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Many types of spherical robots use friction-drive systems for locomotion because such systems enable omnidirectional movement and are more capable of climbing steps than mobile robots equipped with multiple omni-wheels. Slipping between spheres and rollers is a remarkable issue with friction-driven mechanisms. However, the previously established sphere kinematic models do not consider slipping, and kinematic models consider slipping in only two constraint rollers. In this study, we propose a mathematical model that allows for slipping on three constraint rollers and simulate the angular velocity vector of the sphere and slip speed at each contact point.