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.

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.

The structure of cylindrical tri-sine oscillating tooth gear drive is presented. Based on the space meshing theory, equations of meshing and tooth profile are established and its meshing theory in studied. Using Pro/E, this system is modeled and simulated, which is compared with the above-established equations.

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.

Conventional fault tree and reliability analysis do not reflect the characteristics of basic events as non-stationary and ergodic process. To overcome these drawbacks, theory of fuzzy sets is employed to run fault tree analysis (FTA) of roller oscillating tooth gear drive (ROTGD), the relative frequencies of basic events are considered as symmetrical normal fuzzy numbers, from the logical relationship between different events in the fault tree and fuzzy operators AND and OR, fuzzy probability of top event is solved. Finally, an example is given to demonstrate a real ROTGD system.