January 2013 an Key

8/13/2019 January 2013 an Key

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1(a) Construct a hyperbola when the distance between the focus and the directrix is 40 mm and

the eccentricity is 4/3. Draw a tangent and normal at any point on the hyperbola.

Procedure

1. Draw a line AB as directrix.2. From point C on AB draw a line CE perpendicular to AB. Mark the focus point F such that

CF = 40 mm.

3. Divide the line CF into 7 equal parts.4. Mark the vertex D such that CD = 3/7 thof CF.5. Draw a line DG = DF perpendicular to DF(also draw DG1)6. Draw the line joining C & G and extend it (also CG1)7. Make a point 1 on the line CE.8. Draw a line through 1 perpendicular to CE to intersect at 1 on CG, if produced.


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9. With F as centre 11 as radius draw an arc , cutting the line 11 at 1(also 11)10.Similarly mark points 2,3,4 on the line CE and get the points 21,31,41,.and 21,31,41,..11.Join all the points by freehand. The curve obtained is HYPERBOLA.12.Mark the point P on the Hyperbola. Draw the line joining P & F.13.Draw a line perpendicular to FP till it meets the line AB at Q. Also draw the line joining Q and P.14.Now the line PQ is the required tangent.

1(b) Draw the involute of a circle of 40 mm diameter. Also draw a tangent and normal to the curve ata point 95 mm from the centre of the circle.

Procedure

1. With O as a centre and radius OP=20 mm, draw a circle.2. Draw a line PQ = 40 = 126mm, tangent to the circle at P.3. Divide the circle into 12 equal parts and number the divisions as 1, 2, 3, etc.4. Divide PQ into 12 equal parts and number of divis ions as 1, 2, 3, etc.5. Draw the tangents to the circle at point 1, 2, 3, etc. On these tangents, locate points P1, P2, P3,

etc. Such that 1-P1 = P-1, 2-P2 = P-2, 3-P3 = P-3 and so on.

6. Join P, P1, P2, P3,.Q by a smooth curve.To draw Tangent and Normal

1. First locate point M on the curve such that OM = 95 mm.2. Join OM.3. Draw a semicircle with OM as a diameter, cutting the circle at N.4. Join NM for the required normal. Draw T-T, perpendicular to NM at M.


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2(a) The top view of a 75 mm long line AB measures 65 mm while the length of its front view is

50 mm. itsone end A is in H.P and 12 mm in front of the V.P. Draw the projections of AB

and determine its inclinations with H.P and the V.P.

Procedure

1. Draw the reference line XY to locate a at a distance of 12mm below XY reference line and mark ain the XY line itself. Draw the locus of a and a.

2. Mark b2 in the aline such as ab2 = 50mm(Front View length). From the b2draw a downwardvertical line and take aas centre and true length = 75 mm as radius draw an arc which creates b2.

Join ab2.

3. Similarly mark b1in the locus a such as ab1= 65 mm(Top View length). From b1draw an upwardvertical line and take aas centre and true length = 75 mm as radius draw an arc which creates b1.

Join ab1.4. To get final top view (ab), take ab1as radius and aas centre draw an arc(clockwise direction) upto

the locus of b2. Join ab.

5. Similarly to get final front view (ab), take ab2 as radius and a as centre draw an arc(anticlockwise direction) upto the locus of b1. Join ab.

6. Determine the inclinations with HP and VP such as shown in the figure.


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2(b) Draw the projections of a regular hexagon of 25 mm side having one of its sides in the HP

and inclined at 60 to the VP and its surface making an angle of 45 with the HP.

Procedure

1. Draw the top view, assuming the plane lying on the ground with one edge cd perpendicular to XY.Draw projectors from a,b,, f to get front view.

2. Tilt the front view at an angle of 45oto XY plane.3. Draw projectors from this tilted front view a, b,.,dand horizontal lines from the top view

a1,b1,f1to get points in the new top view.

4.

Tilt this top view an angle of 60o

to XY. Again draw projectors from this top view points a1,b1,.,f1and horizontal lines from front view points a, b,,f.

5. The base edge afin touching the XY, since the plane is resting on an edge in the H.P


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3(a) A hexagonal prism side of base 25 mm and axis and axis 60 mm long, lies with one of its

rectangular faces on the H.P such that the axis is inclined at 45 to the V.P. Draw the

projections.

Procedure

1. The top view and the front view of the prism are drawn asuming that the axis is perpendicular tothe VP. The front view is a hexagon with one of its sides in xy.

2. The position of the top view is changed such that the axis is inclined at 35 oto xy. As said earlier,mere change in position will not alter the shape and size of the top view.

3. The different corners of the tilted top view are projected upwards. Horizontal lines are drawn fromdifferent points in the first front view. The meeting points of the projectors and horizontal lines fix

the points in the second front view. For instance, the point of intersection of the projector from p1

and the horizontal line from p1 locates p11. One of the corners in the second front view. Similarly,

other corners also are located.

4. The corners of the visible end are joined first. Here p11q11r11s11t11u11represents the visible end andhence is drawn by using full lines. Then, the outermost lines are drawn in full lines. The lines for thelonger edges are drawn next. The lines for the end which is partly hidden are then drawn. The

hidden edges are shown by dashed lines.

5. Here, the edges 111211. 111611 and p11111 are hidden. Part of p11 111 coincides with the visibles11411. The hidden edge coincides with visible edges.


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3(b) A pentagonal prism, side of base 25 mm and axis 50 mm long, rests with one of its shorter

edges on H.P such that the base containing that edge makes an angle of 30 to H.P and its

axis parallel to V.P. Draw its projections.

Procedure

1. Draw the plan of the prism of base side 30 mm and with one of its base edges is perpendicular toXY.

2. Draw the corresponding elevation of the prism of height 70 mm.3. With the base inclined at 30oto HP. Draw final elevation of the prism.4. From a1,b1,c1,11,21, & 31 draw projectors which meets lines parallel to XY5. Join these points to get the plan of the prism. Here since the points 3 and 4 are nearer to XY line,

the lines passing through these two points are not visible. So draw these by dashed line type in the

final plan.


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4(a) A hexagonal pyramid base 30 mm side and axis 70 mm long is resting on its slant edge of

the face on the horizontal plane. A section plane perpendicular to the V.P inclined to the H.P

passes through the highest corner of the base and intersecting the axis at 25 mm from the

base. Draw the projections of the solid and determine the inclination of the section plane

with the H.P.

Procedure

1. Draw the plan of the pyramid of base side 30 mm such that one of its sides is parallel to the XYline.

2. Draw the corresponding elevation of height 70 mm.3. Tilt the pyramid such that such that oa, one slant edge, lies on the ground. Draw the

corresponding plan.

4. Draw the cutting plane line in elevation such that it is perpendicular to VP and parallel to HP andbesides the axis of the solid.

5. Mark the cutting plane points wherever the plane cuts the solid as 1,2,3,4,5,6 in front view.6. Project the cutting points to the corresponding edges in the plan. Join these projected points, in the

plan, in sequence to get the final sectional plan and hatch it.


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4(b) A cone of base 50 mm diameter and axis 60 mm long, is resting on its base on H.P. it is cut

by a section plane, perpendicular to V.P and parallel to an extreme generator and passing

through a point on the axis at a distance of 20 mm from the apex. Draw the development of

retained solid.

Procedure

1. Draw the projections of the cone with diameter 50 mm and axis 60 mm length. Divide the basecircle into 8 equal parts in the plan and draw generators from all the points in the elevation.

2. Here the extreme generators o1a1& o1e1 show the true slant height. So draw the full developmentof the cone which is a sector with o as centre and o 1a1as radius such that = r * 360o /R.

3. Draw the cutting plane line in the elevation perpendicular to VP. Meeting the axis at 20 mm fromthe apex. Give notation for cutting points such as 1,2,3,4,5,6, 7.

4. Mark the cutting points 1,2,3,4,5,6,7 in the full development drawn nearer to the front and topviews.

5. Join these in proper sequence by free hand.


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5(a) A pentagonal pyramid, with edge of base 40 mm and axis 70 mm long is resting on its base

on H.P. one of the base edges of the pyramid is perpendicular to V.P. A section plane,

perpendicular to V.P and inclined to H.P at 30 o passes through the axis at a height of 30 mm

from the base. Draw the isometric projection of the truncated pyramid.

Procedure

1. Draw the plan and elevation of the pentagonal pyramid showing the section plane with the givendata.

2. Assuming that the pyramid is contained in a solid box, draw the isometric view of the solid box first.On this draw the section plane in isometric by setting the heights of the points from the elevation.

3. Measure the cutting point distances from the plan and mark in the isometric area.4. Follow the same to get the other cutting points in the section plane in isometric.5. Join all these in sequence and darken the visible slant, base edges.


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5(b) A rectangular lamina of size 30 mm x 50 mm rests on the ground with one edge on PP

and the remaining portion behind PP. The station point is 60 mm above GP and 30 mm

infront of PP and lies on a central plane 35 mm to the left of the nearest edge of the lamina.

Draw the perspective view of the lamina.

Procedure

1. Draw the plan and elevation of the rectangular plane with respect to PP and GP respectively.2. Draw the CP line 35 mm to the left of the left end of the plane and on it mark the top view of the

station point s 30 mm infront of it S 60mm above GP.

3. Join all the elevation points with s and the plan points with s.4. From the intercepts on PP draw projectors till they meet the respective lines passing through s,

which are the necessary points in perspective.

5. Join the points in sequence to complete the perspective view.

January 2013 an Key

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