Gear Transmission: How Small Gears Rotate The Big World

• The meshing line is a straight line: The trajectory of the meshing point of the two gears is a fixed straight line.

• Constant transmission ratio: Ensures the smoothness of transmission.

• Divisibility of center distance: Changes in center distance do not affect the transmission ratio.

• Constant force direction: The pressure angle remains unchanged during meshing.

To keep the transmission ratio of a pair of gears constant, the basic law of tooth profile meshing must be satisfied:
When the tooth profiles of two gears are in contact at any position, the common normal line through the contact point must pass through the pitch point P (i.e., the tangent point of the two pitch circles);
The involute tooth profile fully satisfies this law, thus ensuring a constant transmission ratio.

• Gear Transmission Ratio Relationship

  
  

  
  

  The transmission ratio (i) is the ratio of the rotational speed of the driving wheel (n₁) to the rotational speed of the driven wheel (n₂), and it is also equal to the ratio of the number of teeth of the driven wheel (z₂) to the number of teeth of the driving wheel (z₁), that is:
  i = n₁/n₂ = z₂/z₁
  For example, if the number of teeth of the driving wheel is 20 and that of the driven wheel is 40, the transmission ratio i = 2, which means that when the driving wheel rotates 2 circles, the driven wheel rotates 1 circle.

• Pitch circle diameter: d = m × z

• Addendum circle diameter: da = d + 2ha = m(z + 2ha*)

• Dedendum circle diameter: df = d - 2hf = m(z - 2ha* - 2c*)

• Base circle diameter: db = d × cosα

• Standard center distance: a = (d1 + d2)/2 = m(z1 + z2)/2

• Module (m): The basic dimension parameter of a gear, in mm. The larger the module, the larger the gear size.

• Number of teeth (z): The total number of teeth on the gear.

• Pressure angle (α): The standard value is 20°, which is an important parameter for the direction of the gear transmission force.

• Addendum coefficient (ha*): Usually 1.

• Clearance coefficient (c*): Usually 0.25.