A gear including plural teeth 3 to mesh with teeth of a corresponding gear to thereby transmit a rotational motion is provided. A form (b) of a tooth root side of each tooth 3 includes: a first curved surface c that is smoothly connected to a tooth surface a having an involute curve and has a profile expressed by a curve that is convex in an inverse direction of the involute curve of the tooth surface a; and a second curved surface d that is smoothly connected to the first curved surface c and has a profile defined by a hyperbolic function having a curve being convex in the same direction as the first curved surface c. It is possible to reduce a stress generated on the tooth root side at the time of meshing with teeth of the corresponding gear and thus to increase the strength of the teeth.

A gear including plural teeth 3 to mesh with teeth of a corresponding gear to thereby transmit a rotational motion is provided. A form (b) of a tooth root side of each tooth 3 includes: a first curved surface c that is smoothly connected to a tooth surface a having an involute curve and has a profile expressed by a curve that is convex in an inverse direction of the involute curve of the tooth surface a; and a second curved surface d that is smoothly connected to the first curved surface c and has a profile defined by a hyperbolic function having a curve being convex in the same direction as the first curved surface c. It is possible to reduce a stress generated on the tooth root side at the time of meshing with teeth of the corresponding gear and thus to increase the strength of the teeth.

The present invention achieves a machining apparatus which can easily be composed and a machining method which can perform gear machining or splined shaft machining easily by using an existing lathe. More specifically, the invention achieves a machining apparatus 1 comprising: a cutter 11 which includes a blade part 20 formed in the shape of a ring around a peripheral surface thereof and which is driven to rotate about an axis thereof; a workpiece holder 13 which holds a workpiece W rotatably; and a cutter driver 12 which moves the cutter 11 and the workpiece W relative to each other along an axial direction, wherein a gear or a splined shaft is formed on the peripheral surface of the workpiece W by synchronizing the rotation of the workpiece W with the relative movement of the cutter 11 and the workpiece W and by rotating the cutter 11, and wherein a plurality of the blade parts 20 are disposed side by side along the axis, the cutter driver 12 drives the cutter 11 to rotate in one direction around the axis and to reciprocate relative to the workpiece W along the axis, the workpiece holder 13 rotates the workpiece W in a forward/reverse direction in accordance with reciprocation of the cutter 11, and cutting is performed on the workpiece W so as to form thereon an external shape of a gear or a splined shaft by placing each of the blade parts 20 of the cutter 11 in contact with the peripheral surface of the workpiece W.