Abstract: An apparatus for shaping a three-dimensional workpiece by inducing the following relative motions between an abrading die member and the workpiece: a feed motion, periodical retract and advance motions in a z-direction, and a planetary or orbital motion in the x and y directions. The mechanism which generates the planetary or orbital motion is provided with means for infinitely adjusting the eccentricity of this motion and is provided with means for selectively and releasably fixing the chosen amount of eccentricity. An assembly is provided to adapt the following process values to conditions within a gap between the die and the workpiece such that the abrading process is optimized: (i) feed pressure between the die and the workpiece during an abrading period of a work cycle; (ii) speed of the feed motion; and (iii) speeds of periodical retract and advance motions.