4.30 Textbook of Enginnering Drawing------------------
- A smooth curve through the points P1,P 2'P 3 etc., is the required epi-cycloid.
Notel: The above procedure is to be followed to construct a hypo-cycloid with the generating·
circle rolling inside the directing circle (Fig. 4.43).Note 2 : T-T is the tangent and NM is the normal to the curve at the point M.
4.4 Involutes
An involute is a curve traced by a point on a perfectly flexible string, while unwinding from around
a circle or polygon the string being kept taut (tight). It is also a curve traced by a point on a straight
line while the line is rolling around a circle or polygon without slipping.
To draw an involute of a given square.
Construction (Fig 4.44)- Draw the given square ABCD of side a.
- Taking A as the starting point, with centre B and radius BA=a, draw an arc to intersect the
line CB produced at Pl. - With Centre C and radius CP 1 =2 a, draw on arc to intersect the line DC produced at P 2.
- Similarly, locate the points P3 and P 4 •
o·Fig. 4.43 Construction of a Hypo-Cycloid