Engineering Graphics ''Planes''

Projection of planes

Introduction Rectangle Circle Rhombus

problem 1: Rectangle 30mm and 50mm sides is resting on HP on one small side Construction

Step 1. Draw a rectangle abcd of sides 30mm & 50mm, which is parallel to HP. This is the top view of the rectangle. Now, draw the projection of it's sides above the XY axis. This is the front view of the rectangle i.e. a'b'c'd'.

Step 2. Now, the front view a'b'c'd' of the rectangle makes 45^o inclination to the HP. Draw it's projection below XY axis, which gives the top view a₁b₁c₁d₁.

Step 3. Now, make 30^o inclination of one of the small side of rectangle a₁b₁c₁d₁. to the VP. Finally draw the points a₁'b₁'c₁'d₁' as shown above .

problem 2 : A circle of 50 mm diameter is resting on Hp on end A of it’s diameter AC which is 30^o inclined to Hp while it’s Tv is 45^o inclined to Vp. Draw it’s projections.

Construction

Step 1.. Firstly, draw a circle of 25 mm radius(or 50 mm diameter) parallel to HP.
This is the top view of the circle. Name it abcd as shown in figure & draw it's projection above the XY axis, which is the front view of the circle i.e. a'b'd'c'.

Step 2.. Now, the front view a'b'd'c' of the circle makes 30^o inclination to the
HP. Draw it's projection below XY axis, which gives the top view a₁b₁c₁d₁.

Step 3. Now, make 45^o inclination of the diagonal a₁c₁ to the VP. Finally draw the points a₁'b₁'c₁'d₁' as shown above


Construction

Step 1. . Draw a rhombus abcd of diagonals 40 mm and 70 mm long respectively parallel to HP. This is the top view of the rhombus. Now, draw the projection of it's sides above the XY axis, which shows it's front view i.e. a'b'd'c'.

Step 2. . Now, the front view a'b'd'c'of the rhombus makes 45^o inclination to the
HP.Draw it's projection below XY axis, which gives the top view a₁b₁c₁d₁.

Step 3. . Now, make 35^o inclination of the longer diagonal a₁c₁ to the VP. Finally draw the points a₁'b₁'c₁'d₁' as shown above

Engineering Graphics ''Lines''

Projection of lines



PROBLEM 3 : Fv of line AB makes 45^o with XY line and measures 60 mm. Line’s Tv makes 30^o with 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.

Construction

Step 1. Draw xy line, one projector and locate fv a’ 15 mm above xy.

Step 2. Take 45^o from a’ and marking 60 mm on it locate point b’.

Step 3. Draw locus of VT, 10 mm below xy & extending Fv to this locus locate VT. Draw projector from vt, locate v on xy.

Step 4. From v take 30^o downward as Tv and it’s inclination can begin with v. Draw projector from b’ and locate b i.e.Tv point.

Step 5. Now rotating views as usual TL and it’s inclinations can be found. Name extension of Fv, touching xy as h’ and below it, on extension of Tv, locate HT.

PROBLEM 2 : Fv of line AB is 50^o inclined to xy and measures 55 mm long while it’s Tv is 60^oinclined to xy line. If end A is 10 mm above Hp and 15 mm in front of Vp, draw it’s projections,find TL, inclinations of line with Hp & Vp.

Construction

Step 1. Draw xy line and one projector. Locate a’ 10 mm above xy and a 15 mm below xy line.

Step 2. Draw locus from these points.

Step 3. Draw Fv 50^o to xy from a’ and mark b’ cutting 55 mm on it. Similarly draw Tv of 60^o to xy from a & drawing projector from b’ Locate point b and join a b.

Step 4. Then rotating views as shown, locate True Lengths ab₁ & a’b₁’ and their angles with Hp and Vp.

PROBLEM 1 : Line AB 75 mm long makes 45^o inclination with Vp while it’s Fv makes 55^o . End A is 10 mm above Hp and 15 mm in front of Vp. If line is in 1st quadrant draw it’s projections and find it’s inclination with Hp.

Construction

Step 1. Draw x-y line. Draw one projector for a’ & a Locate a’ 10 mm above x-y & Tv a 15 mm below xy.

Step 2. Draw a line 45^o inclined to xy from point a and cut TL 75 mm on it and name that point b₁ Draw locus from point b₁ .

Step 3. Take 55^o from a’ for Fv above xy line. Draw a vertical line from b₁ up to locus of a and name it 1. It is horizontal component of TL & is LFV.

Step 4. Continue it to locus of a’ and rotate upward up to the line of Fv and name it b’.This a’ b’ line is Fv.

Step 5. Drop a projector from b’ on locus from point b₁ and name intersecting point b. Line a b is Tv of line AB. Draw locus from b’ and from a’ with TL distance cut point b₁‘

Step 6. Join a’ b₁’ as TL and measure it’s angle at a’. It will be true angle of line with HP

Engineering Graphics ''Spiral''

Spiral

Definition :-

SPIRALS : IT IS A CURVE GENERATED BY A POINT WHICH REVOLVES AROUND A FIXED POINT AND AT THE SAME MOVES TOWARDS IT.

Construction

Step 1. With PO radius draw a circle and divide it in EIGHT parts. Name those 1,2,3,4, etc. up to 8

Step 2. Similarly divided line PO also in EIGHT parts and name those 1,2,3,-- as shown.

Step 3. Take o-1 distance from op line and draw an arc up to O1 radius vector. Name the point P1

Step 4. Similarly mark points P2, P3, P4 up to P8.
And join those in a smooth curve.

It is a SPIRAL of one convolution