The curve traced is an epicycloid, which is generated when a circle of radius 25 mm rolls around the outside of a larger circle of radius 150 mm without slipping. To draw the epicycloid: (1) Mark points around the smaller circle to divide it into 12 equal parts as it rolls, (2) Draw radii from the center of the large circle to these points to locate the centers of the smaller circle as it rolls, and (3) Draw arcs from these centers to trace the curve of the epicycloid. A tangent and normal are then drawn to the curve at a point 85 mm from the center of the large circle.

1. Q) A circle of 50 mm rolls on another circle of 150 mm and outside it. Name the curve.
Trace the path of a point P on the circumference of the smaller circle. Also draw a
tangent and normal to the curve at a point on the curve, 85 mm from the centre of the
bigger circle.
Ans) The Curve is an epicyloid as the circle rolls on outside of another circle.
The angle for one revolution will be equal to (360 * d/D).
1) Draw a circle of 25 mm radius with centre C and mark P as the bottom most point. Divide
the circle into 12 parts and label them as 1, 2, 3…12 after P.
2) From P, mark O, centre of big circle (base circle) at PO=R=75 mm.
3) Mark ∟POA = θ= 360*(d/D) and draw OA at θ from OP.
θ
θ =1200
R.C ROLLING CIRCLE (GENERATING CIRCLE)
B.C BASE CIRCLE (DIRECTING CIRCLE)
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P
C 3
11
6
9
3
1
2
11
1
2
P
O
6
A
R. C (d)
B.C (D)
Epi-Cycloid

2. The above figure is the profile of the Epi Cycloid that is generated when the rolling circle
of d rolls on a base circle of D.
4) With O as centre and OP radius, draw base circle up to A. PA is part of the base Circle.
5) With O as centre and OC radius, draw an arc through centre to get Centre Arc CB. On
CB, the centers C1…C12 will lie.
6) To get the centers, divide ∟POA into 12 equal parts (here 120/12 = 100
) and join O to
each of these 100
to get C1, C2,…C12.
7) Now, similar to cycloids, with C1 centre and radius CP (=25), cut arc on 1-11 arc of
rolling circle to get P1. Repeat with C2, C3, etc on 2-10, 3-9, etc to get the epicycloid.
Note: While dividing the θ into 12 parts, mark centers C1,C2,..C12 on centre arc CB passing
through C only and not on the arc passing through 3-9.
Arc passing through 3-9 will be separate and is used for getting P3 and P9 while
cutting arcs.
Tangent and Normal:
1) Mark M on the epicycloid at 85 mm from O by taking O as centre and radius 85.
2) With M as center, radius CP (=25), cut arc Q on CB.
3) Join QO, cutting base circle PA at N.
4) Join NM to get normal NN’, and ┴ to NN’ draw the tangent TT’.
P
6
O
C
A
B
C1
C3
C5
C7
C9
C11
3
1
2
11
ENGG GRAPHICS: EPICYCLOID S.RAMANATHAN ASST PROF MVSREC
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M
Q
N
T
T’
N’