Elements of Metric Gear Technology

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4.7 Rack And Spur Gear
   Table 4-6 presents the method for calculating the mesh of a rack arid spur gear. Figure 4-9a shows the pitch circle of a standard gear and the pitch line of the rack.
   One rotation of the spur gear will displace the rack one circumferential length of the gear's pitch circle, per the formula:
   i = pmz                                          (4-6)
Figure 4-9b shows a profile shifted spur gear, with positive correction xm, meshed with a rack. The spur gear has a larger pitch radius than standard, by the amount xm. Also, the pitch line of the rack has shifted outward by the amount xm.
   Table 4-6 presents the calculation of a meshed profile shifted spur gear and rack. If the correction factor x₁, is 0, then it is the case of a standard gear meshed with the rack.
   The rack displacement, i, is not changed in any way by the profile shifting. Equation (4-6) remains applicable for any amount of profile shift.

SECTION 5 INTERNAL GEARS
5.1 Internal Gear Calculations
     Calculation of a Profile Shifted Internal Gear

Figure 5-1 presents the mesh of an internal gear and external gear. Of vital importance is the operating (working) pitch diameters, d_w, and operating (working) pressure angle, a_w They can be derived from center distance, a_x, and Equations (5-1).

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4.7 Rack And Spur Gear Table 4-6 presents the method for calculating the mesh of a rack arid spur gear. Figure 4-9a shows the pitch circle of a standard gear and the pitch line of the rack. One rotation of the spur gear will displace the rack one circumferential length of the gear's pitch circle, per the formula: i = pmz (4-6)	Figure 4-9b shows a profile shifted spur gear, with positive correction xm, meshed with a rack. The spur gear has a larger pitch radius than standard, by the amount xm. Also, the pitch line of the rack has shifted outward by the amount xm. Table 4-6 presents the calculation of a meshed profile shifted spur gear and rack. If the correction factor x₁, is 0, then it is the case of a standard gear meshed with the rack. The rack displacement, i, is not changed in any way by the profile shifting. Equation (4-6) remains applicable for any amount of profile shift.