# Description of involute profile of the most complete gear transmission

#### The basic requirements of gear transmission for tooth profile curve

First, the transmission should be stable; second, the bearing capacity should be strong

#### The formation and property of involute

1.The formation of involute

When a moving line (occurrence line) rolls purely along a fixed circle (base circle), the trace of any point K on the moving line is called the involute of the circle.

2.Properties of involute

It can be seen from the formation of involute:

(1) The segment KB on which the occurrence line rolls over the base circle is equal to the arc length AB on the base circle.

(2) The normal of any point K on the involute must be tangent to the base circle.

The radius of curvature of each point on the involute is not equal.

The farther away the point is from the base circle, the larger the radius of curvature and the straighter the involute. vice versa.

(4) The shape of the involute determines the size of the base circle.

The base circle is the same, and the shape of the involute is the same.

When the radius of the base circle is infinite, the involute will become a straight line, and the gear will become a rack.

(5) There is no involute in the base circle.

#### Basic law of involute profile engagement

In order to keep the instantaneous transmission ratio constant, no matter where the tooth profile of the two wheels contacts, the common normal line passing through the contact point must intersect the connecting center line of the two wheels at a fixed point.

#### Meshing characteristics of involute profile

1.Constant transmission ratio

2.The transmission ratio of the two gears is inversely proportional to the radius of the two pitch circles and the radius of the two base circles. Because the pitch radius and base radius of two meshing gears are fixed values, the transmission ratio can be kept constant

3.Separability of transmission

When the center distance of two wheels changes slightly, the instantaneous transmission ratio will remain unchanged, which is called the separability of involute gear transmission.

4.Due to the manufacturing and installation errors of gears, there are some errors between the actual center distance and the design center distance of involute gears. However, due to the separability, the transmission ratio can still remain unchanged. Engagement angle is fixed

Cos α′ = RB1 / R1 ′ = Rb2 / r2 ′ = constant

It shows that the engagement angle α ‘of the involute profile is a fixed value.

Since the meshing angle is constant, the pressure direction between the tooth profiles will not change, which is very beneficial to the stability of gear transmission.

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