Drawing an Involute Curve is a tough one to draw. I will give you tips to draw easily. Involute is very important in Gear industry.
I am explaining the steps.
1. First draw a circle by given dimension of Diameter.
2. Make four part of that circle.
3. Draw a line from bottom point equal to 2Πr or DΠ.
4. Now make part of the line. Eight equal part will be ok but the more part the more clean Involute will appear.
5. As that line is parted 8 equal part it is now time to make circles eight part. 45 degree lines.
6. Now have to draw perpendicular lines from each circles parts. If we give numbers it will be easier.
8. After drawing all the perpendicular lines you will have to join some points. from 8 to perpendicular of a, perpendicular of a to perpendicular b and so on. and at last perpendicular g to point h.
Here is an example of Involute by an Involute To A Circle Of Diameter 50mm.