This study investigates the kinematic and differential geometric properties of curve pairs on the unit sphere in three-dimensional Euclidean space that share a common geodesic normal direction. In particular, curvature relations between such curves undergoing rolling without slipping are analyzed. The transformations between their Sabban frames are derived, and the corresponding rotation angles associated with the rolling motion are characterized. Furthermore, the geodesic curvatures of the curves and the geometric relationships between them are examined. Mathematics Subject Classification: 53A04, 53A17, 53C22