Abstract: Provides an annular frame for attachment to the outer end of a circle of soft jaws carried by a radially adjustable chuck of a rotary machining assembly, whereby in spite of looseness or misalignment of the chuck jaws, their soft jaws can then be shaped to hold a subsequent workpiece in absolute alignment with the spindle. Frame has number of movable attachment arms corresponding to the number of jaws, which arms are adjustable along respective radial or arcuate guideways so as to engage the circle of soft jaws when opened to different circumferences. When each arm has two adjustable frame-attachment points, annulus is thereby self-centering. For use with (radially slidable) arms having single frame-attachment point, auxilliary centering device is provided.