Curves:- Involute



Q.1 A thread of 130 mm length is wound round a solid section of a regular hexagon of 20 mm side, keeping one end of the thread firmly attached to a corner of the hexagon. It is unwound in an anticlockwise direction, keeping the unwinding end tight. Draw the path traced by the unwinding end of the thread & Name the curve.

Q.2 A line PQ =120 mm long rolls without slipping on the periphery of a semicircle of diameter AB = 70 mm as shown in figure 1. Initially the line is tangent to the circle at A such that AP=100 mm. Draw the loci pf ends of the line. Name the curve.

Q.3 Draw the path of the end of thread 140 mm long, when it is wound on a half hexagon of sides 25 mm.

Q.4 Take length PQ=50 mm. Draw a semicircle considering this as diameter. On the other side of the semicircle, construct a half of a regular hexagon of 25 mm side. Let R and S be the remaining two corners of the half hexagon PSRQ, an inelastic string 150 mm long is attached to corner R . Draw the curve traced out by the free end of the string, when it is completely wound around the figure 2. Keeping the string always tight & in clockwise direction. Name the curve.

Q.5 A Semicircle with O as centre & 60 mm diameter is fixed as shown in figure 3. PQ is an inelastic string of 130 mm length end P of the string is fixed & is 20 mm above the centre O. the string is rotated in clockwise direction, Draw the locus of the Point Q.

Q.6 A disc in the form of a semicircle & a semi triangular hexagon of thickness 10 mm is shown in figure 4 . A disc is firmly fixed at point O. An inelastic string of length 160 mm is fixed at point A & the free end B of the string is wound round the disc in anticlockwise direction. Draw the locus of B.

Q.7 A pole Shown in figure 5 is to be wrapped by means of thread AB, by keeping the thread always tight. Draw the locus of point B if the end A is fixed at position.

Q.8 A disc is in the form of a square of 30 mm side surrounded by a semicircle on one side & a half hexagon on the opposite side as shown in figure 6 . Draw the path of the end of string unwound from the circumference of the disc. Name the curve.