Roller shapes play a very critical role in the performance of antibacklash double-roller enveloping hourglass worm (ADEHW) gears; however, their influence is seldom reported in the literature. Based on the theories of differential geometry and gear meshing, this paper presents generic models of meshing characteristics for ADEHW gears, including both the contact curve and the tooth profile. We present different meshing functions and their derivatives with respect to each drive type and their associated roller shapes. We also compare the effects of contact curve, tooth profile, tooth undercutting, lubrication angle, induced normal curvature, and autorotation angle in order to design the most optimal tooth profile for the ADEHW gear. Finite element analysis was also conducted in order to minimize the contact stresses as a function of the roller type. Our results show that a spherical roller has the smallest value among the three available meshing roller shapes but is the most difficult design to procure. A cylindrical roller, however, incurs the greatest contact stress.

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