Based on the space engagement theory, a special type of noninvolute beveloid gears meshing with line contact between intersecting axes has been studied in this paper for the first time. The engagement equation and tooth profile equation have been presented by applying the theory of gearing. Meanwhile the tooth profile errors and axial errors have been calculated by means of numerical analysis in this paper. As a numeri cal example, the three-dimensional simulation of beveloid gears between intersecting axes has been finished by means of the CAD system, Pro/Engineer.

A mathematical model has been developed using the space engagement theory and the differential geometry for the line contact of noninvolute beveloid gears with intersecting axes with their tooth profile equations and engagement equations established for the first time and their meshing theory analysed. It can be seen from the fact that the tooth profile equation finally derived is no longer a standard involute helicoid and standard involute beveloid gears with intersecting axes have no way to satisfy the line contact requirement. However, the noninvdute beveloid gears derived in this paper satisfy the line contact requirement very well. All these work will inevitably facilitate further investigations into gear tooth generation, stiffness, backlash and efficiency of transmission.

This paper presents a new type of gear transmission, the quasi-ellipsoidal gear transmission with inner-toroidal teeth. According to the double DOF conjugate surface theory, the function of the transmission ratio is derived. The pitch surfaces which satisfy the meshing conditions in the whole meshing zone can be obtained easily. The tooth profile of the inner-toroidal rotatary surfaces have high contact strength and can satisfy no pointing of addendum. This type of transmission is very suitable for the precise flexible joint of robot.