 Hello. Hello everyone. Today we are going to study projection of lines. Myself Mr. S.P. Mankani, Assistant Professor, Department of Mechanical Engineering, Walsh and Institute of Technology, Solapur. At the end of this lecture, students will be able to represent the slope, grade and bearing. So, here some different types of the lines I have representing in this particular diagram. If the line is parallel to both HRP and FRP, we are going to draw this as a x-y line, then this line has a true length and this is also a true length. Both the lines are parallel to the x-y line. The next one is line is on the both HRP and FRP. It means here what exactly are going to make it in the first diagram, this distance above the horizontal plane or in front of the vertical plane. That distance is going to be becoming zero. So, that time, so the line is coming here as a on the x-y line only. You can represent this line as AH, BH you are represented. It is nothing but A and B or A dash and B dash. Similarly, we are going to the next class vertical line perpendicular to HRP. Vertical line perpendicular to HRP. It is above the x-y line. This line is a straight line and in the front in the top, you are going to get this as a single point. Top, you are going to get this as a single point. This you are going to calling it as a vertical line. In the next diagram also, we are going to see the detail of this one line. Line is perpendicular to FRP. Line now it is perpendicular to FRP means below the x-y line line is perpendicular. In the front, you are going to get this as a point view. This front, you are going to get as a point view. Next, we are going with the frontal line. It is inclined to the HRP and parallel with FRP. Parallel with FRP means in the another view, we are going to get this as a true length. If the line is parallel to any one, any this line is parallel to the reference plane. In another view, you are going to get this as a true length. Similarly, the frontal line it is inclined with the HRP in the FRP. Line is inclined with the HRP and in the HRP. Similarly, this distance they have made it as a zero in this particular line. Similarly, horizontal line it is a parallel to the HRP and inclined with the FRP. Parallel to the HRP means this line is a true length line because it is a distance. This distance and this distance of both points are same and the line joining those two points are looking as a true length in the another view. Similarly, this distance you are going to make it in the next step as a zero and it will come on the horizontal reference plane only. So now our main intention is to study different types of the problems related with this particular diagram, which is the line is you are going to calling it as a oblique line. It is inclined to both horizontal plane as well as vertical plane. In the previous lecture, she has studied how exactly the angle is taken in the HP and VP both angles as well as the representation of the line you have studied in the previous lecture. So now we are going with the important part as the horizontal line. So this is a horizontal line it is a clarity for you are given one more diagram as this line is parallel with the XY line and this is a true length and the frontal line in some of the problem they are going to be given as the line is horizontal line or a frontal line. For that reason you should have the knowledge of this particular diagram. Frontal line means it is parallel with the vertical plane below the XY line. It is parallel means in another way you are going to get this line as a true length and similarly the next line as profile line. It is perpendicular to both HP as well as VP perpendicular to both HP as well as VP. So that time you are going with the profile. So now you are going to bring this projector in the horizontal direction you are going to get this as a true length because this is at the same distance from this particular reference plane. Here you are going to get this as a true length. How exactly you are going to get this true length and how exactly you are going to look at this one we are going to study that part in the next lectures. So here it is a oblique line which you are particular about the line is inclined to HP as well as line is inclined with the VP. In the next the important part as grade slope gradient and inclinations. So grade slope gradient and inclination just it is for representation of the lines are concerned. Instead of giving the angle directly they are going to be given in this particularly format. The slope it is a tangent of the slope angle theta that is expressed as a tan theta. If you are going to take this line here it is a tangent if you are going to consider this as opposite side is this and adjacent side is this tan theta of this angle you are going to be representing it as a slope of a given line. Opposite sign this is the y and this is the x. y upon x representing it as a this slope that is a theta degree tan theta of this one if you are going to take it this distance you will get as a slope. The gradient it is same as the tan theta it is same as the tan theta gradient you are going to be representing it as the same as tan theta denoted in the proportionate form that is A is to B. A is to B like this you are going to represent as a gradient. So here this is 3 is to 4. This is y is to x you can represent in any fashion of these three that is a gradient. Previously a slope you are represented as slope is equal to tan theta that is equal to 3 upon 4. So now you are going with the grade so it is a percentage of the slope percentage of the slope you are going to take this as 3 upon 4 3 upon 4 you are going to get it this is multiplied with the 100. So that you are going to get it as 75 percent 75 percent. So means grade you are going to represent it in the form as 3 upon 4 that is a y upon x into 100 that is in terms of percentage you are going to write it this as a 75 percentage means slope you are going to represent in tan theta form and gradient you are going to represent it in the ratios that is A is to B then grade you are going to represent in the percentage. The meaning is the position of the line they are going to be given in this particular format. You are expected to remember how exactly the slope is taken, grade is taken and gradient is taken. So it is a positive line if the slope is upward sometimes so if you are going to consider this line so this is coming in the upward direction or it is coming in the downward direction. So you are going to take it suppose so this you are taken with the reference to this particular point it is in the upward direction if you are going to take this with reference to this particular point it is coming in the downward direction. So angle of elevation and angle of depression this is one more important part you are going to represent the line. So here this comes above the x-y line this is x-y line I represented here it comes as an above the x-y line. So here this is if you are going to consider this as a point as your eye sight if you observe the object in the upward direction it is nothing but if you observe it in the upward direction like this so then it is coming as an angle of elevation if your going to consider if you observe it my eye sight if I am observing it in the upward direction that comes as an angle of elevation. If I am going to see by this particularly eye sight as in the downward direction that comes as an angle of depression. They are going to be given this particular information related with any one of the position either angle of elevation or angle of depressions with the reference to any one of the point. The important thing in this one as this is an angle substituted by the object with respect to the horizon at the eye level. So this we are going to consider this as eye sight. This is eye sight we are going to consider it as a observer. If the object is at the higher level angle of elevation if the object is at a lower level angle of depression and these are true angles so employed with the true length only. This is one more important thing is this particular position suppose if you are going with this particular problem this is a position this we are going to consider with the true length only. This is with a true length only and this is located here in the detail it is with the true length only. This is related with grade slope and gradient. So now one more important part of the representation of the line is concerned. This is the oblique line just it is represented as a this given angles I have taken directly the front view length as well as top view and if you are going to draw one more x1 y1 line as a reference line to this particular line you are going to project this particularly line here and then you are going to get this as a true length because it is parallel with this one okay parallel with this one. So here what exactly are going to get in this one as here this particular a1 and b1 as a true length line and for getting this length you are going to refer previous to previous previous to previous to previous. This word you are expected to remember previous to previous means for this this is a previous and for this this is a previous previous to previous means so this is p distance and this is q distance measure it from keeping compass here take this distance measure this distance from keeping compass here take this distance and that you are expected to transfer it this is a projector line it is going to cut it here if you want to transfer q you keep the compass here cut at this projector line you are going to get it this as a position similarly take this distance keep the compass here even you can give this notation like this and you can give notation like this that is p distance keep the compass here cut at this and you are going to get it this as a line. If you draw one more x2 y2 line projector line one more x2 y2 line here if you are going to draw it. So, project it here for this getting this particular point what is previous to previous this is previous, previous to previous is this one major this is distance this is I represent it here as a r and that r you can take it here distance means the projector line is going to cut it here. From this particular line you measure this position r transfer that information here and you are going to get this as a end point. Here in this particular diagram is only to understand how to get the end point is concerned. So, now we are going with the one more important thing as a bearing. So, it is nothing but a direction and only can be seen in top view. So, this is the important is just have drawn this as a line here as a xy line it comes below the xy line means this information you are going to be taken only the information related it below the xy line that is in the top view only and that to top view projection only. So, now if supposed to be this point is nothing but a this point consider this for just reference purpose. If you are considering this point here and here you are going to draw this as a line like this. This is a north south east west this position I am going to be shifting it here this is a and I am going to write it here as a if you want to locate any information related to the position of A. In the previously they are going to be given as position of A is 15 millimeter in front of the vertical plane means you have taken this as a 15 millimeter then position you have taken it here. So, that point I am explaining here how to represent the bearing bearing it is nothing but a direction and only can be seen in top view and it is associated with the top view only. So, for this particular line only. So, now if you are going to take it this one as now we are going to be representing this as a north 50 east means from north reference you have to measure towards east and that angle is 50 degree angle. In the problem they are going to be given as the angle is north 50 east north 50 east means you have to locate this x y line take it this position draw this north south east west and this is north east north 50 east 50 degree measure it and this is a position of top view length. So, like this you are expected to locate it. So, similarly you go for the rest of the lines as this is south east south east means this is south and this is east is supposed to be if you are supposed to be taken this as south east directly. So, this is a 45 degree only directly here angle is not given means it is a 45 degree south towards east 45 degree. So, like this this is west towards east 45 degree and similarly this is north towards west north towards west means 60 degree you are going to measure it here. So, this you are going to be representing it as a representation of the bearings are concerned bearing you are going to be taken only in the top view not in the front view this information you are expected to get it clarification. So, this is supposed to be a given as south 30 west where exactly it comes south 30 west suppose third south 30 west if I given it where exactly it comes south 30 west it comes in the as a south towards west and this is 30 degree. And if you are going with a similarly that is a south 60 east where exactly it comes south 60 degree towards east like this you are expected to measure all the angles.