Involute curve is the path traced by a point on a line as the line rolls without slipping on the circumference of a circle. Involute curve has a contact angle between two gears when the tangents of two gears pass through the contact point without friction.

INVOLUTE:It is a locus of a free end of a string when it is wound round a circle or polygon.
In an involute gear, the profiles of the teeth are involutes of a circle. (The involute of a circle is the spiraling curve traced by the end of an imaginary taut string unwinding itself from that stationary circle called the base circle.)

In involute gear design contact between a pair of gear teeth occurs at a single instantaneous point (see figure at right). Rotation of the gears causes the location of this contact point to move across the respective tooth surfaces. The path traced by this contact point is known as the Line of Action (also called Pressure Line or Line of Contact). A property of the involute tooth form is that if the gears are meshed properly, the line of action is straight and passes through the Pitch Point of the gears. When this is true, the gears obey the Fundamental Law of Gearing:[1]

The angular velocity ratio between two gears of a gearset must remain constant throughout the mesh.

In volute curves are used in the gears because-
1)They are easy to manufacture compare to cycloidal since they are made up of single curve
2)The change in center distance between gears within limit does not cause change in velocity ratio
3)The pressure angle remains constant throughout the path of contact which ensures the smooth motion. this pressure angle varies in cycloidal curve

its simple:-
its just because involute curve satisfies the law of gearing ie: its is the curve for which the common normal at the point of contact always passes through the pitch point and hence the velocity ratio remains constant.
there are only two curves which satisfy this condition ie: involute and cycloidal. but involute is preferred because it bears a constant value of pressure angle all the time,/.
hopwe this helps..

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