A generalized approach for parametrizing conjugate tooth surfaces in cylindrical gears is presented in this work. Developed are the polynomials expressions to define the tooth surfaces of pinion and gear based on kinematics synthesis for planar gears. The polynomials expressions incorporate the motion generation (points or positions of precision) and function of transmission errors. It is interesting to note that if the desired pressure angle for the tooth profile is constant, the output polynomial of profile becomes a conventional involute. Polynomials expressions are given for the profile modifications necessary to compensate for any specified or anticipated errors of assembly and/or manufacturing. In addition property of rack as the limits of zone active, transverse contact ratio and contact asymmetry ratio are analysed.
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