Anti-backlash roller enveloping hourglass worm gears, as a new precision transmission system, has been extensively applied in robot joint design, packaging production line, and CNC (computer numerical control) machine tools. However, their corresponding transmission principles are seldom reported in the literature. Based on the theories of differential geometry and gear meshing, this paper carefully analyzes and compares meshing characteristics of anti-backlash single- and double-roller enveloping hourglass worm gears in terms of their transmission principle, engagement equation, induced normal curvature, lubrication angle, autorotation angle, entrainment velocity, helix angle, and distribution of contact curves. Major differences between these two roller enveloping hourglass worms are theoretically demonstrated through this study. Our results show that the anti-backlash single-roller enveloping hourglass worm (ASEHW) gears provide better performance with respect to gear meshing and transmission than the anti-backlash double-roller enveloping hour glass worm (ADEHW) gears. Also, compared with the ADEHW gears, the ASEHW gears are easier to fabricate, install, and calibrate. However, the ADEHW gears are more auto-adjustable in eliminating gear backlash. The outcomes of this study will form a theoretical background for futuristic design, application, and promotion of the anti-backlash roller enveloping hourglass worm gears.

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