Rolling gear rack mechanism with tooth profile having hyperbolic tooth line structure based on a parabolic function

A rolling gear rack mechanism with tooth profile having hyperbolic tooth line structure based on a parabolic function, comprising:

• a gear, and
• a rack, wherein
• an end face tooth profile of the gear and an end face tooth profile of the rack are composed of an end face working tooth profile curve and a tooth root transition curve, and the end face tooth profile of the gear and the end face tooth profile of rack are both symmetrical left and right;
• the end face working tooth profile curve of the gear and the end face working tooth profile curve of the rack are parabolic, and a tooth surface of the gear and a tooth surface of the rack have a hyperbolic tooth line structure;
• and at least one pair of gear teeth meshing points of the gear and the rack are located at nodes to achieve rolling meshing contact, and a meshing line formed by moving trajectories of the meshing points of the gear and the rack forms a gear contact line and a rack contact line on the tooth surface of the gear and the tooth surface of the rack respectively.