Abstract: A tool for deburring or finishing a workpiece is mounted for common reciprocatory movement with the wheelhead of a grinding machine. The tool, which is form of an elongated rod, is supported in a housing which is in turn pivoted about an axis transverse to the tool. A biasing means urges the tool toward a predetermined angular position about the pivotal axis of a housing. The tool cooperates with a workpiece to selectively overcome the bias and oscillate the tool in accordance with the relative reciprocatory movement between the grinding wheel and the workpiece.