## Problem 3.4 Engineering Curves – A string is unwound from a circle of 30 mm radius. Draw the locus or Involute of circle of the end of the string for unwinding the string completely. String is kept tight while being unwound. Draw normal and tangent to the curve at any point.

**Procedure: **

**Procedure:**

* Step-1* Draw a circle of the given dimension that is 30 mm radius in this problem.

* Step-2* Divide this circle into 12 equal divisions and give their notations.

* Step-3* Draw a horizontal line from the bottom point of the circle, which is numbered 12; of the length equal to the circumference of the circle, which is equal to πd = 188 mm.

* Step-4* Divide this horizontal line into the same number of divisions as that of the circle which is 12. And give the notations p

_{0}, p

_{1}, p

_{2}, p

_{3}etc. up to p

_{12}as shown into the figure.

* Step-5* Now from the points 1,2,3 etc. of the circle draw tangent lines of some suitable length.

* Step-6* Cut the line -1 tangent to the circle with the point-1 as center and the radius equal to the distance between the points p

_{0}& p

_{1}on the horizontal line and mark the cutting point as p

_{1 }as shown into the figure.

* Step-7* Like in the same way mark the points up to p

_{12}.

* Step-8* Draw a smooth medium dark free hand curve passing through the points p0

_{, }p

_{1}, p

_{2}, p

_{3 }etc. up to p

_{12 }in sequence to get Involute of the circle.

* Step-9* To draw a tangent and normal to the curve mark a point say M on the involute of the circle and from this point M draw a line connecting to the center of the circle, with this line MO draw a perpendicular line in clockwise direction which will intersect on circumference of the circle, through this point from the circumference of the circle draw a medium dark line passing through the point M , which is normal to the curve and draw a line which is perpendicular to the normal of the curve and passing through the point M is tangent of the curve.

* Step-9* Give the dimensions by any one method of dimensions and give the name of the components by leader lines wherever necessary.