Research on transmission principle and kinematics analysis for involute spherical gear

Abstract

A new kind of transmission-type spherical gear called ‘ring involute spherical gear mechanism’ is introduced. Compared to the famous TRALLFA spherical gear, this new spherical gear has an involute tooth profile, and a ring tooth that is distributed continuously on the surface of the sphere. This allows the gear to overcome two disadvantages of the TRALLFA spherical gear: the drive principle error and the manufacturing difficulty. The new transmission and the formation principle of the tooth’s surface of the new spherical gear mechanism are first introduced, then another mechanism, called disk rack, is introduced, which is derived from the spherical gear mechanism when one of the spherical gear’s tooth number reaches infinity. To make the research more convenient, every part of the new spherical gear mechanism is named. In the following sections, some problems are discussed, such as the assembly form, the construction characteristics, the correct meshing condition, the continuum transmission condition and so on. Furthermore, the paper deduces the surface formula of the conjugate teeth profiles, which proves that the conjugate teeth profiles is also one of the ringed involute spherical gear. In order to analyze the relationship between two coordinate systems, which is attached respectively to the diving spherical gear and the driven spherical gear, the orientation cosine matrix method is utilized. By series rotational transformation, the kinematics model and inverse kinematics model are deduced. Using the method for calculating the transmission ratio of planet gear train, the relationship of the two oscillating angle between output axis and the bracket is established. Based on the research, the kinematics graphic simulation of spherical gear mechanism and disk rack are made respectively. The results prove correctness of the kinematics model.