 Myself, Professor S.P. Mankani, Assistant Professor, Department of Mechanical Engineering, Walchand Institute of Technology, Solapur. Today we are going to study projection of profile lines. So at the end of this lecture, students will be able to understand the profile, projection of profile lines. So now we are going to have a bit previous review. The cases of lines in auxiliary vertical plane, auxiliary inclined plane. So then we can go for the profile plane. So based on this one, here just you can observe, this is auxiliary inclined plane. Means it is making a certain degrees of angle. Here this is a certain degrees of angle it makes with the HP. That we are given the notation as alpha degree of angle it is going to make with the horizontal reference plane. So this particular part you already studied because the line is situated in the auxiliary inclined plane. The line is situated in the auxiliary inclined plane. If this is a case, we are going to get it here as a front view. A dash, B dash you are going to represent as a front view. Here this angle is alpha angle. So that is what the angle is made by the line with the horizontal reference plane. This is the case of previous, we have studied this all the details. So in the same continuation here, we are going to be taken another as, so one more here this particular angle, the auxiliary vertical plane. We are going to be calling this as auxiliary vertical plane which is making as a beta degree of angle. So there the line is situated in the auxiliary vertical plane. If this is a case, you are going to observe this line from the top. So that projection you are going to be getting it in the horizontal reference plane. So that time it is going to make the angle as a beta here. So this alpha angle is the front view is going to make an angle of alpha degree with the horizontal XY line, this the reference line. We are going to consider this as a reference line XY line. The angle made by the plane with the HP. So here because the line is situated in the plane only. So continuation with this same thing, we are going to observe this one as a, this line is situated in the auxiliary vertical plane. We are going to observe from the top here. We are going to get this as a view. So here this is a top view. So that is nothing but the angle beta is the angle made by the line with this particular vertical plane. That we are going to be representing here as a below the XY line to the XY line. So this particular detail you have studied in the previous one of the lecture. So the continuation, this is the information required because we are going to tilt this, we are going to tilt this particular plate in the perpendicular to the vertical plane as well as perpendicular to the horizontal plane. That is what we are going to be considering it as a profile plane. So the next slide you are going to study as a line in a profile plane means in a plane perpendicular to both HP and VP. If this is the case just you can observe the same diagram that is a vertical plane, horizontal plane. Here we are going to set up this profile plane. The previously I have considered this is making certain degrees of angle either with the horizontal plane or with the vertical plane as we are called this as a AIP and AVP. So based on this one if supposed to be the line is situated on the profile plane. So this theёл the importance of this particular lecture is considered as line is situated in the profile plane. And one thing to observe here as, you are going to be observing from the left hand side. So here this line is situated, perpendicular line indicating the line is situated in the profile plane. So if the line is situated in the profile plane you are going to be observing as a front view as well as the top view. So here we have here is a front view we are going to observe in this direction top view where we are going to be observing in this direction. how exactly it looks. So suppose this line is you are going to be observing in this way and it is a front view that comes on the vertical plane. So it is looking as a straight line only. It is looking as a straight line only situated on the vertical plane. Similarly if you go for the top view that is also going to be observed in the this way as on the horizontal reference plane. So here it is this one. So if you tilt it this plate in the downward direction so that you are going to be getting as a single page in the next diagram. So here it is a top view are going to be representing here as a a b and front view are going to write it as a a dash b dash. The line is situated in the profile plane. So here the important thing is this particular line how exactly it looks in the front view as well as top view are going to draw it in the orthographic pattern. So here it is a the color code I given it as a same color here I take and means it's a vertical plane. The blue color I am going to be considering it as a horizontal plane that is coming as a below the xy line because intersection of these two are going to be considering it as a xy line. So now you are going to be taken this particular as a profile plane. So this profile plane you have taken it as a this side here profile plane is here. So now based on this one this line you are going to draw it on the orthographic pattern. So here this is a vertical line. So this is representing it as a front view and this is representing it as a top view here. So here both the points of the end point of this line is coming on the same projector line here. So this is xy line and now this is a dash and here we are going to be taken as a b dash and similarly we are going with the this is a and this is b. So we are going to consider this one as a front view and this as a top view. We are going to bring this particular projectors in the horizontally in this direction and here also you are going to bring it this particular projectors. You are going to bring it this one to bring it up to horizontal this particular point and this particular point that is an intersection point. So then keep the compass here take it this particular point as a length and draw the arc and similarly keep the compass here take it this length and draw the arc. So both the projectors are coming in this particular figure as like this. You bring it in the upward direction. So now this a point is going to be coming the projector here and this is a dash is coming here and both are going to be intersecting at this particular point. And that you are going to be given the notation as a double dash here we are going to give the notation as a double dash. Similarly you are going to get this b point as a, so here we are to bring it this b point and it is coming it as a intersecting point as a b double dash. A double dash, b double dash are the length of this particular line here this length is a true length. Just you can imagine here this the line is parallel to the this particular line okay the profile line this particularly a front view is parallel with this one means one in one view it is a parallel in another view the automatically are going to get this as a true length this is a true length of the line is concerned. So here the important thing is the line is making a certain degrees of angle with the horizontal plane and this is a horizontal plane and this is a vertical plane. So in one of my previous lecture you have studied that particular as a quadrants first in the first quadrant it is a vertical plane and the horizontal plane if you are going to tilt this one you are going to be getting this as a one more as a profile plane here. So based on this one and this angle and this angle is very important here. So summation of these two angles this is a horizontal reference plane and this is a vertical reference plane. So if you consider this is a vertical reference plane and this is a horizontal reference plane this is also making a certain degrees of angle with the horizontal reference plane and this is a certain degrees of angle with the vertical reference plane. So HP angle you are going to be considering it as alpha and this is a beta. So based on this particular angle if the summation of these two angles are 90 degree then the line is situated in the profile plane you are going to be considering it as a profile plane then you are going to solve the problem based on this one. So here just you can observe it here. So this is front view and this one is a top view and this is a profile line as in the side view. So here this is you are going to be observing from the left hand side and this particularly plate you are going to be treating in this way and it is coming on the right hand side of this particular figure. Right hand side of this particular figure is concerned. So here is the left hand side view. So now you are drawn this as this particularly a double dash b double dash it is looking as a true length it is looking as a true length. So here just you can think it so why you are drawing this one this side only why not you can take it this side just you think it a minute why you are drawn this green color square on the right hand side of this figure. So why not you can draw it on the left hand side of the figure just you think it. So now as far as the first angle method is concerned you are going to draw the right hand side view on the left hand side of the figure and left hand side view you are going to draw it on the right hand side of the figure is concerned. So as far as this particularly lines problems are concerned so even you can take it this way or you can take it this way is concerned. So here you doesn't have any problem but the thing is that in another whenever you are going with the orthographic projection there you have a constraint of to draw the line as either it is there as a left hand side view or right hand side view based on that one you are going to draw this particularly as a profile plane is concerned. So now here you are going to consider this as a profile plane as so this side only. In generally you are going to be taking it as the right hand side only. So now we are drawn this as the one more point as this is a horizontal trace and this is a vertical trace. So this is just an extension of this line where it intersects with the this horizontal plane as well as a vertical plane. If it is intersecting with the horizontal reference plane we are going to be calling it as a HD and if it intersects with the vertical reference we are going to be calling this as a vertical trace. So this detail I have one more lecture in my lecture series. So there you can study the detail of this what exactly the horizontal trace as well as a vertical trace. So here this is a theta and phi this angle is summation of this angle is 90 degree. Theta angle is angle made by the line with the horizontal plane and phi is angle made by the line with the vertical and these are the true inclination here I taken as a previously as alpha and beta those are apparent angles. Here it is a theta and phi as a true inclination. So the same explanation is also given here you can refer it once again this information also. So this concludes the information related to the profile line is concerned the line which having an angle as 30 degree or 60 degree like this the summation of this angle as 90 degree. In this type of problems you can solve with this particular method. Thank you.