General Case of the line inclined to both HP & VP.

General Case of the line inclined to both HP & VP.

( BASED ON 10 PARAMETERS )

PROBLEM 1:

Line AB is 75 mm long and it is 30^. & 40^. inclined to Hp & VP respectively. End AA is 12 mm above hp and 10 mm in front of VP. Draw projections. The line is in 1^st quadrant.

SOLUTION STEP:

1. Draw XY line and one projector.


2. Locate a^, 12 mm above XY line &a 10 mm below XY line


3. Take 30^. angles from a^, & 40^. from a and mark TL i.e. 75 mm on both lines. Name those points b₁^, and b₁ respectively.


4. Join both points with a^, and a resp.


5. Draw horizontal lines (Locus) from both points.


6. Draw horizontal component of TL a b₁ from point b₁ and name it 1.(the length a-1 gives the length of FV as we have seen already)


7. Extend it up to locus of a' and rotating and as center locate b' as shown. join a' b' as FV.


8. From b' drop a projector downward & get point b₁ to join a & b

PROBLEM 2:

Line AB 75 mm long makes 45^. inclination with VP, while it's FV, makes 55^. End A is 10 mm above HP and 15 mm in front of VP. if the line is in 1 quadrant draw its projections and find it's an inclination with HP.

SOLUTION STEPS:-

1. Draw the X-Y line.


2. Draw one projector for a^, & a


3. Locate a^,  10 mm above X-Y & TV a 15 mm below XY.


4. Draw a line 45^. inclined to XY from point a and cut TL 75 mm on it and name that point b₁ Draw locus from point b₁


5. Take 55^. angles from a for FV above the XY line.


6. Draw a vertical line from b₁ up to locus of a and name it 1. It is a horizontal component of TL& is LFV.


7. Continue it to the locus of a^, and rotate upward up to the line of FV and name it b^, This a^, b^, line is FV.


8. Drop a projector from b^, on locus from point b_1, and name intersecting point b. Line a b is Tv of line AB.


9. Draw locus from b^, and from a^, with TL distance cut point b_1^,


10. Join a b as TL and measure its angle at a^,

It will be a true angle of line with HP.



PROBLEM 3:

FV of line AB is 50^. inclined to XY and measures 55 mm long while its TV is 60^. inclined to the XY line. if end A is 10 mm above Hp and 15 mm in front of VP, draw its projection, find TL, inclinations of line with HP &VP.

SOLUTION STEPS:

1. Draw XY line and one projector.


2. Locate a^, 10 mm above XY and a 15 mm below XY line.


3. Draw locus from these points.


4. Draw FV 50 to XY from a^, and mark b^, cutting 55 mm on it.


5. Similarly, draw TV 60^. to XY from a & drawing projector from b^, Locate point b and join a b.


6. Then rotating views as shown, locate True lengths ab₁ & a^, b_1^, and their angles with HP and VP.

PROBLEM 4:

Line AB is 75 mm long. it's FV and TV measure 50 mm & 60 mm long respectively. End A is 10 mm above HP and 15 mm in front of VP. Draw projections of line AB if end B is in the First Quadrant. Find angle with HP and VP.

SOLUTION STEPS:

1. Draw XY line and one projector.


2. Locate a^, 10 mm above XY and a 15 mm below XY line.


3. Draw locus from these points.


4. Cut 60 mm distance on the locus of a^, & mark 1^, on it as it is LTV.


5. Similarly cut 50 mm on the locus of a and mark point 1 as it is LFV.


6. From 1^, draw a vertical line upward and from a^, taking TL (75 mm) in compass, mark b_1^, the point on it. Join a^, b_1^, points.


7. Draw locus from b_1^,


8. With the same steps below get b₁ point and draw also locus from it.


9. Now rotating one of the components l.e a-1 locate b^, and join a^, with it to get FV.


10. Locate TV similarly and measure angles θ & Φ

PROBLEM 5:

T.V. of a 75 mm long Line CD, measures 50 mm. End C is in HP and  50 mm in front of VP. END D is 15 mm in front of VP and it is above HP. Draw projections of CD and find angles with HP and VP.

SOLUTION STEPS:

1. Draw XY line and one projector.


2. Locate c^, on XY, and c 50 mm below the XY line.


3. Draw locus from these points.


4. DDraw locus of d 15 mm below XY


5. Cut 50 mm & 75 mm distance on the locus of d from c and mark points d & d₁ as these are TV and line CD lengths resp. & join both with c.


6. From d₁ draw a vertical line upward up to XY l.e. up to the locus of c^, and draw an arc as shown.


7. Then draw one projector from d to meet this arc in d^, point & join c^, d^,


8. Draw the locus of d^, and cut 75 mm on it from c^, as TL


9. Measure angles θ & Φ

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