Abstract: In order to get aid of some drawbacks of spherical gear transmission apparatus assembled in flexible joint ofthe spraying paint robot "Dongfang", this paper has developed a new type of transmission mechanism calledquasi-ellipsoid gear transmission, which can precisely realize variable gear ratio transmission in all directions inspace. In accordance with the requirements of 2-DOF gear meshing, some related parameters about gear ratiofunction and pith surface of the quasi-ellipsoid gear pair are optimized.