 Hello friends, myself, Professor S. P. Mankani, Assistant Professor, Department of Mechanical Engineering, Walchand Institute of Technology, Soolapur. Today we are going to study projection of profile lines. At the end of this lecture, students will be able to draw the projection of given profile line. So, here is the question, a line AB 75 millimeter long has one end A in VP, other end B is 15 millimeter above HP and 50 millimeter in front of VP. Draw the projection of the line when some of its inclination with HP and VP is 90 degree. Means it is lying in profile plane. Find true angles with reference planes and its traces. So here the important thing is here the inclination with HP and VP is given 90 degree. Means it is lying in a profile plane. Even if the this particular wordings are not given also you consider that the summation of those two angles are 90 degree means you have to go with the profile plane only. So the given line is 75 millimeter length. So initially we are going to be set up in the given conditions. Here just you draw the XY line. So then you just draw the vertical line as a to locate the points as per the given condition. So this is the point is given as in the vertical plane. In the vertical plane we are given this point as a A point here. This point is given as a A point. This point is situated in the vertical plane. So this another position you are taken as a front tube point. It is a B dash point you are taken it. So the situation of this one he has given it as a 15 millimeter above and this point he has given as a 50 millimeter here below the XY line you are going to be taken as a 50 millimeter. This is all the given condition just you are going to be locating this given condition. Here this is a vertical reference plane and this is a horizontal reference plane. Vertical reference plane and this is a horizontal reference plane. These are the reference plane. So as if you are going to be considering this as a side view it is nothing but a side view. If you look the one of my previous lecture you will find it as a these are actually a plane. So plane like this and this one is plane like this. So that is what you are going to be observing from the left hand side you are going to be drawing on the right hand side of the figure. So if you observe this one you are going to get this as a single line and this also as a single line. Just you are located the position of this B point he has given in the problem and this A point is situated on the vertical plane it is touching the XY line below the XY line and this B position also given in the problem as 50 millimeter in front of the vertical plane. So now we have to bring it this projector on the this particular profile lines. So I brought it this one B point here the projector line like this. So means you bring it up to this particular line where the intersection line is there keep the compass here take it this much as a dimension draw the arc. So it will cut this horizontal reference plane this horizontal reference plane. So here the intersecting point and if you bring it this particular point it is going to intersect at this particular point. So now we are going to be locating this as a B double dash point. All front has to be naming with the dash mark and top view without dash mark and the side you are going to be taken as a profile line as a with a double dash mark as a just it is for the reference purpose even you can use another notations also. So this is the intersection point as a double B dash. So here in the problem he has given as a summation of theta as well as phi angle summation of theta as well as phi angle theta is angle made by the line with the horizontal reference plane and angle made by the line with the vertical reference plane the summation of these two angles he has given as a 90 degree. So this particular type of the problems fall in this particular group as the summation of the angle of the horizontal plane angle with the horizontal plane angle with the vertical plane if it comes as a 90 degree then you are going to be following this particular method as a profile method. So here this particularly theta and phi is a given in the problem as a 90 degree that's why you have taken this particular line and this is this length is he has given in the problem as 75 millimeter. So 75 millimeter this length is 75 millimeter here constraint if you move in the upward direction the length is goes on increasing if you come in the downward direction the length is comes in the decreasing fashion. Now it is 75 millimeter you are taken this as a 75 millimeter length. So now you have to consider this one as so here so just it is a just you can go it back so here is given as a one more word as the traces find the true angles with the reference planes and its traces and it traces he has given we should think it this particular as a in my separate lecture about the stresses this particular traces are concerned. So now we have to study up to this particular point I will explain this particular part also up to the point where you have stopped here. So now you are given the naming here okay so now we can start it up to this particular as a a dash a double dash b double dash is a true length this is a true length and this angle this angle and this angle is 90 degree angle. So here we are going to be writing this as a vertical trace and here we are going to be writing this as a horizontal trace just I will give a small information about this one as if the line here going to be extended and it going to touch the horizontal reference plane you are going to be calling that as a horizontal trace and if it touches the vertical reference plane you are going to be calling this as a vertical traces so the detail we are going to be studying the separate lecture so you bring it this point in the same point in the downward direction as you are flowing for this particular point you can come back to the same condition in the backwards so now you projected this point this coming as a dash a dash b dash is the frontier of the given line a dash b dash is the frontier of the given line this is a given line the true length this is a true length this line is a true length and this is a frontier length so and this point if you are going to bring it back and it is going to touch this particular line extension of this particular line it is extension of this particular line but it is touching on the same point that is a reason you are going to call this as a vertical trace here only you need not to bother about the detail part of this one so now you bring it this point like this then it is going to touch it here and this is a horizontal traces concern this is a horizontal plane and this is a vertical plane and here it is a front view and this one is a top view and here you can write it as this is a true length this is a true length and we are going to call this as a side view so here this line this line and these lines are a dark lines and rest of this projector should be drawn as a thin line here this projection line also you are going to write as a thin line the important part is you are drawn this particular figure on the right hand side of the figure why you are going to draw it on the right hand side why not you can draw it on this side also so as far as the lines are concerned the same thing you can take it this side also same thing you can take it on this side also only thing is so this is coming as a left hand side view you are going to be drawing it on the right hand side of the figure is concerned if you are going to draw it this side it is coming as a right hand side view so that time this figure is a reverse of this one only nothing more than this one the same figure you are going to get it this side also it is a mirror image of this one you are going to get it this line it will come like this that time rest of all the informations are exactly similar okay this is theta angle this one is phi angle okay so here this concludes the problem on the profile plane is concerned so if you are having this particular type of the problems especially when there is a summation of the angle is 90 degree summation of the angle is 90 degree that time you are expected to follow this particular procedure is concerned so now we have to come back to the original given condition he has given the conditions just to verify all the conditions are satisfied or is there any condition is remaining the summation of the angle is 90 degree that is the reason you have gone for this particular procedure and he has given the position of a is in the vertical reference plane so that is the reason you have taken this particular point is here only vertical reference plane and this particular as a distance given as a 15 millimeter you have taken as above the x y lines 15 millimeter then you are located this particular point and this length he has given as a 50 millimeter you have taken this up to this one as a 50 millimeters so means all the given conditions are satisfied we are going to be comparing this particularly a 3D dimensional 3 dimensional figure and as well as a two-dimensional figure whatever you are drawn here so just you can observe it this particular radical line true length line is available with the profile plane here so this is a profile plane line here so this is a vertical plane and this is a horizontal plane if you are going to observe this particularly in this direction that is a left hand side if you are going to observe this one this particular line and this particular line and the junction is a x y line so now you can observe this line and this line here so this is a vertical reference plane and this is a horizontal reference plane and here this particularly angle is the angle made by the line with the horizontal reference plane that is a theta angle so that is what you are representing here as a theta angle here and this is the angle made by the line with the vertical reference plane this angle we are going to be calling this as a this particular angle so this angle we are going to write it here as this is a five angle so means this is a vertical reference plane and this is a horizontal reference plane this is a vertical reference plane and horizontal reference plane we are going to observe in this direction and we are going to draw this particularly these two lines so here these two lines are vertical reference plane and horizontal reference plane and this is a profile plane so this profile plane is this particularly as a profile plane here so if you are going to open it this one in this particular direction means you are going to be opening this particularly plane in this direction. So that time you are going to get it this particularly a green color plate here. So on this one you are going to get it this image means you are going to be observing from the left hand side you are going to observe from the left hand side and that particular image is coming here. So that is what this particular figure here so you are going to draw this diagram as a on this particular as a green plate nothing but a profile plane. So one of my this particularly as a question previously I put as if the plate is available here. So then you are going to draw this on the left hand side you as if nothing but you are going to tilt this plate in this direction you will get it as an image. If the plate is available at this particularally here and the image is this particular line is back side this plate. So that time we are going to be tilting this particular plate in this direction. If you are going to be tilting this plate in this direction so that time you will get this same image on this side only with the reverse direction. Thank you.