Projection of points questions with answers | Projection Of Points [DOWNLOAD-PDF] VTU-notes


Problem:1- A point P is 15mm above HP and 25mm infront of VP.Another point Q is 25mm behind VP and 40mm below HP . Draw their projections when the distance between their projectors parallel to XY line is zero mm and show the right side view of the point Q.

Solution:


Steps:

1--draw XY line 1st. Draw a line perpendicular to XY line on which the front and top view of point P and Q is going to be lie as the distance between the projector of point P and Q is zero.
2--take a point p'(front view) 15mm above XY line as the point is 15mm above HP.
3--take another point p(top view) 25mm below XY line as the point is 25mm infront of VP and it's in the same line on which the point p' lies.
4--take a point q(top view) 25mm above XY line as the point is 25mm behind VP and it's in the same line on which the point p and p' lies since the distance between the two points is zero mm.
5--take another point q'(front view) 40mm below XY line as the point is 40mm below HP and in the same line on which the Points p',p and q lies.
6--draw a perpendicular line X1Y1 perpendicular to XY line which represents the PP (profile plane).
7--now from the intersection of the X1Y1 line and the XY line draw a 45degree line .
8--project the point q(top view) towards the 45degree line and project it down after intersecting the 45degree line.
9--also project the point q' towards the projected point p which intersect each other and this intersection point is the point q" i.e, the Right Side view of the point Q.
10--mark the dimensions.


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Problem:2- Draw all the three views of a point P lying 60mm below HP,70mm infront of VP and 40mm  from the RPP (Right Profile Plane).

Solution:

Steps:

1--draw XY line 1st. Draw a line perpendicular to XY line on which the front and top view of point P is going to be lie.
2--take a point p'(front view) 60mm below XY line as the point is 60mm below HP. And take this point on the perpendicular line.
3--take another point p(top view) 70mm below XY line as the point is 70mm below HP.
4--draw a perpendicular line X1Y1 perpendicular to the XY line and 40mm away from the projector of point P this X1Y1 line forms the RPP.
5--draw a 45degree line from the Point of intersection of the X1Y1 line and the XY line in downward direction.
6--now project the point p towards the 45 degree line. Simultaneously project the point p' also bothe the projector intersect each other at point p"(Right Side view)
7--mark the dimensions.


Problem:3- Two points R and S are on HP. The point R is 35mm infront of VP, while S is 50mm behind VP.The line joining their top views making an angle of 40degree with XY line find the horizontal distance between the two projectors.

Solution:

Steps:

1--draw XY line 1st. Draw a line perpendicular to XY line on which the front and top view of point R is going to be lie.
2--take a point r'(front view) on XY line.Since the point R lies on HP.
3--take another point r(top view) 35mm below XY line on the same line on which the r' lie.
4--draw a locus(line parallel to XY line) 50mm above XY line since we don't know the exact position of point S we know only that S is 50mm above XY line ( behind means draw the point above XY line)
5--at point r draw a locus from Point r draw a line making an angle of 40degree to locus r and passing XY line it cuts the locus s this point is the point s.
6--from point s draw a line perpendicular XY line and the point at which it cuts is the point s'.
7--now find the distance between the Points r' and s' this will be the distance between the two projectors. The distance between the two projectors is 99mm



Problem:4-The point P is 45mm above HP, 60mm  behind VP and 30mm from RPP(Right Profile Plane).Draw the three principle views of the point.

Solution:

Steps:

1--draw XY line 1st. Draw a line perpendicular to XY line on which the front and top view of point P is going to be lie.
2--take a point p'(front view) 45mm above XY line.
3--take another point p(top view) 60mm above XY line (60mm behind VP) on the same line on which the point p' lies.
4--draw a line X1Y1 line perpendicular to XY line and 30mm away from the projector of p and p' this X1Y1 line will be the RPP.
5--from the intersection of XY and X1Y1 line draw a 45degree line on the right side.
6--Now from the point p draw a projector   which cuts the 45degree line then from this intersection point draw another projector  towards XY line.
7--from the point p' draw another projector  which cuts the downward projector  passing through the 45degree line this this intersection point of the projectors is p".
8--mark all the dimensions.



Problem:5- A point M is 30mm infront of VP and 20mm above HP and another point N is 15mm behind VP and 25mm below HP. The horizontal distance between the points parallel to XY line is 50mm. Draw the projection of the Points M and N and join their front and top views.Draw the right side view of the point N only.

Solution:

Steps:

1--draw XY line 1st. Draw a line perpendicular to XY line on which the front and top view of point M is going to be lie.
2--take a point m(top view) 30mm below XY line as the point is 30mm infront of VP.
NOTE - if the point is related to HP then this point is taken as front view and if the point is related to VP then this point is considered as top view.
3--take a point m'(front view) 20mm above XY line on the same line in which the point m lies as the point is 20mm above HP.
4--draw another line perpendicular to XY line and 50 mm away from the projector of point m in which the point n is going to be lie.
5--take a point n(top view) on the perpendicular line and15mm above XY line as the point is 15mm behind VP.
6--take another point n'(front view) 25mm below(as the point is below HP) XY line and on the same line on which the point n lies.
7--join the points m'n' and the points mn.
8--draw another line X1Y1 perpendicular to the XY line and this line will be the RPP.
9--from the point of intersection of the X1Y1 line and XY line draw a 45degree line on the right side of the X1Y1 line.
10--from the point n draw a projector  which cuts the 45degree line after intersecting the 45degree line project the projector downward.
11--from the point n' draw another projector which cuts the downward projector the intersection of this two projectors is the point n".
12--mark the dimensions.



Problem:6- Two points P and Q are on HP. The point P is 30mm behind VP, while the point Q is 50mm infront of VP.The line joining their top views makes an angle of 40degree with XY. Find the horizontal distance between their projectors parallel to XY line.

Solution:

Steps:

1--draw XY line 1st. Draw a line perpendicular to XY line on which the front and top view of point P is  going to be lie.
2--take point p'(front view) on XY line as the point P is on HP.
3--take point p(top view) 30mm above XY line(on the same line on which the point p' lies) as the point is 30mm behind VP.
4--draw a locus, 50mm below XY line this locus is the locus Q since the point Q is 50mm infront of VP.
5--from point p draw another locus P and draw a line making an angle 40degree with locus P and which cuts the XY line at 40degree and it meets the locus Q and this intersection point of locus Q and 40degree line is the point q( top view).
6--take a point q'(front view) on the XY line and in the same line on which the point q(top view) lies.
7--measure the distance between the two projectors of p and q i.e, 96mm and also mark the dimensions.



Problem:7- A point A is 20mm above HP and in the first quadrant. It's shortest distance between the XY line is 40mm.Draw the projection and determine the distance from VP.

Solution:

Steps:

1--draw XY line 1st. Draw a line perpendicular to XY line on which the front and top view of point A is going to be lie.
2--take a point a'(front view) 20mm above XY line as the point is 20mm above HP.
3--since the point is in first quandrant therefore the top view of the point is below XY line and the front view will be above XY line.
4--since XY line is the intersection of the vertical Plane(VP) and horizontal plane (HP) therefore draw a line X1Y1 (represents Vertical plane) perpendicular to XY line.
5--draw the projection of point a' which passes the X1Y1 line.
6--now from the point of intersection of XY line and X1Y1 line draw an arc of length 40mm which cuts the projection line of a'. And this intersection point is a".
7--Now again from the intersection of XY line and X1Y1 line draw a 45degree line in downward direction.
8--project the point a" downward which cuts 45degree line and then again project it back towards the line of the point a' and cuts this line and this interesting point is the point a(top view).
9--now measure the distance between the point a(top view) and XY line i.e, 34mm. And mention the dimensions.



Problem:8-  Point A is 35mm below HP, 15mm behind VP and 25mm from RPP .Draw it's projection and name the right side view.

Solution:

Steps:

1--draw XY line 1st. Draw a line perpendicular to XY line on which the front and top view of point A is going to be lie.
2--take a point a'(front view) 35mm below XY line as the point is 35mm below HP.
3--take another point a(top view) 15mm above XY line as the point is 15mm behind VP.
4--draw a perpendicular line X1Y1 25mm away from the projector line of point A. This X1Y1 line will be the PP(profile plane).
5--from the intersection of the line X1Y1 and XY line draw a 45 degree line.
6--project the point a towards the 45degree line and after cutting the 45degree line then project it downward.
7--draw the projector of point a' which meets the downward projector of point a this interesting point of projectors is the point a" and also the right side view of the point A.
8--mark the dimensions.



Problem:9- A point 'A' is 30mm infront of VP(Vertical Plane) and 40mm above HP. Another point 'B' is 20mm behind VP and 35mm below HP.The horizontal distance between the points measured parallel to XY line is 60mm. Draw the three projection of the points.join their front and top views.

Solution:

Steps:

1--draw XY line 1st. Draw a line perpendicular to XY line on which the front and top view of point A is going to be lie.
2--take a point a(top view) 30mm below XY line as the point is 30mm infront of VP.
3--take another point a'(front view) 40mm above XY line (as the point is 40mm above HP) on the same line on which the point a lies.
4--draw another perpendicular to XY line at a distance of 60mm from the projector of point A on which the point B is going to be lie.
5--take a point b(top view) on the perpendicular line and 20mm above XY line as the point is 20mm behind VP.
6--take another point b'(front view) 35mm below XY line as the point is 35mm below HP and take the point on the same line on which the point b lies.
7-- draw a perpendicular line X1Y1 perpendicular to XY line and this line is the profile plane.
8--from the intersection of the X1Y1 line and the XY line draw two 45degree lines one is in upward direction and another one is in downward direction.
9--project the point a towards the 45degree line and parallel to XY line,then project it in upward direction simultaneously project the point a' towards the projected point a which intersect each other and this intersection point is the point a"(side View of point A).
10--project the point b towards the 45degree line and parallel to XY line,then project it in downward direction simultaneously project the point b' towards the projected point b which intersect each other and this intersection point is the point b"(side View of point B).
11--join a' b' (front views) and ab(top views) and mark the dimensions.



Problem:10- A point P is on HP and 30mm infront of VP.Another point Q is on VP and 40mm above HP. The distance between the projectors parallel to XY line is 50mm find the distance between front and top views of the points P and Q.

Solution:

Steps:

1--draw XY line 1st. Draw a line perpendicular to XY line on which the front and top view of point P is going to be lie.
2--take a point p'(front view) on XY line as the point is on HP.
3--take another point p (top view) 30mm below XY line as the point is 30mm infront of VP and on the same line on which the point p' lies.
4--draw a perpendicular line to XY line 50mm away from the projector of point P,on this line the point Q is going to be lie.
5--now take a point q (top view) on XY line as the point Q is on VP and the point is along the perpendicular line of point Q.
6--take another point q'(front view) 40mm above XY line as the point is 40mm above HP and on the same line on which the point q lies.
7--mark all the dimensions and measure the distance p'q' and pq i.e., the distance between the point p' and q' is 64mm and the distance between the point p and q is 58mm.
 


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