Abstract: A dental hand-piece of the type known as "contra-angle" uses a pair of helical gears on shafts that rotate on respective axes which pass by each other but do not intersect. The gears, one set of which is on a tool driver and the other set of which may be formed in the shaft of a dental tool, engage in respective pitch circles, the diameters of which are smaller than their respective outer diameters.

Abstract: A dental contra-angle which supports a tool socket for combined motion consisting of two oscillatory movements simultaneously, one motion being a linear reciprocating motion parallel to the axis of rotation, and the other motion being an oscillatory motion around the axis of rotation. A tool receiving aperture opens through one end of the socket and extends along the axis toward the other end. A tool for treating a root canal, when installed in the socket, will be given a combined motion consisting simultaneously of a linear reciprocating motion in the axis of the root canal, and an angular oscillatory motion around the axis of the root canal. The resulting motion of such a tool is one of dipping with simultaneous partial rotation.