Abstract: One new kind of invented transmission type of spherical gear called ring involute spherical gear mechanism is introduced. Compared to famous Trallffa spherical gear, one of the two main features of this new spherical gear is its involute tooth profile, the other one is its ring tooth distributed continuously on the surface of sphere. Which makes the gear overcome two disadvantages of Trallffa spherical gear: the principle error and difficulty in manufacturing. The new transmission and the formation principle of the tooth’s surface of new spherical gear mechanism are first introduced, then another new mechanism, called disk rack, is introduced, which is derived from spherical gear mechanism, when one of spherical gear’s tooth number go to infinite. In order to research conveniently, every part of new spherical gear mechanism is named. In the following part, some problems are discussed, such as the assembly form, the construction characteristics of new mechanism and the correct meshing condition, the continuum transmission condition and so on. Further more, the surface formula of the conjugate teeth profiles is deduced, which proves that the conjugate teeth profiles of ringed involute spherical gear is also one of ringed involute spherical gear. In order to analyze the relationship between two coordinate systems, which is attached respectively to diving spherical gear and driven spherical gear, the method called orientation cosine matrix is utilized. By series rotational transformation, the kinematics model and inverse kinematics model are deduced. Using the method for calculating transmission ratio of planet gear train, the relationship of two oscillating angle between output axis and bracket is found up. Based on the research above, the kinematics graphic simulation of spherical gear mechanism and disk rack are made respectively, the results prove correctness of the kinematics model.

Key words: Kinematic analysis, Mechanism, Robot, Simulation, Spherical gear transmission