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and the pitch-circle dimensions are related as follows:
D₁ = R₁ = N₁                                                                      (6)
D₂    R₂    N₂
4.3 Velocity Ratio
The gear ratio, or velocity ratio, can be obtained from several different parameters:
Z = D₁ = N₁ = w_{1                                                                                     (7)}
       D₂    N₂     w₂
The ratio, Z, in this equation is the ratio of the angular velocity of gear 2 to that of gear 1.

4.4 Pressure Angle

The pressure angle is defined as the angle between the line- of-action (common tangent to the base circles in Figs. 1.3 and 1.4) and a perpendicular to the line-of-centers. See Figure 1.14. From the, geometry of these figures, it is obvious that the pressure angle varies (slightly) as the cen distance of a gear pair is altered. The base circle is related to the pressure angle and pitch dinmeter by the equation:

D_b = D cos f                               where D and f are the standard values or alternately,    (8)
D_b = D cos f                               where D and f are the exact operating values.

This basic formula shows that the larger the pressure angle the smaller the base circle. Thus, for standard gears, 14½° pressure angle gears have base circles much nearer to the roots of teeth than 20° gears. It is for this reason that 14 ½° gears encounter greater undercutting problems than 20° gears. This is further elaborated on in section 4.8.

4.5 Tooth Thickness
This is measured along the pitch circle. For this reason it is specifically called the circular tooth thickness. This is shown in Figure 1.1. Tooth thickness is related to the pitch as follows:
   T = P_c =  p                                                                                                  (9)
            2         2P_d

T38