 The projection of lines, myself, Mr. S. P. Mankani, assistant professor, department of mechanical engineering, wall change institute of technology, Solaapur. So, at the end of this lecture, students will be able to solve problems on projection of lines inclined to any given plane. So, here in the previous lecture, we have studied the basics of the quadrants. So, with the reference of the basics of the quadrants, we are going with the next basic concept of drawing projection of lines. So, in the previously taken x y as a reference line, the front is coming above the x y line and the top becomes below the x y line. As in the case of first quadrant, we are going to study particularly the first quadrant. The rest of the information related to the second quadrant, third quadrant and fourth quadrant, we are not going with the detail of those quadrants. So, now we are going to study as the first quadrant only. And here is the front view is in the above the x y line and the top is below the x y line. Usually, you are going to call in almost all the, our lectures, the x y line as a reference line above or below, like this you are going to be using the word. So, here any point, now you are going to be representing above the x y line is the front view. Suppose, this is a point P dash, you are representing P as a one point situated in the first quadrant, you are representing this as a P dash. So, any distance from the x y line, it indicates that this distance is from the horizontal reference plane. All the measurements, you are going to make it from the x y line only, from the x y line. It is in the upward direction. Suppose, it might be a 30 millimeter, 40 millimeter, 60 millimeter, you are going to be measuring from the x y line in the towards in the upward direction. Suppose, this point is situated at the 40 millimeter means from this particular point, from this particular line is a 40 millimeter distance, you are going to consider as any point situated above the horizontal plane at a distance, that distance you are going to be measuring from the this particular reference line. Similarly, if any point supposed to be there given as 30 millimeter, 40 millimeter, any distance from the vertical reference plane below the x y line, all the distance from the vertical plane you are going to be measuring from this particular point in the downward direction. Here it is representing it as any distance from vertical plane is going to be measured from the x y line only below the x y line, below the x y line, the notation given here as a dash mark and notation here given as a without dash mark. All the top view you are going to be representing as like a A, B, C, D and the front view are going to be representing as a A dash, B dash, A dash like this. So, this is studied as a front view above the x y line, top view below the x y line, next part as any distance from the horizontal plane it is measuring from the reference line above the x y line, any distance from the vertical plane below the x y line from the x y line, this much only information yesterday. Next, if the any line is making a certain degrees of angle to the horizontal plane, that you are going to be representing as a theta angle and that angle you have to take it in the direction as like this, this is the theta degree, this is the theta degree angle, it is in the direction like this, angle you can take it in this direction or you can take it in this direction, you can take angle either in this direction or in this direction, but that is a theta angle to the horizontal reference plane. Similarly, you are going with the any angle is given to the vertical reference plane, you are going to be taken below the x y line to the x y line, that you are going to be representing it as a phi angle, phi angle you can take it to this particular reference line below the x y line either in this direction or in this direction, we are represented only one direction, you can take it in both the direction depends upon the space availability in the problem. So, now supposed to be here point is situated above the horizontal reference plane and in front of the vertical plane you are taken now supposed to be point is situated on the horizontal plane itself means this distance is going to be becoming as a zero, this distance become zero means that point is situated on the x y line and that you are representing it as p dash point, that is dash mark indicating it as a point is in the front view as shown. Similarly, if the point is there in the vertical reference plane that time it is going to touch the x y line from below the x y line, this distance is going to be becoming as a zero, any distance from vertical plane that distance is going to be becoming zero because it is there in the vertical plane that time the point is situated on the x y line from below the x y line, it touches from the below the x y line that you are going to quote it as a p point. So, now this is an important part starts as how to draw the projection of a line with a given position. So, I have taken this as a first part and this position is x y line and this is like a your notebook page. So, here this is a vertical plane is coming above the x y line and horizontal plane below the x y line. In later stages we are not going to be calling this vertical plane as well as a horizontal plane to avoid the confusion. So, now here this x y line and having a certain distance above the horizontal plane this distance and that point is situated as a point and here certain degrees of angle is given as a theta degree of angle and this is a dash b dash a dash and b 1 dash representing because it is a front view line, it is a front view line the notation part of it why you have taken b 1 dash I will explain this part in the later part. So, here just it is a front view line. So, similarly here you are going to be representing this as the true length. So, here it is a true length this side also this theta angle as well as phi angle this theta angle as well as phi angle is going to be taken for the true length only true length with the HP true inclination with the HP and true inclination with the vertical plane. You can take angle in this way or in this way both the things I explained in the previous slide also. So, here this is phi and this is theta you are expected to remember these angle notations very clearly and this is a locus of b point here also you are going to be taken as a locus of b point means this length is true length this length is true length means these are true inclinations. So, now we are going to bring it in the upward direction this point you are going to bring it in the upward direction. So, this gives a dash and b 2 dash it gives as a front view length this gives a front view length. So, keeping compass at this particular point you are going to be rotating this point in this direction it is cuts the locus of b point means b has to come anywhere on this particular locus line only. Now, we are going to be joining this point and this point with a red color this indicating as you are expected to draw this line as a 1 dash and b 1 dash as a dark line as a dark line and as far as this a 1 dash a dash and this b 1 dash you are going to be representing with the medium thickness line and if you are going to bring this line directly in the downward direction once again to get a this a and this particularly as a b 2 point is given as the top view length. This is top view length keep the compass here bring this distance then you rotate it in the downward direction it is going to cut the this locus line of b 2 it is going to cut the locus line of b 2. So, here you have to join this line it becomes as a a b as a top view length this becomes as a top view length. So, now one more angle is included here as alpha degree here and this is beta degree alpha is indicating the angle made by the front view length with the horizontal plane that is a alpha degree we are going to represent this as a alpha similarly angle made by the top view length with the vertical plane this you are going to be representing as a beta these alpha and beta are apparent angles alpha and beta are apparent angles all the details has been represented and you are expected to remember all these 10 points all these 10 parameters you are expected to remember here. So, true length so this particular line is a true length in the front view and this is in the top view these are true lengths and theta and phi angles are related with the true lengths only angle made by the horizontal plane with the angle made by the line with the horizontal plane and here it is a angle made by the line with the vertical plane theta as well as phi and alpha and beta is angle of front view with xy line and similarly angle of top view with xy line that is a beta angle and this is LTV that is the length of here it is a LTV it is not LTV it is a length of front view it is a LFV there is a correction you make it this as a correction and this is point is length of front view and here it is a length of top view okay and this point is situated A is the distance from the horizontal reference plane and distance from the vertical reference plane same information I have distributed in the three steps here is the first step you are just drawn the first step the given angles then the second step you are going to be locating the rotating the this particular line and then bringing it in the next upward direction then you are going to locate that true length this is a true inclination similarly in the third step you are going to bring it in the this particular point in the downward direction just you can observe here so now you are going to bring it the last step bringing keeping this particular point and you are going to bring it this projector in the downward direction it will cut the this a locus of a and wherever it will cut keep the compass at a point take it this distance and rotate it in the downward direction this gives the top view length of a given line and alpha and beta angles are alpha is related with the angle made by the front view with horizontal reference plane angle made by the top view with the vertical reference plane so these are the three steps just you can think it so what are the angles alpha and beta where should we denote the angle alpha and beta in today's problem what are alpha and beta these are apparent angles and they're going to locate this alpha above the x-y line and beta below the x-y line thank you