The Machining of the Spherical Gear With Concave Cone Teeth and Its Cutting Tool

The spherical gear, or globular gear is a ball, on the ball there are a series of holes. The spherical gear is the key component of the robot’s wrist. As shown in fig.1, by using the spherical crowns of two different spherical centers as a joint curve surface, and their spherical center as a rotational center, the spherical gearing can be formed on two spherical surfaces with convex teeth and concave teeth engaging each other. The robot’s wrist differs from the wrist of human kind in that, it can transmit rotational movement from the upper arm to the lower arm continuously, while the angle between the upper arm and the lower arm is changing. In the formal papers, the protruding teeth have the shape of a cone, while the concave teeth are the conjugate surface of them. The protruding teeth with straight surface are of cause easy to be machined. But the concave teeth are very hard to be machined. The special machining method such as the electric spark machining has to be employed to deal with this kind of work. Theoretical analysis show [1] that the concave tooth profile of spherical gear can be rotate involutes surface. The curved surface of convex tooth profiles are formed according to concave tooth profiles through the envelopes of dual parameters. It is approximately a rotate involutes surface. The processing technique of convex and concave tooth profiles is quite complex. Reference [2] gives a new tooth profile. That is, to use cone instead of convex tooth profile with a rotate involutes surface. The rough manufacturing and grinding of convex tooth cylinder can thus become much easy. But the manufacturing of concave tooth surface remains complex. This paper proposes that concave teeth profiles take the place of cone. In that case we can use cone milling. In order to underline the originality of my work, I should say: In the former approach the convex teeth are the cones, while the profile of the concave teeth are the conjugate tooth surfaces of the cone. In my approach the concave teeth are the cones, while the profile of the convex teeth are the conjugate tooth surfaces of the cone. Just small change, the machining properties improved dramatically.