An epi – trochoid is a curve traced by a point situated either within (or) outside the generating circle, when it rolls without slipping on the circumference of another circle [directing circle] outside it.
(a) If the tracing point lies out side the generating circle the curve traced is called a superior epi-trochoid.
SUPERIOR EPI-TRICHOID:
Q.A circle of 40 diameter rolls outside another circle of 120 diameter for one revolution clock-wise. Draw the locus of a point, which lies at a distance 30 mm from the centre of the generating circle.
SOLUTION:
CONSTRUCTION: STEPS TO BE FOLLOWED :
1. Draw a part of the directing circle with “O'” as centre and radius (R) as 60 mm.
2. Draw any radial line O’ * A and extend it.
3. Locate the point ‘O’ on the above line such that OA [r] 20 mm, the radius of the generating circle.
4. With ‘O’ as centre and radius 20 mm, draw the generating circle.
5. Locate the tracing point P on OA such that OP = 30mm .
6. Again draw a circle with centre O and radius equal to 30 mm.
7. Locate the point ‘B’ on the directing circle, such that the arc length AB is equal to the circumference of the generating circle.
ZAO’B 360° arc’AO’ circumference of directing circle 2πτ 2πR = R
angle A * O’ * B = 360 deg * r/R = 360 deg * 20/60 = 120 deg
8. With centre o’ and radius equal to O’ O draw an arc intersecting line O’ B produced at C
9. Divide the 30 mm radius circle and the arc AB into the same equal number of parts.
10. Join O’1′; 02; 0’3′; etc. etc., and extend to meet the arc OC at O_{1} , O_{2} 03
11. Draw the arcs with O’ as centre through the points 1, 2, 3, radius circle. etc., on 30 mm
12. With centre O_{1} and radius equal to 30 mm, draw an arc intersecting the arc through 1 at P_{1}
13. In the same way mark the points P_{2} P3, P4, etc., on the arcs passing through the points 2, 3, 4, etc., of the circle R 30.
14. The smooth curve which is drawn through these points gives the required superior epi-trochoid.
