A brick-shape magnet–assisted magnetorheological (MR) lapping was proposed for ultra-smooth flat surface finish, where a straight ribbon was produced to enhance polishing efficiency. Finite element analysis was performed to understand the magnetic property of the brick-shape magnet. Polishing marks and surface topographies were compared with the removal functions and distributions to reveal effects of translational oscillation, period ratio, work gap, eccentricity and trough speed on surface finish. Trajectories were calculated for kinematical...