| This research established gear curvature theory for a three rigid body system. It can synthesize new conjugate curves with any required relative curvature.;Two curves are generated by tracing a random selected point's trajectories under three rigid body's pure rolling with coincident instant centers. Such curves are conjugate to each other, which is guaranteed by the Ting's conjugation theorem. The newly generated conjugate curves can be used as tooth profiles for gears in order to transmit a smooth motion with no extra clearance or interference.;The generating point's location will decide the conjugate curves' relative curvature. The relative curvature is the geometric intrinsic property to decide a pair of gears' Hertzian contact stress. The gear curvature theory offers a systematic methodology to locate all the possible generating points in order to find new conjugate curves with desired Hertzian contact stress by synthesizing their relative curvature.;Started from using a single point as the generating element to trace conjugate planar curves, the theory has been extended to synthesize conjugate unit spherical curves. Furthermore, the unit spherical curves have been expanded into conjugate conical surfaces by using homogenous coordinate transformation. Straight line envelope gear curvature theory for planar motion is also finished.;By the gear curvature theory, new conjugate curves or surfaces have been systematically found and used as tooth profiles for different types of gears, such as circular gear, non-circular gear, bevel gear, and spiral bevel gear. What's more, the conjugate tooth profiles with desired relative curvature will reduce tooth contact analysis's iteration process. Applications in gearing and rotor pump are used to prove and verify the gear curvature theory. |
