4.46 Textbook of Enginnering Drawing------------------
5, The required curve (epicycloid) is the path of the point P on the circumference of the circle
which rolls over C. Cb, Let Po be the initial position of the point P and it coincides with the
point A. When the rolling circle rolls once on arc AB, the point P will coincide with B and it
is marked by Po'
6, The intermediate positiions of the point P such as PI ' P 2 ' P 3 ' P 4 ' etc., can be located as
follows. Draw arcs through points 1,2,3, etc. To get one of the intermediate positions of the
point P (say P 4)' with centre C 4 draw an arc of radius equal to 25 mm to cut the arc through
the point 4 at P4'e=~X360
100
Fig. 4.65 Epicycloid- Similarly obtain other intermediate points PI P 2 P 3 , etc.
centre, C- Draw a smooth curve passing through all these points to get the required epicycloid.
- To daw a tangent at any point M on the curve, with centre M draw an arc of radius equal to
25mm to cut the arc Ca Cb at S. From point S, Join NM which is the required normal to the
curve. - Draw a line TMT perpendicular to NM. Now, TMT is the required tangent at M.
Problem: Draw an epicycloid of rolling circle of diameter 40 mm which rolls outside another
circle (base circle) of 150 mm diameter for one revolution. Draw a tangent and normal at any point
an the curve.
Solution: (Fig.4.66) - In one revolution of the generating circle, the generatin point P will move to a point Q, so that
the arc PQ is equal to the circumference of the generating circle. e is the angle subtended
by the arc PQ at the centre O.