This is the invention by Elon musk

1. Prob.5 :
Soln. :
The focii of an ellipse are 100 mmapart andthe minor axis 70 mm long. Determine the length of the
maior ax0s and draw the elipse by concentric circles method.
2'
P
1'A F1
Pi2
12'
3'
2
12
11'
4
10
Fig.Prob. 5
5
7
9
B7
|P,
To draw the ellipse by concentric circles method, follow the simple steps given below :
Step 1: Draw a vertical ine CD = 70mm as minor axis and mark the mid-point of CD as 0.
Step 2: Draw aline perpendicular to CD and passing through 0.
Step 3: Mark F,and F, on the line perpendicular to CD at adistance of
100
2
=50 mm fromO.
Step 4: We know that CE, +CF, =major axis.

2. Engineering Graphics (MSBTE-Mech)
Step 6:
Step 5: With O
Step 7 :
Step 8:
Step 9:
OR CF, =
CF, =X major axis.
2-13
Engineering
Dy ustng this relation, mark points A
and B2s CE, 0A = OB. Hence will get the line AB
perpendicular bisector of CD, as the major axis.
ints
Wi O as centre, draw two concentric circles with major and minor axes as diameter
respectively.
Divide the outer circleinto 12 equal parts and name the pointsas 1',2,3 * I2.
Draw radial lines 0- 1 0-2% 0-3...0-12 tointersectsmaller circle at points 1, 2,
3,... 12.
Draw a vertical line through 2' and hori~ontal line through 2, both these horizontal and
vertical lines will intersect each other at point P,.
Similarly, by drawing vertical and horizontal lines through the points 3 and 3, 5 and 5, 6
and 6, 8´and 8, 9and 9, 11 'and 11, 12 and 12 respectively will get point P3, Ps PÙ P& P
Pyand Pi2
Step 10 : Draw a smooth curve passing through these points to get the ellipse.

3. Prob.
6:
Soln.: To drawthe parabola by the directrix focus method
follow
thesimple steps given below
Step1:
Step2:
Construct a parabola, when the distance of the focus from the directrix is 50 mm and draw a tangent
and normal at a point on it 40 mm from F.
Step3:
Draw a straight line DD as directrix and mark
any point C
on it.
Draw a line perpendicular to DD at C
as axis.
Mark focus as point F on the axis at a distance
of 50 mm from C ie: CF = 50 mm.
Sten 4: Since eccentricity (e) = I, mark Vas the mid
point of CF i.e.CV= VE.
Sten5: Construction of scale for ratio1,
To construct ascale for ratio 1, draw VA= VE,
perpendicular to the axis. Join CA and extend it.
Step 6: Mark any point 1 on the axis to the right of V
and through 1, draw a perpendicular to the axis.
such that its intersection with the inclined line
CA (extended) is marked as 1.
Step 7: With centre F and radius equalto 1-l, draw an
arc to the perpendicular line drawn through 1
and mark the points P, and P;:
D
D|
A
P3
P
4
P
Fig. Prob,
4
2 34F 4
N'

4. Engineering Graphics (MSBTE-Mech)
Step 8: Mark the points 2, 3, 4 .... etc. and construct perpendicular lines to the axis and
points 2,3,4' ....tc. similarly.
2-15 Engineering Curves &
Loci of Poin
Step9:With centre Fand radius equal to 2-2, 3-3'and 4-4, mark the points P, and P, P and P:
and P, similarly.
Step10 :Draw asmooth curve through the located points, which gives the required parabola.
Construction of tangent and normal to the parabola at given point :
Step 1: Select point Mon the parabola at adistance of 40mm from F and joint MF.
2.
Step 2: Through F,draw a perpendicular line to MF and mark Twhere the line MF intersects the line
DD.
Step 3: Draw alinethrough Mand T. Then line TMT is the required tangent to the parabola.
mark
Step 4: Draw aline NMN´perpendicular to TMT throughMas the required normal to the parabola.

5. Engineering Graphics (MSBTE-Mech)
150 mm from the centre of the circle.
Prob.
19: Draw an involute of a circle 120 mm diameter. Also, draw a normal and tangent to it at a point
Soln.
: To,drawthe involute of acircle, follow the simple stepss given below
Step
1: Draw a circle of diameter 120 mm.
circumference of the circle,
Step
2: Dividethe circle into 12 equal parts and namethe points as I, 2, ..... 11.
Step
3: Draw a horizontal tangential line to the circle at point Phaving its length equal to the
i.e. PP =D=2
2-26
7X 120 = 377.142 mm.
mark P;.
Step
4: Divide thetangential line into12 equal parts and namethe points as12....11!
Step5: Drawthe tangents tothe circle at the points 1, 2, .. 11.
Step6: With centre I and radius equal 1'P cut an arc to the tangent drawn through the point I and
Cen 7: Similarly, with centres 2, 3, .... land radius 2'P 3'p'.... 11'P mark P, P3... Pu
respectively.
Engineering Curves &Loci of Points
Step8: Draw asmooth curvethrough the points P, P, P, .... Pj, P, to get the requiredinvolute.
ow todraw tangent and normalto an involute:
Step 2: Draw a line joining MwithO.
Step1: With centre 0and radius 150 mm, draw an arc on involute to cut it on point M.
P
Sten3: Draw asemicirclewith OMas diameter andmark N
where semicircle intersects the circle.
Sien4: Draw aline through NandM. Thenline NMN istherequirednormal to the involute.
Sien 5:DrawTMT'perpendicularto NMNthroughMas therequiredtangentto the involute.
Pa
P
P
4 2 3 4 5' 6 7 8 9 10 11' P
Fig. Prob.19

6. Prob, 25: Acircle of 40 mm dlameterrolls along àstaightline withoutslipping. Drawthecurve
point Pon the circumference, for one completerevolutionofthecircle. Namathe curNe. Dra
explain different cycloids with the nelp
Soln.: In this problem we are going tofindthe locus of apoint Pwhichlies atthe bottor
of
Ihe cit
tangenttothe curve at a point on it 35 m
mmfromthedirectingline.
Followthesimple steps given below
Step 1: Draw the circle of diameter 40 mm, marksits centre as Co Mark point Pas
he ge
point on the circumference of the circle. Draw aline of length t X D=IY
mm, fromthe base of thecircletotheleft orright. Theline shouldbetothe rioht
he cirds
is rotating clockwise and tothe left if the circleis rotatinganti-clockwise,
(ReferFig. Prob. 25(a)).
040
3
STep 2: Now divide the circle into 12 eaual partsand name the points as 1, 2y J, . 1Z.
(Refer Fig. Prob. 25(b).
2
12 1
8
Fig. Prob. 25(a)
10
Fig. Prob. 25(b)
Step 3: Divide the directing line into l2 equal parts and name the points as 12 3 ... 12. Draw
lines perpendiculartothe directing line at the points 1,2,3, ... 12 andmark C, C, C, ..
Cro, where it intersects the centre line respectively. (Refer Fig. Prob. 25(c).

7. 1 5
Fig. Prob. 25(c)
C
PA,
7
P
8
Fig. Prob: 25(d)
Ca
Siep
4: Draw horizontal lines through points 1, 2, 3, 4,...etc. We assume that the generating circle
completes one revolution in 12steps. If the circle rolls /12 of complete rotation towards
right, the position of point P is lifted up to the height of the horizontal line drawn through the
Fig. Prob. 25(e)
10
point l and centre C,is shifted to a new centre C.. So, with centre C, and radius = 20 mm
(radius of generating circle), cut an arc to the horizontal line, which is drawn through the point
Iand mark;. Similarly, mark P,Pa, P..... etc. on horizontal lines drawn through 2, 3, 4,
.. etc. (Refer Fig. Prob. 25(d)).
Step 1: Mark apoint M35 mn above the directing line.
C11
N
Howto draw atangent and a normal to a cycloid :(Refer Fig. Prob. 25)
11'
G12
P
12'
Sten5: Draw a smooth curve through the points P, P P, .. Pi2: This is the required cycloid.
(ReferFig. Prob. 25(e),.
M
PA2
Sep 3: Through draw aperpendicular line to the directing line and mark N.
Step 2: With centre Mand radius R = 20 mm (radius of the generating circle), cut an arc on the ce
line and mark .
Sep 4 : Draw alinethrough Mand N.The line MN is the required normal to the cycloid.
Dep 5: Draw TMT´perpendicular toMN, through Mwhich is the required tangent to the cycloid.