2 the shortest distance is found by constructing a perpendicular to get point P. OP is projected back.
25 Main Points to remember Normal Line: A line lying in one principal plane will appear normal in one view. A line lying on two principal planes will appear normal in two views Shortest distance: Shortest distance from a point to a line is a perpendicular from the point to a line. Shortest distance shows true length (TL) when original line is a point view.?
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