A general mathematical model for describing the geometries and geometric properties of conjugate tooth profiles is presented. Three kinematic parameters and a first order differential equation are introduced to characterize this model. The condition for determining the cusp of tooth profiles is also presented. Using this model, two types of tooth fillets with their minimum radii of curvatures generated by the rack cutter and pinion cutter are described. The peculiar application of this model is that the investigated tooth profiles can be parameterized by specifying one of the three kinematic parameters as a parametric function. It is believed that the parameterization may provide a logical method for gear design.
A general mathematical model is derived for describing the conjugate tooth profiles and meshing properties of composite gears. Via a typical gear parameter, the pressure angle, necessary conditions that determine the continuity of composite gears in tooth geometry and meshing properties are introduced. The peculiarity of the presented model is that composite gears can be parametrically characterized by the specific functions in terms of pressure angle. An example is demonstrated that the discontinuity in composite gears will be efficiently and logically solved.
In this paper the LogiX gear, a special composite gear which consists of many segmental “S” curves in gear profiles and possesses zero values of relative curvature and specific sliding at the joints of connected segmental profiles, will be parametrically investigated by this model. The “ideal” LogiX gear profile, theoretically, is constructed by infinite numbers of segmental profiles such that it may have infinite numbers of zero values of relative curvature and specific sliding. However, this “ideal” LogiX gear profile is characterized as a linear parametric profile that is a monotonous curve substantially and no more has infinite numbers of the zero values. Finally, many parametric gears which own power relative curvature and specific sliding than that of the “ideal” LogiX gear profile are presented.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.