Question

The radius of curvature changes continuously in case of an involute curve and it changes sharply near the base circle.

Answer 1

In the differential geometry of curves, an involute (also known as evolvent) is a curve obtained from another given curve by one of two methods.

By attaching an imaginary taut string to the given curve and tracing its free end as it is wound onto that given curve; or in reverse, unwound. For example, an involute approximates the path followed by a tetherball as the connecting tether is wound around the center pole. If the center pole has a circular cross-section, then the curve is an involute of a circle.

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Answer 2

In the differential geometry of curves, an involute (also known as evolvent) is a curve obtained from another given curve by one of two methods.


By attaching an imaginary taut string to the given curve and tracing its free end as it is wound onto that given curve; or in reverse, unwound. For example, an involute approximates the path followed by a tetherball as the connecting tether is wound around the center pole.