A grinding cup for detachable connection to the output drive shaft of a grinding machine for grinding buttons on drill bits or cutters, said grinding cup having top and bottom surfaces and consisting of a lower grinding section and an upper body section with a centrally disposed recess formed in the bottom surface of the grinding section; said body section having a centrally disposed upright drive section formed on the top surface of the grinding cup, said drive section shaped and sized to both driveably engage within a corresponding recess at end of the output drive shaft and provide axial and radial support and retaining means for detachably connecting the grinding cup to the output drive shaft wherein said drive section has a non-circular cross section and is tapered from the top surface of the grinding cup to the free end of the drive section.

A grinding cup for detachable connection to the output drive shaft of a grinding machine for grinding buttons on drill bits or cutters, said grinding cup having top and bottom surfaces and consisting of a lower grinding section and an upper body section with a centrally disposed recess formed in the bottom surface of the grinding section; said body section having a centrally disposed upright drive section formed on the top surface of the grinding cup, said drive section shaped and sized to both driveably engage within a corresponding recess at end of the output drive shaft and provide axial and radial support and retaining means for detachably connecting the grinding cup to the output drive shaft wherein said drive section has a non-circular cross section and is tapered from the top surface of the grinding cup to the free end of the drive section.

A sander apparatus for use with a drill press having a chuck defining a drill chuck axis. The sander apparatus includes a base assembly and a sander assembly supported by the base assembly, the base assembly locating the sander assembly in a predetermined location relative to the drill press chuck, in which a central pin axis of the sander assembly is aligned with the drill chuck axis. When a portion of an upper shaft of the sander assembly is secured in the chuck, rotation of the chuck about the drill chuck axis causes corresponding rotation of a body element of the sander assembly about the central pin axis. The base assembly supports the sander assembly in the predetermined location thereof as a workpiece is engaged with one or more abrasive elements on the body element while the body element rotates about the central pin axis.