In order to extend the type of meshing profile of multiply wraps,the regular polygon involute is proposed to form the profile of multiply wraps.

In order to improve the overall performance of scroll compressors, a profile modification method using multi-pairs of circular arcs in the starting part, which can generate perfect meshing profile, is proposed for the first time.

The space perpendicular relationship between the gearing line and the straight generating lines of gear tooth in gear shaving is proved with the analytic mathematics,which can help people understand the relation deeply and can lay down a foundation for making further study of the meshing theory in gear shaving.

The equations of the meshing limit line in the first and second enveloping of the dual-torus double-enveloping toroidal worm drive are presented in this paper.

In this paper,based on the setting mathematical model of hourglass worm gear drive by using the theory of gearing meshing and the knowledge of differential geometry,the program of drawing axial sketch of hourglass worm gear tooth meshing line is worked out and the worm gear tooth meshing line are simulated by using the computer graphic technology.

The gear teeth and meshing line are distorted in the meshing process as a result of wearing and rise in temperature.

Comparing with normal involute gear transmission,point-line meshing gear transmission has a serial of advantages: good meshing capability,small abrasion,high efficiency,low noise,great carrying capacity,high intension,long life etc.