Involute Curve (Metrology)

15.2,
An involute curve is defined as the locus of a point on straight line which rolls, around
a circle without slipping. It could also be defined in another way as the locus of a point on a piece of string which in unwound from a stationery cylinder.
Thus it is obvious that in an involute curve the length of the generator (Gi Ri) will always be equal to the arc length (GRi) of the base circle from the point of tangency to the origin of involute at G (Fig. 15.1).
Similarly generator G2 R2 = arc GR2.
It is also clear that the tangent to the involute at any point will be perpendicular to the generator at that point. This condition fulfils the requirements of laws of gearing.
Further, will also be noticed that the shape of the involute curve is entirely dependent upon the diameter of base circle from which the involute is generated. The curvature of the involute goes on decreasing as the base circle diameter goes on in-

Fig. 15.1
creasing and finally involute becomes straight line when base circle diameter is infinity.