Based on the space engagement theory

the meshing function of the non-backlash hourglass worm gearing

the tooth surface equations of worm and the contacting line equation of worm gear are established. The formulas of induced normal curvature

lubrication angle

relative entrainment velocity and rotation angle of the non-backlash hourglass worm gearing are derived. The meshing analysis system of the non-backlash hourglass worm gearing is developed based on MATLAB. The radius of the rollers

laryngeal quotient of worm and offset distance of the rollers to influence on the parameters of the transmission meshing performance are analyzed.