An optimized harmonic drive (OHD) is disclosed. The OHD includes a wave generator, a flex spline, and a circular rigid spline. The wave generator includes a wave generator contour that minimizes a velocity profile of the wave generator during a high load condition. The flex spline is attached to the wave generator and the circular rigid spline is mechanically engaged to the flex spline. The flex spline includes a plurality of flex spline teeth and the circular rigid spline includes a plurality of rigid spline teeth. The plurality of rigid spline teeth is greater than the plurality of flex spline teeth and the high load condition exists when the rigid spline teeth of the plurality of rigid spline teeth are fully engaged with flex spline teeth of the plurality of flex spline teeth.

A relieving portion is formed between a first external tooth portion and a second external tooth portion in the external teeth of a flexible externally toothed gear of a flat strain wave gearing. The length L1 of the relieving portion in the tooth trace direction is within the range of 0.1 to 0.5 of the tooth width L of the external teeth. The maximum relieving amount t from the tooth top land of an external tooth in the relieving portion is 3.310.sup.4<t/PCD<6.310.sup.4 where the PCT is defined as the pitch circle diameter of the external teeth. The tooth face load distribution of the external tooth in the tooth trace direction can be equalized, and a flat strain wave gearing having a high transmitted-load capacity can be achieved.

According to a tooth profile designing method for a strain wave gear device, a first curve from a point A (?=0) to a point B (?=?/2) in a moving locus of external teeth with respect to internal teeth is extracted. A similarity curve is obtained by multiplying the first curve by (1??) using the point B as a center of similarity, and a second curve is obtained by rotating the similarity curve by 180? about a midpoint C between the point A and the point B as a center of similarity. A third curve is obtained by multiplying only the x-coordinate of the second curve by ? (?<1), or a fourth curve is obtained by multiplying only the y-coordinate of the second curve by ? (?>1). An addendum tooth profile of the external teeth is defined using the third curve or the fourth curve.

A gear device includes an internal gear, an external gear partially meshing with the internal gear, relatively rotating around a rotation axis to the internal gear, and having flexibility, and a wave generator being in contact with an inner circumferential surface of the external gear and moving a meshing position of the internal gear and the external gear in a circumferential direction about the rotation axis, wherein a virtual straight line as an extension of a tooth trace of the internal gear intersects with the rotation axis in a sectional view cut along a plane containing the rotation axis.

A flat strain wave gearing (1) has a mechanism for preventing a flexible externally toothed gear (4) from moving in the direction of the device center axis (1a) with respect to a rigid internally toothed gears (2, 3). The mechanism has an inner-peripheral groove (11) formed on inner teeth (3a) of the internally toothed gear (3), an outer-peripheral groove (12) formed on outer teeth (4a) of the externally toothed gear (4), and a flexible ring (13) mounted between the inner-peripheral groove (11) and the outer-peripheral groove (12). The ring (13) is engageable with groove inner-peripheral surfaces (11a, 11b, 12a, 12b), from the direction of the device center axis (1a), at meshing positions of the both gears (2, 4).

An externally toothed gear of a dual-type strain wave gearing is provided with first and second external teeth having different teeth numbers, and a gap formed between these teeth as a cutter clearance area for tooth cutters. The maximum width L1 of the gap is 0.1 to 0.3 times the width L of the externally toothed gear. The depth from the tooth top land of the first external teeth to the deepest part of the gap is 0.9 to 1.3 times the depth of the first external teeth, and the depth from the tooth top land of the second external teeth to the deepest part of the gap is 0.9 to 1.3 times the depth of the second external teeth. The tooth bottom fatigue strength of the externally toothed gear provided with differing numbers of first and second external teeth is increased.

A gear mechanism includes a gear including external teeth, the external teeth including a plurality of tooth parts defined by a cycloid curve, a plurality of contacting members disposed on an outer side and in a circumferential direction of the external teeth, the external teeth being brought into pressure contact with the plurality of contacting members, and a mechanism configured to eccentrically move the gear. A plurality of through holes penetrating the gear in a thickness direction of the gear are formed in the gear in the circumferential direction of the gear, the cycloid curve extends outward from an ideal cycloid curve without the external teeth interfering with the plurality of contacting members, the plurality of contacting members being in contact with the ideal cycloid curve.

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.

The invention relates to a harmonic pin ring drive with an outer gear ring toothing comprises a quantity of teeth which is greater by exact one than the quantity of teeth of an inner gear ring toothing. The invention further relates to a motor unit comprising such a harmonic pin ring drive and to an electrically assisted bicycle.

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.