A honing tool for elliptical bores uses a unique rotary to linear to radial translation mechanism to translate the primary rotary motion of the drive shaft into axial motion of rods and sleeves within the drive shaft, which ultimately wedge the honing stones out, and pull them rigorously back in, in the desired elliptical pattern, with no loss of bore accuracy. A cam sleeve rotating with the drive shaft has undulating cam grooves that push and pull a pair of cam followers together and apart with every quarter turn. The cam followers shift a rod and sleeve up and down to wedge the honing stones in and out. The shape of the cam groove and the angle of the wedges are predetermined so as to create the proper elliptical pattern.