The invention relates to a gear and a method for designing and machining the same. The gear is particularly characterized in that each of tooth crest curved surfaces and tooth root curved surfaces is a part of a convex ring surface or a concave ring surface, each of the tooth crest curved surfaces and the tooth root curved surfaces of the involute gear with the concave and convex ring surfaces is a part of a ring surface, an arc circularly rotates around an axis of the gear to form the ring surface, a tooth profile curve of the end section of each gear tooth is an involute, and the teeth are synchronously distributed around a center point of the tooth width. By the aid of the gear, three gear transmission forms can be realized, the gear not only can be used for driving of parallel axes, but also can be used for driving of intersecting axes with small axial intersect angles, high axis deflection installation errors are permitted when the gear is used for driving of parallel axes, the axial intersect angles are allowed to dynamically change when the gear is used for driving of intersecting axes, transmission ratio can keep constant when the gear is used for driving of parallel axes and driving of intersecting axes, and the gear teeth are not interfered with each other. By the aid of the method for designing the gear, the involute gear with the ring surfaces is divided into a plurality of tiny tapered involute gears, geometric parameter design of the involute gear with the ring surfaces is carried out, and a process of the method is carried out simply, conveniently and feasibly.