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        Although these are approximate relationships they are adequate for most uses. Their derivation, limitations, and correction factors are detailed in Reference 5.
        Note that backlash due to center distance opening is dependent upon the tangent function of the pressure angle. Thus, 20° gears have 41% more backlash than 14½º gears, and this constitutes one of the few advantages of the lower pressure angle.
        Equations 22 are a useful relationship, particularly for converting to angular backlash. Also for fine-pitch gears the use of feeler gages for measurement is impractical, whereas an indicator at the pitch line gives a direct measure. The two linear backlashes are related by:

                       B_LA                                                                       (23)  
        B  = ^_____
                     cos f
       The angular backlash at the gear shaft is usually the critical factor in the gear application. As seen
from Figure 1.20a this is related to the gear’s pitch radius as follows:
                               B                                                     (24)
       _aB = 3440   ^____  (arc minutes)
                               R₁

       Obviously, angular backlash is inversely proportional to gear radius. Also, since the two meshing gears are usually of different pitch diameters, the linear backlash of the measure converts to different angular values for each gear. Thus, an angular backlash must be specified with reference to a particular shaft or gear center.

4.11 Summary of Gear Mesh Fundamentals

The basic geometric relationships of gears and meshed pairs given in the above sections are summarized in Table 1.7.

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