Gear is an important basic component in mechanical transmission. Different from other types of gears,, as a special universal spatial transmission mode, is suitable for parallel shaft, intersecting shaft and staggered shaft transmission 1658. Since beam first proposed the concept of “bevoid” gear in 1954, a large number of theoretical researches on bevel gears have been put forward. Huston and coy proposed the tooth surface geometry of bevel gears. Litvin et al. Proposed to use a cutting machine to machine conjugate surfaces to produce bevel gears. Mitone et al. Put forward the concave gear design to increase the surface durability, and applied it to the shipbuilding industry. The meshing and contact characteristics of bevel gears mainly depend on the conjugate surface conditions. In order to obtain high quality conjugate tooth surface, the method of designing conjugate surface by TCA and LTCA is proposed.
It is worth noting that Chen Yangzhi and others put forward a kind of space curve meshing theory and line gear mechanism. Yao Li processed the concave convex arc gear mechanism by numerical control, and realized the two-way backlash free transmission of parallel axis and intersecting axis. In the follow-up work, a large number of scholars have carried out relevant research in the field of online gear. In order to improve the transmission performance of the line gear, Chen Yangzhi studied the influence of assembly error and hook bar deformation on the transmission accuracy. He Enyi studied a kind of gear mechanism with circular section line which can not parallel to the side clearance. Chen Zhen et al. Put forward a kind of linear gear mechanism with parallel axis and vertical intersecting axis with zero sliding rate. Because of the existence of side clearance, there is the possibility of vibration in the transition of positive and negative rotation.
Based on the meshing principle of line gear, a pair of conjugate conic helix is taken as the contact line, perpendicular to the angular velocity direction of driving wheel and the circle passing through the contact point as the contact section, and the non backlash concave convex contact tooth surface passing through the contact line is constructed. Compared with the bevel gear constructed by the surface conjugate principle, the bevel gear can also realize the transmission of the spatial orthogonal axis, but its surface construction is more flexible. In order to verify the feasibility of the tooth surface construction method, a specific example, model and motion simulation experiment are given. This paper provides a new idea for the construction of the tooth surface of the linear gear and expands the transmission of the linear gear, which has certain theoretical and application value.