A hypo-trochoid is a curve traced by a point situated either within (or) outside the generating circle, when it rolls without slipping on circumference of another circle [directing circle], inside it.
(a) If the tracing point lies outside the generating circle, the curve traced is called a superior hypo trochoid.
SUPERIOR HYPO – TROCHOID:
Q. A circle of 40 diameter rolls inside another circle of 160 diameter for one revolution counter clockwise. Draw the locus of a point, which is at a distance of 30 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 80 mm.
2. Draw any radial line O’A.
3. Locate the point ‘O’ within the 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 30 mm.
6. Draw another 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.
ZAOB 360° arc’AO’ circumference of directing circle 2π 2 πρ r R = =
ZAO’B 360° x 360° x 20 60 120°
8. With centre O’ and radius equal to O’O draw an arc intersecting the line O’B produced at C.
9. Divide the 30 mm radius circle and the arc AB into the same number of equal parts.
10. Join O’1′; 0’2′;… etc., to meet the arc OC and 01, 02,… etc.
11. Draw the arcs with O as centre through the points 1, 2, 3, … etc., on 30 mm radius circle.
12. With centre 01 and radius 30 mm draw an arc Intersecting the arc passing through 1 at P1 13. In the same way mark the points P2, P3, P4,
etc., on the arcs passing through the points 2, 3, 4,… etc.
14. The smooth curve which is drawn through these points gives the required interior
15.
