The Controllable Ball Joint Mechanism

A controllable ball joint mechanism with three rotational degrees of freedom is proposed in this paper. The mechanism is composed of three bevel gears, one of which rotates with respect to a fixed frame and the others rotate with respect to individual floating frames. The output is the resultant motion of the differential motions by the motors that rotates the bevel gears at the fixed frame and the floating frames. The mechanism is capable of a large rotation, and the structure is potentially compact. The necessary inverse and forward kinematic analyses as well as the derivation of kinematic singularity are provided according to the kinematical equivalent structure described in this paper.