An apparatus for chemical mechanical planarization includes a spindle assembly structure and at least one substrate carrier, which make a linear lateral movement relative to each other while abrasive surfaces of a plurality of cylindrical spindles in the spindle assembly structure contact, and rotate against, at least one substrate mounted on the at least one substrate carrier. The direction of the linear lateral movement is within the plane that tangentially contacts the plurality of cylindrical spindles, and can be orthogonal to the axes of rotation of the plurality of cylindrical spindles.