Abstract: The present disclosure provides a parabolic tooth trace gear mechanism with a combined tooth profile of an end face circular arc and a parabola, which belongs to the field of gear transmission. The parabolic tooth trace gear mechanism with the combined tooth profile of the end face circular arc and the parabola includes a small wheel and a big wheel geared externally with parallel axes, tooth surfaces of the small wheel and the big wheel both have a parabolic tooth trace structure, and both are formed by the motion of a combined tooth profile curve of an end face along a contact point, contact lines are all parabolas after being unfolded along a cylindrical surface, and the parabola is determined by a meshing line parameter equation and basic design parameters such as a coincidence degree, the number of teeth, a transmission ratio and the like. When correctly installed, at least one pair of gear teeth of the small wheel and the big wheel, implement pure rolling meshing contact at a node.

Abstract: A rolling gear rack mechanism with tooth profile having hyperbolic tooth line structure based on a parabolic function includes a gear and a rack. 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. At least one pair of gear teeth meshing points of the gear and the rack are located at nodes to achieve rolling meshing contact.

Abstract: The present disclosure provides a parabolic tooth trace gear mechanism with a combined tooth profile of an end face circular arc and a parabola, which belongs to the field of gear transmission. The parabolic tooth trace gear mechanism with the combined tooth profile of the end face circular arc and the parabola includes a small wheel and a big wheel geared externally with parallel axes, tooth surfaces of the small wheel and the big wheel both have a parabolic tooth trace structure, and both are formed by the motion of a combined tooth profile curve of an end face along a contact point, contact lines are all parabolas after being unfolded along a cylindrical surface, and the parabola is determined by a meshing line parameter equation and basic design parameters such as a coincidence degree, the number of teeth, a transmission ratio and the like. When correctly installed, at least one pair of gear teeth of the small wheel and the big wheel, implement pure rolling meshing contact at a node.