Torsional vibration of roller oscillating tooth gear drive (ROTGD) is studied in this paper. On the basis of conservation law for kinetic energy and potential energy, the mathematical expressions are developed which describe transformation of moment of inertia of inertial components into input shaft. Also, the formula is derived which expresses transformation of contact stiffness of elastic components into input shaft torsional stiffness. Besides, torsional vibration model of ROTGD is presented by using the transfer matrix method, and natural frequencies and vibration mode shapes are determined. Eventually, an example is given.

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.

Quasi-ellipsoidal gear drive is suitable for the precise flexible joint of robot, but some meshing problems of this transmission are rarely involved in the related papers. According to the two-parameter conjugate surface theory, this article studies on the induction normal curvature and critical curves, the method of analysis is efficient for not only the quasi-ellipsoidal gear drive but also the other types of spatial gear drive.