A strain wave gearing has a cup-shaped externally toothed gear that is provided with a body formed with external teeth, a diaphragm extending from an end of the body, and a rigid boss integrally formed in the diaphragm. The ratio B/A is set equal to or less than 0.59 where A is the reference pitch circle diameter of the external teeth and B is the outer diameter of the boss. The radial length from the inner peripheral edge of the diaphragm to the outer peripheral edge thereof in the present externally toothed gear is large. This enables to reduce bending stress generated in each part of the externally toothed gear due to coning, and a meshing state of the external teeth with the internal teeth in the tooth trace direction can also be improved, whereby further flattening of the externally toothed gear can be realized.

In a strain wave gearing, the addendum tooth profile of an inner gear is defined by a formula and that of an outer gear is by another formula at a principal cross-section located at a tooth-trace-direction center of the outer gear, on the basis of a movement locus (Mc) of =1 by the teeth of the outer gear with respect to those of the inner gear. The tooth profiles of the dedenda of each of the inner gear and the outer gear are set to any shape that does not interfere with the tooth profile of the addendum of the other gear. It is possible to avoid superimposed flexion-induced bending stresses and tensile stresses caused by load torque arising at the long-axis locations of the outer gear, and the transmission torque capacity of a strain wave gearing can be improved.

The dedendum tooth profiles of the internal teeth and external teeth of a strain wave gearing are prescribed by a first homothetic curve BC and a second homothetic curve AC obtained from a curve segment from a point A, at which the angle formed by the tangent to a movement locus Mc when meshing is approximated by rack meshing and the major axis is A, to a low point B. The dedendum tooth profile of the internal teeth is prescribed by a curve formed on the internal teeth in the course of the addendum tooth profile of the external teeth moving from an apex of the movement locus to point A. The dedendum tooth profile of the external teeth is prescribed by a curve formed on the external teeth when the addendum tooth profile of the internal teeth moves from the apex to arrive at point A.

A robot includes a first member, a second member provided rotatably with respect to the first member, a gearing that transmits drive power from one side to the other side of the first member and the second member, the gearing includes an internal gear, an external gear having a flexible barrel portion in a tubular shape with an opening portion in an end part, and rotating about a rotation axis relative to the internal gear, and a wave generator, the wave generator includes a cam having a non-circular outer circumferential surface, and a bearing including an inner ring, an outer ring, and a plurality of balls, the first member includes a counter body provided to face the end part on the opening portion side of the barrel portion, and a first seal member is provided between the outer ring and the counter body.

A strain wave gearing wherein the tooth profile of an external teeth of a cup-shaped or silk-hat-shaped external gear is set as follows. The tooth-tip tooth thickness decreases gradually from an external-teeth outer end toward an external-teeth inner end along an external tooth trace direction. In addition, a pressure angle at a pitch point (P) increases gradually from the external-teeth outer end toward the external-teeth inner end along the external tooth trace direction. Thus, it is possible to realize a cup-type or silk-hat-type strain wave gearing in which external teeth mesh with internal teeth in a wide range along the tooth trace direction, rather than only in one cross-section perpendicular to the axis in the tooth trace direction.

The flexible external gear of a strain wave gearing is provided with: a cylindrical body part capable of flexing in the radial direction; external teeth formed on the outer circumferential surface thereof with a constant pitch; and grooves formed on the inner circumferential surface of the cylindrical body section along the circumferential direction thereof with the same pitch as the external teeth. The grooves are grooves with a wave-shaped cross-sectional shape having the center line of the tooth crest of the external tooth as the center and extend in the width direction of the external teeth. It is possible to increase the tooth bottom fatigue strength of the flexible external gear by increasing the tooth bottom thickness, while maintaining ease of flexing and a tooth shape that can withstand tangential forces due to meshing.

Provided are an actuator for a link mechanism for an internal combustion engine and a wave gear speed reducer, which improve both input efficiency and driving efficiency. According to the invention, the wave gear speed reducer is configured so that a flexible external gear is bent into an elliptical shape using a wave generating device rotated by an input shaft to partially engage external teeth of the flexible external gear with internal teeth of an internal gear portion, and further configured so that an engaging part between the flexible external gear and the internal gear portion is rotated. The external teeth are larger in curvature than the internal teeth in a contact portion between the internal and external teeth.

In a strain wave gearing, the addendum tooth profile of an internal gear is defined by the formula a and that of an external gear is by the formula b at a principal cross-section located at a tooth-trace-direction center of the external gear, on the basis of a movement locus (Mc) of =1 of the teeth of the external gear with respect to those of the internal gear in the principle cross-section taken at the center of the tooth trace of the external gear obtained when the tooth meshing is approximated by rack meshing. It is possible to avoid superimposition of flexion-induced bending stresses and tensile stresses caused by load torque at the major-axis locations of the external gear, and the transmission torque capacity of a strain wave gearing can be improved.

In a strain wave gearing, the addendum tooth profile of an internal gear is defined by the formula a and that of an external gear is by the formula b at a principal cross-section located at a tooth-trace-direction center of the external gear, on the basis of a movement locus (Mc) of =1 by the teeth of the external gear with respect to those of the internal gear. It is possible to avoid superimposition of flexion-induced bending stresses and tensile stresses caused by load torque at the major-axis locations of the external gear, and the transmission torque capacity of a strain wave gearing can be improved.

A wave bearing of a wave generator of a strain wave gearing is provided with steel or stainless steel cylindrical hollow rollers between an inner-race-side raceway surface and an outer-race-side raceway surface, the hollow rollers serving as rolling elements. The ratio Di/Do of the inner diameter Di to the outer diameter Do of the hollow rollers is set to 0.95 or more. The relative radius of curvature of hollow rollers that have been flexed into an ellipsoidal shape increases with respect to the inner-race raceway surface and the outer-race raceway surface with which the hollow rollers are in contact, and the Hertz maximum contact stress is reduced. The hardness of the hollow rollers, the inner-race raceway surface, and the outer-race raceway surface can be reduced.