公开(公告)号：WO1996036489A1

公开(公告)日：1996-11-21

申请号：PCT/JP1996001290

申请日：1996-05-16

Applicant: HARMONIC DRIVE SYSTEMS INC.

Inventor： HARMONIC DRIVE SYSTEMS INC. ,  TANAKA, Kazuo ,  KIYOSAWA, Yoshihide

IPC: B41F33/00

CPC classification number: F16H35/008 ,  B41F13/12 ,  F16H49/001

Abstract: A phase adjustment unit (100) for effecting phase adjustment between rolls of a multi-color printing press comprises a phase adjustment gear device (10) and a phase adjustment motor (6) fitted to the rear end of the gear device (10). The phase adjustment gear device (10) includes a hollow input shaft (12) inside a hollow casing (11) and an output shaft (14) inside the input shaft (12), and spline shafts (121, 141) for fitting are disposed at the distal ends of these shafts (12, 14). Cup type first and second wave motion gear devices (16, 25) are coaxially disposed at the rear end of the spline shafts, and input rotation returns to the first wave motion gear device (16) from an inner gear (161) of the first wave motion gear device through a gear train (30) and the second wave motion gear device (25), and is transmitted to the output shaft (14). While the motor (6) is locked, each constituent element of the first wave motion gear device rotates integrally, and the input and output shafts rotate in the same way. At the time of phase adjustment, the rotation speed of the motor (6) is drastically reduced and outputted through the gear devices (25, 16). Since the input and output shafts protrude from one of the sides, fitting and removal of the unit can be conducted easily.

Abstract translation: 用于在多色印刷机的辊之间进行相位调整的相位调整单元（100）包括相位调节齿轮装置（10）和安装在齿轮装置（10）的后端的相位调节电动机（6）。 相位调整齿轮装置（10）在中空壳体（11）的内部具有中空的输入轴（12）和输入轴（12）内的输出轴（14），并且配置用于配合的花键轴（121,141） 在这些轴（12,14）的远端处。 杯型第一和第二波动齿轮装置（16,25）同轴地设置在花键轴的后端，并且输入旋转从第一和第二波动运动齿轮装置的内齿轮（161）返回到第一波浪运动齿轮装置（16） 波浪运动齿轮装置通过齿轮系（30）和第二波浪运动齿轮装置（25）传递到输出轴（14）。 当马达（6）被锁定时，第一波浪运动齿轮装置的每个构成元件一体地旋转，并且输入和输出轴以相同的方式旋转。 在相位调整时，通过齿轮装置（25,16），马达（6）的旋转速度急剧减小并输出。 由于输入和输出轴从一侧突出，所以可以容易地进行装置的拆卸。

公开(公告)号：WO1996019683A1

公开(公告)日：1996-06-27

申请号：PCT/JP1994002141

申请日：1994-12-19

Applicant: HARMONIC DRIVE SYSTEMS INC. ,  ISHIKAWA, Shoichi

Inventor： HARMONIC DRIVE SYSTEMS INC.

IPC: F16H01/32

CPC classification number: F16H55/0833 ,  F16H2049/006 ,  Y10T74/19

Abstract: An object of this invention is to provide a flexible meshing type gear having improved retaining force for lubricating oil film between gear surfaces. In a flexible meshing type gear (1), a flexture amount (w) in a radial direction of a cross section normal to a reference axis set at a predetermined position along a tooth trace of a flexible external gear (3) thereof is made a negative deflection flexture amount which is smaller than a normal flexture amount (wo), and a rigid internal gear (2) and the flexible external gear (3) are each constituted by a spur gear. The number of teeth of the flexible external gear (3) is made smaller by 2n (n is a positive integer) than that of the rigid internal gear (2). The working tooth profile of one of these two gears (2, 3) is formed into a convex curve, and the configuration thereof is made such that a portion (L1(O, A)) belonging to a convex relative to the other gear of the top portion of a moving path (L1) by a rack approximation drawn by the teeth thereof relative to the other gear on the cross section normal to the reference axis of the tooth trace is formed into a convex curve (L2(O, B)) which is similarity transformed using an extension ratio ( lambda ) with the apex of the moving path as an origin or a similarity curve thereof, while the working tooth profile of the other gear is formed into a concave curve, and the configuration thereof is also formed into a concave curve (L3(O, C)) resulting from similarity transforming of a portion of a moving path which is identical to that portion of the one of the two gears using an extension ratio ( lambda +1) with the apex of the moving path as an origin, whereby the meshing between the two gears is made an over-running type meshing in which continuous contact is made possible at a cross section normal to the reference axis.

Abstract translation: 本发明的目的是提供一种在齿轮表面之间具有改进的润滑油膜保持力的柔性啮合型齿轮。 在柔性啮合型齿轮（1）中，将与设置在沿其柔性外齿轮（3）的齿迹的预定位置处的基准轴垂直的横截面的径向的弯曲量（w）设为 小于正常挠曲量（wo）的负偏转挠曲量，以及刚性内齿轮（2）和柔性外齿轮（3）均由正齿轮构成。 柔性外齿轮（3）的齿数比刚性内齿轮（2）的齿数小2n（n为正整数）。 这两个齿轮（2,3）中的一个的工作齿廓形成为凸曲线，并且其构造使得属于相对于另一个齿轮的凸形的部分（L1（O，A）） 形成凸曲线（L2（O，B）），通过齿的相对于另一个齿轮在与牙轨的参考轴线相垂直的横截面上拉伸的齿条近似的移动路径（L1） ），其中使用与移动路径的顶点相关联的延伸比（lambda）作为其原点或相似曲线进行相似变换，而另一齿轮的工作齿廓形成为凹曲线，并且其构造也是 形成为通过与两个齿轮中的一个的一部分相同的移动路径的一部分的相似变换而产生的凹曲线（L3（O，C）），其使用与顶点的扩展比（λ+1） 作为原点的移动路径，由此两个齿轮之间的啮合 被制成超跑型啮合，其中在与基准轴垂直的横截面上可以进行连续接触。

公开(公告)号：WO1993020451A1

公开(公告)日：1993-10-14

申请号：PCT/JP1993000370

申请日：1993-03-26

Applicant: HARMONIC DRIVE SYSTEMS INC. ,  AKAHANE, Akira ,  GODLER, Ivan

Inventor： HARMONIC DRIVE SYSTEMS INC.

IPC: G01P15/03

CPC classification number: G01P15/0888

Abstract: An angular acceleration detector (10) is provided with two slit-carrying discs (14, 15) mounted fixedly and coaxially in an opposed state on a rotary body (13), and a semiconductor position detecting unit (19) formed as a detecting means and consisting of a light emitting element (20) and a semiconductor position detecting member (21) which are disposed in an opposed state across the slits in these discs, the angular acceleration of the rotary body being detected by using this detecting unit. The slits (17) in the disc (15) cross at a predetermined angle the slits (16) in the disc (14). The disc (15) has an annular weight portion (15b) at the radially outer side of a slit-formed portion thereof, and a resiliently deformable spring portion (15c) circumferentially arranged at the inner side of the weight portion. The angular acceleration of the rotary body can be measured by detecting the movement of the crossing portions of the slits relatively moving due to the inertial force of the weight portion.

公开(公告)号：WO1999031517A1

公开(公告)日：1999-06-24

申请号：PCT/JP1997004695

申请日：1997-12-18

Applicant: HARMONIC DRIVE SYSTEMS INC. ,  ITOH, Yoshinori ,  HORIUCHI, Masashi ,  ASAWA, Hideo ,  TSUJIMOTO, Jun

Inventor： HARMONIC DRIVE SYSTEMS INC.

IPC: G01P15/03

CPC classification number: G01P15/165 ,  G01D5/34723 ,  G01D5/3473 ,  G01P3/486

Abstract: A detecting device (1) is provided with first and second discs (6 and 7) fixed to a rotating shaft (2). In the first disc (6), a first slit row (8) and a slit row (9) for encoder are formed as a common slit row (10). In the second disc (7), a second slit row (12) is formed. The light emitted from a photosensor (13) is led by an optical fiber cable (135) through the first and second slit rows (8 and 12). The angular acceleration of the rotating shaft (2) is detected from the relative movement between the slits. An encoder (14) detects the angle of the shaft (2) by detecting the movement of the slit row (9). Since the light wave guide of the photosensor (13) is formed of an optical fiber, the two discs (6 and 7) can be attached to arbitrary positions. In addition, since the slits are commonly used, the manufacture of an optical rotational information detecting device becomes easier. Therefore, a small-sized compact rotational information detecting device having a high degree of freedom in design can be manufactured inexpensively.

Abstract translation: 检测装置（1）设置有固定到旋转轴（2）的第一和第二盘（6和7）。 在第一盘（6）中，形成用于编码器的第一狭缝行（8）和狭缝行（9）作为公共狭缝行（10）。 在第二盘（7）中，形成第二狭缝行（12）。 从光传感器（13）发射的光通过第一和第二狭缝行（8和12）由光纤电缆（135）引导。 根据狭缝之间的相对运动来检测旋转轴（2）的角加速度。 编码器（14）通过检测狭缝排（9）的移动来检测轴（2）的角度。 由于光传感器（13）的光波导由光纤形成，所以可以将两个光盘（6和7）安装在任意位置。 此外，由于通常使用狭缝，所以光学旋转信息检测装置的制造变得更容易。 因此，可以廉价地制造具有高设计自由度的小型紧凑型旋转信息检测装置。

公开(公告)号：WO1999020917A1

公开(公告)日：1999-04-29

申请号：PCT/JP1997003751

申请日：1997-10-16

Applicant: HARMONIC DRIVE SYSTEMS INC. ,  SHIRASAWA, Naomi

Inventor： HARMONIC DRIVE SYSTEMS INC.

IPC: F16H01/32

CPC classification number: F16H49/001 ,  Y10T74/19

Abstract: A silk hat flexible engagement gear device (1) has first and second end plates (2 and 3) and an input shaft (4) is rotatably supported, with their ends supported, between the two end plates. A cylindrical body part (61) of a silk hat flexible external gear (6) is disposed on the outer circumference of the input shaft (4). A cross roller bearing (8) which also functions as a device housing and a rigid internal gear (5) are provided on the outer circumference. An annular boss (64) of the flexible external gear is held between the outer ring (81) of the cross roller bearing and the second end plate (3) and these three members are coupled with each other with second fixing bolts (9). The rigid internal gear (5) is held between the inner ring (82) of the cross roller bearing and the first end plate (2) and these three members are coupled with each other with first fixing bolts (11). An additional member which is used as a device housing is not necessary. The members are temporarily fixed and fastened and, further, attached to a housing on the motor side or on the load side with the fixing bolts (9 and 11) only. Therefore, the number of components of the device can be reduced and the size of the device can be reduced.

Abstract translation: 丝绸帽柔性接合齿轮装置（1）具有第一和第二端板（2和3），输入轴（4）可旋转地支撑，其端部支撑在两个端板之间。 丝绸帽柔性外齿轮（6）的圆柱体部分（61）设置在输入轴（4）的外圆周上。 在外圆周上还设有也用作装置壳体和刚性内齿轮（5）的十字轴承（8）。 柔性外齿轮的环形凸台（64）保持在交叉滚子轴承的外圈（81）和第二端板（3）之间，并且这三个构件通过第二固定螺栓（9）彼此联接。 刚性内齿轮（5）保持在交叉滚子轴承的内圈（82）和第一端板（2）之间，并且这三个构件通过第一固定螺栓（11）彼此联接。 不需要用作装置外壳的附加构件。 构件被暂时固定和紧固，并且还用固定螺栓（9和11）附接到电动机侧或负载侧的壳体。 因此，可以减少装置的部件数量，并且可以减小装置的尺寸。

公开(公告)号：WO1995028583A1

公开(公告)日：1995-10-26

申请号：PCT/JP1995000738

申请日：1995-04-14

Applicant: HARMONIC DRIVE SYSTEMS INC. ,  ISHIKAWA, Shoichi

Inventor： HARMONIC DRIVE SYSTEMS INC.

IPC: F16H01/32

CPC classification number: F16H55/0833 ,  Y10T74/19 ,  Y10T74/19972

Abstract: A meshing type gear device designed to improve further its strength and wear resistance, and more particularly to improve the wear resistance of the tooth surface. In a meshing type gear device (1), a spur gear is used both for a rigid internal gear (2) and a flexible external gear (3), and the number of teeth of the flexible external gear (3) is made greater by two than that of the rigid internal gear (2). The tooth profile of the flexible external gear (3) is formed into a convex tooth profile which is in the form of a curve AC that is to be obtained through similar transformation at a reduction ratio lambda of a convex portion (a curve between A and B) relative to the internal gear of a moving path L by rack approximation drawn by the external gear relative to the internal gear with a limiting point A of the contact between the two gears on the path serving as an origin, while the tooth profile of the rigid internal gear (2) is formed into a concave tooth profile which is in the form of a curve AD that is to be obtained through similar transformation at an enlargement ratio (1 + lambda ) of the same convex portion relative to the internal gear of the moving path with the limiting point A of the contact serving as an origin, whereby a continuously contactable and passing meshing can be produced between the two tooth profiles. With this configuration, it is possible to remarkably increase the capability of maintaining a lubricating oil film between the tooth surfaces and remarkably improve the permissible delivered torque of the flexible meshing type gear device based on the tooth surface wear.

Abstract translation: 啮合式齿轮装置设计成进一步提高其强度和耐磨性，特别是提高齿面的耐磨性。 在啮合式齿轮装置（1）中，正齿轮用于刚性内齿轮（2）和柔性外齿轮（3），并且柔性外齿轮（3）的齿数大于 两个比刚性内齿轮（2）的刚度大。 柔性外齿轮（3）的齿廓形成为凸齿形，其为曲线AC的形式，其将通过凸部的减速比λ（A和A之间的曲线）通过类似的变换获得 B）相对于移动路径L的内齿轮，通过外齿轮相对于内齿轮拉伸的齿条近似，具有作为原点的路径上的两个齿轮之间的接触的极限点A，而齿廓 刚性内齿轮（2）形成为凹曲线，其为曲线AD的形式，其将通过相同凸部的相对于内齿轮的增大比（1 +λ）的相似变换而获得 的移动路径，其中接触件的限制点A用作原点，由此可以在两个齿廓之间产生连续可接触和经过的啮合。 利用这种结构，可以显着提高在齿面之间保持润滑油膜的能力，并且基于齿面磨损显着提高柔性啮合型齿轮装置的允许传递扭矩。

公开(公告)号：WO1997022818A1

公开(公告)日：1997-06-26

申请号：PCT/JP1996003645

申请日：1996-12-13

Applicant: HARMONIC DRIVE SYSTEMS INC. ,  ISHIKAWA, Shoichi

Inventor： HARMONIC DRIVE SYSTEMS INC.

IPC: F16H01/32

CPC classification number: F16H55/0833 ,  Y10S475/904 ,  Y10T74/19 ,  Y10T74/19972

Abstract: In a deflection mesh type gear (1), basic tooth addendum profiles of a rigid internal gear (2) and a flexible external gear (3) are obtained from the formulas (1) and (2) where m is the tooth module, Zc is the number of teeth of the rigid internal gear (2), ZF, hfF, t and rn are the number of teeth, dedendum, rim thickness at the bottom, radius of the neutral circle of the rim of the flexible external gear (3), respectively, tau is the tooth thickness increase coefficient of both the rigid internal gear (2) and the flexible external gear (3), eta is the supplementary angle variable, and where the datum line is taken as x axis, the center line of tooth profile is taken as y axis, + sign of the composite sign in the formula (1) is for the flexible outer gear (3) and - sign is for the rigid internal gear (2). Formula (1) is x = m[0.25{ pi - n( eta - sin eta )} - (+/- tau )] - 0.5(g1 - g2); Formula (2) is y = 0.5mn(1 - cos eta ), where g1 = (0.5t + hfF + mn - f)[tan {2mn.sin eta / (rn + 2mn.cos eta )} + epsilon ]; g2 = 0.5mn ( eta - sin eta ) - xN + {yN - mn(1 - cos eta )}.0.5tan(0.5 eta ); f = 0.5m[n(1 + cos eta + tan(0.5 eta ){0.25( pi - n( eta - sin eta )) - tau }]; theta = 0.5 eta - (0.5mn/rn)sin eta + (0.5mn/rn) sin(2 eta ); epsilon = theta - 0.5 eta ZF/Zc; xN = (rn + mn.cos(2 theta ))sin epsilon ; yN = rn + mn - {rn + mn.cos(2 theta )}cos epsilon . Such a tooth profile realizes a proper wide-range engagement of teeth can be proposed for a tooth profile of rack approximation in consideration of tooth inclination and variation of locus of movement of the origin of the coordinate system for a tooth profile.

Abstract translation: 在偏转网状齿轮（1）中，从公式（1）和（2）获得刚性内齿轮（2）和柔性外齿轮（3）的基牙齿形轮廓，其中m是齿模块，Zc 是刚性内齿轮（2）的齿数，ZF，hfF，t和rn是齿数，齿根，底部的边缘厚度，柔性外齿轮边缘的中性圆的半径（3 ），tau是刚性内齿轮（2）和柔性外齿轮（3）两者的齿厚增加系数，eta是辅助角度变量，其中基准线作为x轴，中心线 将齿廓作为y轴，公式（1）中的复合符号的+符号用于柔性外齿轮（3），符号用于刚性内齿轮（2）。 公式（1）是x = m [0.25 {pi-n（eta-sin eta）} - （+/- tau）] -0.5（g1-g2）; 公式（2）是y = 0.5mn（1-cos eta），其中g1 =（0.5t + hfF + mn-f）[tan -1] {2mnsinsin eta /（rn + 2mn.cos eta）} +ε g2 = 0.5mn（eta-sin eta）-xN + {yN-mn（1-cos eta）}。0.5tan（0.5 eta）; f = 0.5m [n（1 + cos eta + tan（0.5 eta）{0.25（pi-n（eta-sin eta））-τ}];θ= 0.5 eta - （0.5mn / rn）sin eta + sin（2 eta）;ε=θ-0.5 eta ZF / Zc; xN =（rn + mn.cos（2θ））sinε; yN = rn + mn- {rn + mn 考虑到齿的倾斜和坐标原点的运动轨迹的变化，可以提出这种齿廓实现齿的适当的宽范围啮合的齿廓近似的齿廓 齿廓系统

公开(公告)号：WO1996036822A1

公开(公告)日：1996-11-21

申请号：PCT/JP1996001309

申请日：1996-05-17

Applicant: HARMONIC DRIVE SYSTEMS INC. ,  SHIRASAWA, Naomi

Inventor： HARMONIC DRIVE SYSTEMS INC.

IPC: F16H01/32

CPC classification number: F16H49/001 ,  F16H2049/003 ,  Y10T74/19

Abstract: A flat wave-motion gear (1) which has an input shaft (4) supported rotatably at both end portions thereof between first and second end plates (2, 3). A wave-motion gear mechanism is incorporated between these end plates (2, 3), and a cross roller bearing (8) is provided on an outer circumferential side of the wave-motion gear mechanism. The wave-motion gear mechanism comprises a rigid internal gear (5), a silk hat-shaped flexible external gear (6) provided on the inner side of the internal gear, and an intermittent driving force generator (7) provided on the inner side of the external gear (6). An annular boss (64) of the flexible external gear is held between an outer race (81) of the cross roller bearing (8) and the second end plate (3), whereby these three members are fastened to one another. The rigid internal gear (5) is held between an inner race (82) of the cross roller bearing (8) and the first end plate (2) whereby these three members are fastened to one another. The input shaft (4) may comprise a hollow shaft. Owing to the employment of such a structure, the apparatus as a whole can be formed flat and to a length slightly larger than the axial length of the flexible external gear. Since the outer race of the cross roller bearing can be used also as a housing of the apparatus, the apparatus can be formed compactly by a reduced number of parts.

Abstract translation: 一种扁平波动运动齿轮（1），其具有可旋转地支撑在第一和第二端板（2,3）两端的输入轴（4）。 在这些端板（2,3）之间并入有波动齿轮机构，在波动运动齿轮机构的外周侧设置有交叉滚子轴承（8）。 波动运动齿轮机构包括刚性内齿轮（5），设置在内齿轮内侧的丝帽状柔性外齿轮（6）和设置在内侧的间歇驱动力发生器（7） 的外齿轮（6）。 柔性外齿轮的环形凸台（64）保持在交叉滚子轴承（8）的外座圈（81）和第二端板（3）之间，由此这三个构件彼此紧固。 刚性内齿轮（5）保持在交叉滚子轴承（8）的内座圈（82）和第一端板（2）之间，由此这三个构件彼此紧固。 输入轴（4）可以包括中空轴。 由于采用了这种结构，因此整个装置可以形成为平坦的并且比可挠性外齿轮的轴向长度略大的长度。 由于交叉滚子轴承的外圈也可以用作装置的壳体，所以可以通过减少数量的部件紧凑地形成装置。

公开(公告)号：WO1996018833A1

公开(公告)日：1996-06-20

申请号：PCT/JP1995002567

申请日：1995-12-14

Applicant: HARMONIC DRIVE SYSTEMS INC. ,  TAKIZAWA, Noboru ,  SHIRASAWA, Naomi

Inventor： HARMONIC DRIVE SYSTEMS INC.

IPC: F16H01/32

CPC classification number: F16H49/001 ,  F16H2049/003 ,  Y10T74/19

Abstract: A silk hat type flexible external gear (13) of a flexible mesh engagement gear device (11) comprises a barrel portion (22), a diaphragm portion (23) and a boss portion (25). A thin portion (221) whose thickness is 80 % of the thickness of a main body portion of the barrel portion (22) is formed between the main body portion and a curved portion (222). The thickness of the diaphragm portion (23) is set such that it is the maximum at its internal circumferential end portion (point A), the minimum at its central portion (point B) and a slightly thinner than the maximum thickness at an external circumferential end portion (point C). The contour of the diaphragm is determined by using a group of curves (223, 224) such that the change in thickness is smooth as a whole. It is possible to ease the concentration of stress at the internal and external circumferential end portions so as to realize a gentle stress distribution by disposing the thin portion (221) in a way as described above and determining the thickness of the diaphragm portion (23) also in a way as described above. Consequently, it is possible to realize a silk hat type flexible mesh engagement gear device having a shorter axial length and a smaller outside diameter.

Abstract translation: 柔性网状啮合齿轮装置（11）的丝帽型柔性外齿轮（13）包括筒部（22），隔膜部（23）和凸台部（25）。 在主体部分和弯曲部分（222）之间形成有厚度为筒部（22）的主体部分厚度的80％的薄壁部分（221）。 膜部分（23）的厚度被设定为其内周端部（点A）处的最大值，中心部分（点B）处的最小值，并且比外周部的最大厚度稍薄 端部（点C）。 通过使用一组曲线（223,224）来确定隔膜的轮廓，使得厚度的变化整体上是平滑的。 通过以如上所述的方式设置薄部（221）并确定隔膜部（23）的厚度，可以减轻内周端部和外周端部的应力集中，以实现平缓的应力分布， 也以上述方式。 因此，可以实现具有较短轴向长度和较小外径的丝帽型柔性啮合齿轮装置。

公开(公告)号：WO1994012809A1

公开(公告)日：1994-06-09

申请号：PCT/JP1992001536

申请日：1992-11-24

Applicant: HARMONIC DRIVE SYSTEMS INC. ,  ISHIKAWA, Shoichi ,  KIYOSAWA, Yoshihide

Inventor： HARMONIC DRIVE SYSTEMS INC.

IPC: F16H01/32

CPC classification number: F16H55/0833

Abstract: In cup-shaped flexing contact gears (1), the respective tooth profiles of the rigid internal gear (2) and the cup-shaped flexible external gear (3) are each constructed such that the tooth face portion is formed of a straight line MA disposed in the vicinity of a datum point, a first convex circular arc AB smoothly connected thereto and a second convex circular arc BC smoothly connected to the first convex circular arc AB and having a radius of curvature larger than the first convex circular arc, while, the dedendum portion excluding the root is created by a standard rack consisting of a tooth profile formed by a curve point-symmetrical with respect to the datum point to the tooth profile at the tooth face or a curve obtained by correcting the above-mentioned curve. The curve defined by the above-described first and second convex circular arcs is an approximated curve of a similar curve obtained by subjecting to the conversion of similitude of 1/2 in the reduction ratio from the marginal point of intermeshing, which is selected on a composite curve to be described hereunder, this composite curve obtained by connecting a moving locus of teeth of the flexible external gear in a section of rotation in the vicinity of the end portion of the tooth trace on the side of a diaphragm to an envelope of moving loci obtained by overlapping on one plane of rotation the moving loci obtained by rack approximation of the external gear to the rigid internal gear in sections of rotation at the respective positions in the direction of tooth trace of the cup-shaped flexible external gear.

Abstract translation: 在杯状弯曲接触齿轮（1）中，刚性内齿轮（2）和杯形柔性外齿轮（3）的各齿形分别构造成使得齿面部分由直线MA 设置在基准点附近，平滑地连接到其上的第一凸圆弧AB和平滑地连接到第一凸圆弧AB并且具有大于第一凸圆弧的曲率半径的第二凸圆弧BC， 不包括根部的齿根部由标准齿条产生，该标准齿条由通过相对于齿面处的齿廓的基准点的曲线点对称形成的齿廓或通过校正上述曲线而获得的曲线构成。 由上述第一和第二凸圆弧限定的曲线是通过在相互啮合的边缘点进行从缩小比例的1/2的相似转换获得的类似曲线的近似曲线，其在 复合曲线，该复合曲线通过将柔性外齿轮的齿的移动轨迹在振动膜侧的齿迹的端部附近的旋转部分中移动到移动的包络线 通过在一个旋转平面上重叠，通过在杯状柔性外齿轮的齿迹方向上的相应位置处的旋转部分中将通过外齿轮的齿条近似获得的移动轨迹重叠到刚性内齿轮而获得的轨迹。