Development of Control Method for Active Ball Joint Mechanism Considering Singularity of Spherical Gear

Abstract

This paper presents a control method to avoid the singularity problem in the newly developed active ball joint mechanism. This mechanism is based on gear meshing but allows the driving of three rotational degrees of freedom on a single spherical surface, and it has no theoretical limits in the range of motion. These capabilities were obtained by meshing two innovative gears: Cross Spherical Gear and Monopole Gear. Despite their spherical shape, the gears were able to mesh with each other due to a unique structure ‘Pole’. However, our previous works suggest that in the vicinity of the Cross Spherical Gear poles, there are singularity areas where the velocity of the Monopole Gear changes rapidly. This paper describes the modelling and formulation of the singularity area and a method to avoid the associated problems. Finally, the developed method was embedded in the prototype’s control system, and the effect was verified by experimental results.