Problems involving traces of the line

Problems involving traces of the line

TRACES OF THE LINE:

These are the points of intersection of A-line (or it's extension) with respective reference planes.

A line itself or its extension. Where ever touches H.P. that point is called the trace of the line on H.P. (It is called H.T)

Similarly, A-line itself or its extension, where ever touches V.P., that point is called the trace of the line on V.P.(It is called V.T.)

V.T. : it is a point on VP.

Hence it is called FV of a point in VP.

Hence it's TV comes On the XY line. (Here onward named as V)

H.T. : It is a point on HP.

Hence it is called TV of a point in HP.

Hence it's FV comes on the XY line. (Here onward named as 'h')

Steps To Locate HT.

(when projections are given.)

1. Begin with FV. Extend FV up to the XY line.


2. Name this point h' (as it is an FV of a point in HP)


3. Draw one projector from h'.


4. Now extend the TV to meet this projector. This point is HT

Steps To Locate VT.

(When projections are given.)

1. Begin with TV. Extend TV up to the XY line.


2. Name this point V (as it is a TV of a point in VP)


3. Draw one projector from V.


4. Now extend FV to meet this projector. This point is VT

Observe  and Note:

1. Point h' & v always on x-y line.


2. VT' & V always on one projector.


3. HT & h' always on one projector.


4. TV - v - HT always colinear.


5. FV- h' - HT always colinear.

PROBLEM 1:

FV of line AB marks 45^. angle with the XY line and measures 60 mm. Line's TV marks 30^. with the XY line. End A is 15 mm above HP and it's VT is 10 mm below HP. Draw projections of line AB, determine inclinations with HP & VP, and locate HT, VT.

Solution Steps:

1. Draw XY line, one projector, and locate FV a' 15 mm above XY.


2. Take 45^. angle from a' and marking 60 mm on it locate point b'. Draw locus of VT, 10 mm below XY & extending FV to this locus locate VT. as FV-h'-VT' lie on one st.line.


3. Draw projector from VT, locate V on XY. From V take 30^. angle downward as TV and it's inclination can begin with V.


4. Draw projector from b' and locate b l.e. TV point. Now rotating views as usual TL and its inclinations can be found.


5. Name extension of FV, touching XY as h' and below it, on the extension of TV, locate HT.

PROBLEM 2:

One end of line AB is 10 mm above HP and the other end is 100 mm in front of VP. it's FV is 45^. inclined to XY while it's  HT & VT are 45 mm and 30 mm below XY respectively. Draw projection and find TL with its inclinations with HP & VP.

Solution Steps:

1. Draw XY line, one projector, and locate a' 10 mm above XY.


2. Draw locus 100 mm below XY for points b & b_1, Draw loci for VT and HT, 30 mm & 45 mm below XY respectively.


3. Take 45^. angle from a' and extend that line backward to locate h' and VT, & Locate V on XY above VT. Locate HT below h' as shown.


4. Then join V-HT- and extend to get top view end b. Draw projector upward and locate b' Make a b & a' b' dark. Now as usual rotating views find TL and it's inclinations.

PROBLEM 3:

Projectors drawn from HT and VT of a line AB are 80 mm apart and those drawn from its ends are 50 mm apart. End A is 10 mm above Hp, VT is 35 mm below HP while it's HT is 45 mm in front of Vp. Draw projections, locate traces, and find TL of line & inclinations with HP and VP.

Solution Steps:

1. Draw XY line and two projectors, 80 mm apart and locate HT & VT, 35 mm below XY and 55 mm above XY respectively on these projectors.


2. Locate h' and V on XY as usual.


3. Now just like the previous two problems, extending certain lines complete FV & TV and as usual find TL and it's inclinations.

 

This concept is used to solve the next three problems.

Instead of considering a & a' as projections of the first point, if VT, is considered the first point, then true inclinations of line with HP & VP i.e angle θ & Φ can be constructed with points VT; & V respectively.



Then from point V & HT angle β & Φ can be drawn. & From point VT' & h' angle α & θ can be drawn.

 

PROBLEM 1:

LIne AB 100 mm long is 30^. and 45^. inclined to HP & VP respectively. End A is 10 mm above HP and its VT is 20 mm below HP. Draw projections of the line and its HT.

Solution Steps:

1. Draw XY, one projector, and locate on it VT and V.


2. Draw locus of a' 10 mm above XY. Take 30^. from VT and draw a line.


3. Where it intersects with the locus of a' name it a_1^, as it is TL of that part.


4. From a_1^, cut 100 mm (TL) on it and locate point b_1^, Now from v take 45^. and draw a line downwards & Mark on it distance VT-a_1^, i.e. TL of extension & name it a₁.Extend this line by 100 mm and mark point b_1.


5. Draw its component on the locus of VT' & further rotate to get other ends of FV i.e. b' join it with VT' and mark intersection point (with the locus of a_1^, ) and name it a'.


6. Now, as usual, locate points a and b and h' and HT.

PROBLEM 2:

A line AB is 75 mm long. its FV & TV make 45^. and 60^. inclinations with X-Y line reps ENd A is 15 mm above HP and VT is 20 mm below XY line. The line is in the first quadrant. Draw projections, find inclinations with HP & VP. Also locate HT.

Solution Steps:

Similar to the previous only change is instead of line's inclinations, views inclinations are given.

So first take those angles from VT & V properly, construct FV & TV of extension, then determine its TL ( V-a₁ ) and on its extension mark TL of line and proceed and complete it.



Exercise

The projectors drawn from VT & end A of line AB are 40 mm apart. End A is 15 mm above HP and 25 mm in front of VP. VT of the line is 20 mm below HP. If the line is 75 mm long, draw its projections, find inclinations with HP & VP.

answer

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