Analysis and classification of general sphere kinematics by driving rollers

In recent years, spherical wheels have attracted significant attention for their structural characteristics and are used for step climbing and omnidirectional movement. Although many sphere-driven robots employ friction drive systems and thus face challenges such as traveling on uneven surfaces, roller slippage, and the intrusion of debris between the sphere and the rollers, further improvements in running performance are expected. If a kinematic theory applicable to arbitrary configurations of sphere-based mechanisms is established, their use and applications are expected to expand further. In this paper, we express the general kinematics of mechanisms driven by multiple rollers using forward kinematic equations and discuss their comprehensive relationship with related studies. In addition, we validate the kinematics using a sphere measurement device, assuming various rotational motions of the sphere.