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Involute Tooth Profile

1-4 Involute Tooth Profile

Imagine pulleys with simple indentations on their periphery equally spaced by pitch.
These pulleys, when moved, would :

They are improperly suited for use as gears. Satisfactory gears must transmit power smoothly by rolling action. The involute curve meets all the requirements for a gear-tooth profile.

The involute curve
If a cord is wrapped around a cylinder, as shown in this figure, a point on the cord, as it is unwrapped from the cylinder, traces a curve called an involute.
The circle from which the string is unwound is called the base circle.

making involute curve involute curve

Let us try to make a simple drawing of an eight-toothed gear :
First, divide a cylinder into eight equal parts. Then, from each part unwrap a cord drawing a line with a pencil.
After you have completed eight lines, do the same manual work from the opposite side.
The diagram thus drawn is the involute tooth profile.

eight teeth gear

Involute Gear

This figure indicates how two involute teeth in mesh are moving to transmit rotary motion.

teeth meshing

Important terminologies in this figure :

Rotational sequence of the gears : P1 -> P2 -> P3

When Gear 1 drives Gear 2 by acting at the instantaneous contact point, the contact point moves on the common tangent in the order of P1 -> P2 -> P3.
You can see that the contact point rolls along the involute curves of the gears. Moreover, the points P1, P2 and P3 lie on the common tangent to the two base circles.
It is similar to the point, P, on a criss-crossed belt as the disks rotate.
In effect, the involute shape of the gear teeth allows the contact point to move smoothly, transmitting the motion. Therefore, the involute curve is the ideal shape for gear teeth.

belt wheel

Features :

Related links :
Gear Tooth Profile
Pressure Angle
Spur Gears
Involute Gear Profile

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