A new worm driving,i.e. planar internal gear enveloping crown worm driving,is presented. Its mathematical model of meshing functions and teeth surface equations are established basing on the theory of differential geometry and gear mesh. Various types of the driving,the macroscopic meshing performance and the microcosmic meshing performance are analyzed. The results show that the inclination angle of generating plane determines the distribution of contact lines,the planar internal gear primary-enveloping crown worm driving has ideal lubrication property,and the planar internal gear second-enveloping crown worm driving has high loading capacity. The studies are practicably instructive for developing new worm driving with high loading capacity,ideal lubrication and small volume.
