A method of supporting a workpiece having journal and eccentric regions, in a grinding machine for grinding the eccentric regions thereof, is described which involves mounting the workpiece in a headstock of the grinding machine, providing a coupling between the workpiece and a rotary drive mechanism for rotating the workpiece about its main axis and fitting around at least one remote journal region of the workpiece a pair of members which form a journal bearing complementary to the said region, and fixing the lower of the two members to the machine, thereby providing support for the workpiece at the said remote position. The method is particularly relevant to the grinding of crankpins of a crankshaft. A grinding machine for grinding the crankpins of a crankshaft workpiece comprises headstock means mounted on the machine bed, a grinding wheel mounted on a wheelhead assembly, drive means for moving the wheelhead towards and away from a workpiece when fitted to the headstock, drive means for rotating a workpiece when mounted in the headstock, and two part cradle means mounted in the machine at least one part of which presents at least an upwardly directed curved support surface for engaging the underside of a journal bearing region of a crankshaft workpiece when fitted to the headstock.