JP4811676B2 - Gear using gear teeth and gear transmission device - Google Patents

Description

  The present invention relates to a gear using an arc tooth profile and a gear transmission device using the gear.

Conventionally, the Wilt Harbor-Nobikov gear (WN gear) is well known as a gear having an arc tooth profile, and research and development on the arc tooth profile has been promoted in various fields, and the tooth profile that combines an arc and another curve. Applied to various gears. The tooth profile is used as a tooth of an internal gear type pump gear, a rack and pinion of an automobile steering device, a gear of a reduction gear, a tooth of a toothed belt, and the like. The present invention is an application related to the previously published Japanese Patent Application Publication No. 2007-32836. The basic idea is based on the invention disclosed above.
Patent Publication 2007-32836 Patent Publication 2002-98219

In the previous patent publication 2007-32836, the feature is described in contrast to a gear having an arc tooth shape that has been conventionally used. However, in the gear according to claim 1 in the scope of the patent-published claims, the gear having a tooth profile that can be deformed at equal intervals in the claims. Is not disclosed. It is possible to freely deform the tooth profile by performing an operation of deforming at equal intervals based on the tooth profile curve of the gear according to claim 1 of the published application. As in the case of involute gears, there is a shift gear, and as described above, gears with an arc tooth profile can be finely adjusted by changing the tooth profile curve at equal intervals as described above. There is a need for gears with possible tooth profiles. The gear of claim 1 of the present invention has been devised in view of the foregoing, and provides a gear that satisfies these requirements. Here, terms used in the claims and specification will be explained. Since some technical terms related to gears have different expressions depending on commonly used terms and technical books, they are defined and used as follows in this application text.
External gear A cylindrical gear with teeth arranged on the outside like a spur gear.
External gear In this application, it is used when used as an external gear of an internal gear pump.
Internal gear In this application, it is used when used as an internal gear of an internal gear pump.
Gear Gear Transmission Device A gear device configured using gears such as a device configured by using a pair of gears, a reduction device, a speed increasing device, and a transmission device is shown.
Arc radius R In the external gear, it is the radius (R) of the arc that is the tooth profile shape of the tooth tip surface. In the internal gear, the radius (R) of the arc that is the tooth profile shape of the bottom surface is defined as the arc radius R. . It is used as a unit representing the size of the gear teeth of claim 1. (Equivalent to module m in involute gear)

In the previous patent publication 2007-32836, the use of a gear having an arc tooth profile is disclosed including examples, but the gears deformed at equal intervals are specifically included including examples. Not touching. When various gear devices are configured with a gear having an arc tooth profile, there is a case where it is necessary to adjust the clearance between the shafts of the gear and the gear or it is necessary to adjust the size of the gear. Further, when used as a gear of an internal gear type pump, the suction and discharge capacity may need to be adjusted. When used as a gear of a reduction gear, a gear is required that can give a degree of freedom to the design of the device including the size of the gear, the strength of the teeth, and the size of the casing. Further, there is a need for a gear transmission device that can be composed of a plurality of gears including the gears described above. In view of the foregoing, a gear and gear device that satisfies these requirements is provided.

In the invention of claim 1, the gear tooth size is defined by an arc radius R having a center on the reference pitch line, and the gear tooth profile is centered on a dividing point obtained by equally dividing the reference pitch line by the gear tooth number Z. Is based on a tooth profile formed by a tangent arc formed by circumscribing the two arcs adjacent to the arc of the arc radius R and the reference pitch line, and the center of the arc radius R and the 3 The gear has a tooth profile deformed at equal intervals with the center of the tangent arc as a base point, and has a tooth profile curve connected so that each of the deformed tooth profiles contacts .

  A second aspect of the present invention is a gear transmission device including a plurality of gears including the gear according to the first aspect.

The gear according to claim 1 is a gear having an arc tooth shape, and the tooth size of the external gear is an arc radius R (hereinafter, defined as an arc radius R) which is a tooth shape of a tooth tip surface. In the gear, it is represented by an arc radius R which is a tooth profile shape of the root surface. The arc radius R can be set to an arbitrary value, and the size of the base gear to be deformed at equal intervals is determined by this value and the number of teeth. This arc radius R corresponds to an involute gear module. Compared with the module, there is an advantage that the tooth size is expressed as an actually measured value that can be measured, and the arc radius R can be arbitrarily set depending on the size of the gear device. Further, compared with the involute gear, the meshing is smooth, the vibration is less, and the strength of the tooth portion is increased. Also, there is no tooth-to-tooth interference. The gear train can be formed from a combination of a small number of teeth. Further, the gear according to claim 1 is based on the center of an arc having an arc radius R and the center of a 3-tangent arc where the adjacent two arcs and the reference pitch circle are circumscribed, or inward (plus side) or inward. It becomes possible to deform in the direction (minus side) at equal intervals . The tooth profile curve of the gear can be freely deformed and meshed with each other, and there is a feature that adjustment of the clearance between the shafts and the gear size can be adjusted.

A gear transmission device according to a second aspect of the present invention is a gear device configured using the gear having the arc tooth profile of the first aspect. It can also be used as a gear of a reduction gear. Compared with a reduction gear used in the past, the design range of the device itself can be reduced from the ease of gear design and the freedom of setting of the arc radius R. It becomes possible to have a degree of freedom, and it is possible to design a device having a large reduction ratio. Furthermore, the use of gears deformed at equal intervals also leads to weight reduction of the device. Further, the gear of claim 1 can be used for power transmission by the configuration of the internal gear and the external gear, and if the gear train having a small number of teeth is configured, the device itself can be reduced in weight. . When used as an external gear and an internal gear of an internal gear pump, the discharge amount and the size of the apparatus can be freely adjusted by the amount of deformation at equal intervals . Applications can be extended to power transmission devices using deceleration, speed-up, transmissions and other gears.

The gear according to claim 1 of the present invention obtains basic data of a gear by the internal gear type pump gear basic calculation formula shown in Table 1 and disclosed in the above-mentioned Japanese Patent Publication No. 2007-32836. The tooth profile curve is created by deforming the tooth profile curve at equal intervals based on the center of the arc of radius R and the center of the 3-tangent arc where the adjacent two arcs and the reference pitch circle are circumscribed. A gear with a tooth profile curve. Similar to the above-mentioned application, the present invention can be applied to gears having one tooth to an arbitrary number of teeth.
As a feature of the gear according to claim 1 of the present invention, there is a feature that the setting of the arc radius R which is the size of the tooth and the amount F which is deformed at equal intervals can be arbitrarily set within a certain range. The amount of deformation at equal intervals is set by the value of the arc radius R representing the size of the gear teeth, and the possible range for deformation at equal intervals is shown in FIGS. 1 and 2 for the plus side (outer side). The upper limit on the outside is determined by the value of the arc radii R and r of the three circles, and the point at which the value of r is 0 is the maximum amount of deformation. In other words, it is a point where the arc that touches the 3 contracts and disappears.
On the minus side (inner side), it is up to the point where the value of the arc radius R becomes zero. That is, the arc radius R representing the size of the tooth is 0, and the tooth tip has a pointed shape. In addition, when deforming at regular intervals outward with respect to the base figure to be deformed at regular intervals (here, a tooth profile curve is shown), the amount of deformation at regular intervals is displayed with a positive value. In the case of deformation at equal intervals, the amount of deformation at equal intervals is displayed as a negative value. The gear according to claim 1 of the present invention can be used as an external gear and an internal gear of an internal gear type pump, and can also be used as an element of an individual gear train of a gear transmission device. Further, it has a feature that it can be used as one of the components of the reduction gear disclosed in the previous application.
Here, the tooth profile curve of the gear according to claim 1 of the earlier application is compared with the tooth profile curve deformed at equal intervals, and its features and effects will be briefly described together. Details will be described with reference to the example in the next section.
Features: 1) The arc radius R1 of the tooth profile curve deformed at equal intervals with the arc radius R of the tooth profile curve according to claim 1 of the earlier application ( deformed at equal intervals with the arc radius of the figure deformed at equal intervals ) In order to distinguish the arc radius on which the figure is based, the symbol of the arc radius is indicated by R1 and R). That is, the value of the arc radius R and the pitch circle diameter d increase or decrease by deforming at equal intervals . In addition, the shape of the tooth bottom portion of the external gear and the tooth tip portion of the internal gear formed by a circular arc of a three-tangent circle circumscribing two circles having an arc radius R is deformed by deforming at equal intervals . It is the same that it is composed of three arcs. In this case , the points where the arc radius r = 0 and the arc radius R1 = 0 of the tangent circle shown in FIGS. 1 and 2 are included.
2) The limit of the amount of deformation when deformed outwardly at equal intervals is the case of an external gear. The shape of the bottom of the gear is an arc of 3 circumscribed circles circumscribing 2 circles of adjacent arc radius R and a pitch circle. Although it is formed, the point at which the radius value of this three-tangent circle is 0 is the limit.
3) When the inside is deformed at equal intervals, as shown in FIG. 2 , the arc radius R 1 is zero. Similar results are obtained for the internal gear.
4) One of the features of the gear according to claim 1 of the present invention is that the center of the arc of the arc radius R and the adjacent two arcs and the reference pitch circle are circumscribed with respect to the basic tooth profile curve. Even with a gear whose tooth profile curve is deformed at equal intervals based on the center of the arc , it has a great feature that it meshes accurately as a pair of gears, similar to the gear described in claim 1 of the previous application. Yes.
5) In the previous application, the meshing of the teeth of the gear is defined to be in meshing unless it is the same tooth size. However, the gear of claim 1 of the present invention has a uniform tooth profile curve. Due to the deformation, there is a feature that gears with different tooth sizes (arc radius R) can be engaged with each other. This is described in detail in FIGS . 7, 8 and 11. FIG .

As effects, 1) the value of the arc radius R representing the size of the tooth changes, but the size of the gear can be arbitrarily adjusted.
2) In the meshing of the external gear, it is possible to adjust the axial clearance.
3) The gear tooth size (arc radius R) can be freely set, and the gear design including the gear strength and gear size is easy.
4) When a gear transmission device is designed using the gear according to claim 1 of the present invention, it is possible to easily reduce the weight and labor of the device itself.
Hereinafter, embodiments of the present invention will be described with reference to Tables 1 to 3 and FIGS. 1 to 11 .

Table 1 shows the basic calculation formulas of the external gear and the internal gear when deformed at equal intervals based on the basic calculation formula of the internal gear type pump gear in Table 1 of the previous patent application 2007-32836. It is a list. The arc radius representing the size of the tooth is indicated by R, and the arc radius of the gear deformed at equal intervals is indicated as R1. Similarly, the amount of deformation at equal intervals is indicated by F, the pitch circle diameter is D, the tip circle diameter is Da, and the root circle diameter is Df.
Some of the calculation items refer to the data in Table 1 of the previous patent application 2007-32836 . The eccentricity e has a characteristic that it does not change in an internal gear pump using gears deformed at equal intervals . The calculation formulas in Table 1 can be used not only for gears used for internal gear type pumps, but also for gears (external gears and internal gears) deformed at equal intervals .

FIG. 1 is a drawing of a 5-tooth gear of the external gear (1) in the calculation example of Table 1. R indicates an arc radius representing the size of the tooth. r is the radius of the arc of a 3-tangent circle in which the two circles of the arc radius R constituting the tooth tip part and the pitch circle are circumscribed. The figure deformed at equal intervals can be drawn on the basis of the gear calculation formula shown in Table 1 and the tooth profile curve created by the drawing procedure according to FIGS. 1 and 2 of the previous patent application 2007-32836 . Tooth profile of Figure 2, the arc radius and the two arcs and the reference pitch circle fit Ri arc center and neighboring R is based on 3 contact the center of the arc that circumscribes the outer (positive side) and inside (negative side) It is the figure which deform | transformed the original tooth profile curve by the quantity deform | transformed to arbitrary equal intervals . The value of the arc radius R of the deformed tooth profile curve and the value of the arc radius r of the tangent circle change in conjunction with the value of the amount F deformed at equal intervals .

FIG. 2 shows a figure deformed at equal intervals on the plus side and the minus side based on the tooth profile curve of FIG. The reference tooth profile curve before being deformed at equal intervals is highlighted with a bold line. The possible range of deformation at equal intervals is determined by the value of the arc radius r of the tangent circle on the plus side, and the outer upper limit is the amount of deformation at the maximum equal interval where the value of r is 0 . In other words, this is the point where the arc that touches 3 is contracted and disappears. On the plus side, the amount of deformation at equal intervals F = 0 is increased by 0.2, and the arc radius r of the three-tangent circle is displayed until the point becomes zero. The arc radius R of the tooth profile curve serving as a reference is 1. Up to the point where the value of the arc radius R becomes 0 is used as the tooth profile curve. In other words, the arc radius R representing the size of the tooth is 0, and the tooth tip has a pointed shape. In FIG. 2, on the minus side, the amount of deformation at equal intervals F = 0 is decreased by -0.2, until the arc radius R1 = 0 (the amount of deformation at equal intervals F = -1.0). Is displayed. By variously deforming the tooth profile curve of the base that is deformed at equal intervals, it is possible to design a wide variety of gear transmission devices using these gears. The tooth profile of the group to be deformed at equal intervals, is where are disclosed in the prior patent publication 2007-32836. Small number of the teeth-shaped curve of the teeth to the tooth profile of any number of teeth is deformed at equal intervals has features are possible Rukoto.

FIG. 3 shows a configuration diagram of an internal gear type pump having four teeth on the external gear and five teeth on the internal gear drawn based on the gear calculation formula of Table 1 . Eccentricity e = 0.5 none of the gears was constructed by an arc radius R = 1, in an amount F = 0 to deform at equal intervals, internal gear meshing with one difference using tooth profile to be deformed group This is the confined area of the pump.
The area where the pump can confine liquid in the casing (hereinafter referred to as the confined area. FIG. 3 shows only the confined area, and S0 is the area value. The capacity can be calculated by multiplying the aforementioned area by the tooth width, and the area can be easily calculated using CAD software.

FIG. 4 shows a configuration diagram of an internal gear pump in which a figure with an amount F deformed at equal intervals of 0 is deformed outward at equal intervals and a confined area value. The amount F deformed at equal intervals indicates the combination of the external gear and the internal gear deformed by a value from 0.2 to 0.4. The confinement area S is indicated by S2, S3 and S4, respectively. In the case of an internal gear pump, the direction of deformation at equal intervals between the external gear and the internal gear must be the same as the amount of deformation at equal intervals . The eccentricity e has a characteristic that it does not change even if the base tooth profile curve is deformed at equal intervals . When deformed to the plus side, the tooth strength is increased and the discharge capacity can be increased.

FIG. 5 shows a configuration diagram of the internal gear type pump in which a figure with F of 0 before being deformed at equal intervals is deformed inward at equal intervals and a confined area value. The amount F deformed at equal intervals indicates the combination of the external gear and the internal gear deformed by a value from -0.2 to -0.4. The confinement area S is indicated by S7, S8, and S9, respectively. Although the discharge capacity decreases, the device itself can be reduced in weight. It can be seen that the eccentricity e does not change as in FIG. In FIG. 4 and FIG. 5, the basic tooth profile curve is shown as an embodiment of an internal gear pump constructed by deforming at regular intervals . In designing the gear pump, this will lead to adjustment of discharge capacity including gear strength and weight reduction of the equipment. When it is deformed to the minus side, the area for confining the liquid can be increased as the tooth size R becomes smaller, and the discharge capacity can be freely adjusted by design. In addition, when the arc radius R = 2 of the base tooth profile curve is plotted and the amount F = −1.0 (arc radius R = 1) to be deformed at equal intervals on the minus side and the base tooth profile curve ( If the internal gear type pump is constructed with these gears by drawing with the arc radius R = 1), the internal gear type pump is constructed with the gear teeth having the same size by being deformed at equal intervals. It becomes possible to obtain a larger confinement area S.

Table 2, each equally spaced to the value of the arc radius R1 of the deformed so figure 4 and 5, the value of the quantity F deforming at equal intervals, is deformed at regular intervals the value of the confinement area S to the outside The table shows the case where the case is deformed and the case where it is deformed inward at equal intervals . It can be seen that the value of the arc radius R1 and the value of the confinement area S are proportionally increased / decreased by the value of the amount F deformed at equal intervals . That is, it can be seen that the discharge capacity, the respective gear sizes, and the casing size can be proportionally adjusted by the value of the amount F deformed at equal intervals . According to the first aspect of the present invention, the tooth profile curve can be freely deformed by deforming the base tooth profile curve at equal intervals, and the size of the gear and the gear device including the gear can be changed. It is a gear having a feature that the size and the shape of the tooth profile can be freely adjusted.

FIG. 6 is a meshing diagram configured as a rack and pinion (20 teeth) constructed based on the gear calculation formula of Table 1 . It is a figure that is the basis of a figure to be deformed with a tooth size R = 1 and an amount F = 0 that is deformed at equal intervals . The clearance between the rack and the pinion is indicated by a. In the engagement between the rack and the pinion, the distance between the axes is a = d / 2. Here, d represents the pitch circle diameter of the pinion. If the reference pitch of the rack is P, the equation P = π · R is established. R is an arc radius representing the size of a tooth. Figures 7 and 8 show figures deformed at equal intervals .

FIG. 7 is an engagement diagram configured by deforming the rack and pinion of FIG. 6 at equal intervals . The external gear which is a pinion is deformed by an amount F = 0.5 that is deformed outward (plus direction) at equal intervals , and the rack is larger as the amount that the pinion is deformed at equal intervals . It is the figure which deform | transformed to the reverse direction (minus direction), and was meshed | fitted at equal intervals of F = -0.5. In the case of this meshing, the tooth of the pinion side gear becomes thick and the strength of the tooth can be increased. However, the tooth profile on the rack side has a pointed tip and the strength of the teeth is inferior. Which of the rack side and the pinion side is offset to the plus side or the minus side can be freely selected according to the structure of the apparatus and the magnitude of the transmitted power.

FIG. 8 shows the reverse operation of FIG. That is, (the amount F = -0.5 to deform at regular intervals) the pinion side in the negative direction, the rack side to the plus direction at equal intervals, respectively 0.5 (amount F = 0.5 deform at regular intervals) The amount to be deformed is given. In this case, it is possible to increase the strength of the teeth on the rack side.

Table 3 summarizes the external gear data in FIGS. 9, 10, and 11 in a list. Figure 9 is obtained by plotting on the basis of the gear basic data when the amount F = 0 for deforming at regular intervals, that was constructed by deforming at equal intervals on the basis of the data of FIG. 9, FIG. 10, FIG. 11 and the gear data are shown in Table 3.

FIG. 9 shows an embodiment of a gear train in which external gears are engaged. FIG. 4 is an engagement diagram of an external gear that is a base F that is deformed at equal intervals with an amount F = 0 that is deformed at equal intervals .
The inter-axis clearance a can be obtained by the following equation. a = (d3 + d4) / 2 + R. d3 and d4 are pitch circle diameters of the respective external gears, and R represents an arc radius. The arc radius R is a circular arc radius of a tooth profile comprising a base for deforming at equal intervals, even deformed at equal intervals tooth profile of the base to the positive and negative direction, arc radius value R of this formula is changed Use as a fixed value. In the case of meshing between external gears F = 0 that are deformed at equal intervals, there is some interference between teeth and tooth advancement and delay during meshing. In order to eliminate this phenomenon, the gear train is configured by deforming the basic tooth profile curve at equal intervals in FIGS.

FIG. 10 shows a gear train in which two external gears of FIG. 9 are deformed and combined at equal intervals with an amount F = −0.1 that is deformed at the same equal intervals . Each gear data is shown in Table 3 . In the case of a combination of external gears, tooth interference and tooth advance / delay occur at the time of meshing when the amount F = 0 deformed at equal intervals as described in the above section.
To eliminate this phenomenon, it is possible to eliminate by combining by deforming at equal intervals the tooth profile to the positive or negative direction based on the center of the pitch circle. FIG. 10 is taken up as one of the embodiments.

FIG. 11 shows gear data in Table 3. One external gear is deformed at equal intervals by an amount F = −0.8 (negative direction) that is deformed at equal intervals, and the other external gear is F = It is a combined gear train that is deformed at equal intervals by 0.8 (positive direction). As described in FIG. 2, the range that can be deformed at equal intervals is determined by the values of the arc radii R and r of the tangent circle in the positive direction, and the upper limit of the outside is the value of r being 0. This point is the amount of deformation at the maximum equal interval . In other words, it is the point where the arc that is in contact with the three contracts and disappears. For the negative direction, the range that seems to be effective as a tooth profile curve seems to be the point where the value of the arc radius R becomes zero. That is, the arc radius R representing the size of the tooth is 0, and the tooth tip has a pointed shape. By setting the above-described range of deformation at equal intervals for each gear, it is possible to freely select a gear train having an appropriate meshing state. Further, the external gear on the left side of the gear train in FIG. 11 is a gear deformed at equal intervals in the negative direction. This tooth profile curve can be applied as a roller chain sprocket. For the roller diameter of the chain used for this, it is possible to refer to the arc radius R1 of the external gear in the right diagram of FIG. Since the gear according to claim 1 of the present invention has a feature that it can be freely deformed by deforming the tooth profile curve at equal intervals, it is used as an element of the gear device in various directions. It is speculated that it is possible.

  A rack cutter, a pinion cutter, a hob cutter, a milling cutter having the gear tooth shape according to claim 1 of the present invention, a generating gear cutting method using a method using any one of the above tools, or the gear according to claim 1 Milling cutters with the following tooth shapes, molding gear cutting method with grinding wheel, and machining program by NC data creation, milling cutter molding method, electrical discharge machine processing method, injection molding machine molding method, casting method, If the gear according to claim 1 is manufactured by any one of the methods, a wide range of production methods can be set from single item production to mass production. Further, as one of the methods for manufacturing the gear according to the first aspect, there is the machining of the NC data from the creation of the gear NC data using the CAD / CAM device to the machining by the NC machine tool. Since the tooth profile curve uses only a plurality of circular arcs, the NC data is mainly composed of circular cutting commands. Accordingly, the NC data capacity is small, and the machining time is shortened.

    The gear according to claim 1 of the present invention can be used widely and widely as an element of a gear transmission device including an external gear of an internal gear type pump, an internal gear, and a gear of a reduction gear. It has the following characteristics.

It is a figure which shows the tooth profile curve of a circumscribed gear tooth number 5 teeth. It is a figure which shows the analysis figure of five external gear teeth. It is a figure which shows the confinement area of the internal gear type pump with 4 external gear teeth and 5 internal gear teeth. It is a figure which shows the block diagram of the internal gear type pump of the number of the external gear teeth of 4 which deform | transformed to the positive direction at equal intervals, and the number of the internal gear teeth of 5. It is a figure which shows the block diagram of the internal gear type pump of the number of the external gear teeth 4 pieces and the internal gear teeth number 5 pieces which deform | transformed to the negative direction at equal intervals . FIG. 3 is a meshing diagram of an amount F = 0 deformed at equal intervals between a rack and a pinion (20 teeth). It is a meshing diagram of a rack (amount F = −0.5 deformed at equal intervals ) and 20 pinion teeth (amount F = 0.5 deformed at equal intervals ). A meshing view of the rack and pinion teeth number 20 sheets (amount F = 0.5 obtained by modifying at regular intervals) (the amount was deformation at equal intervals F = -0.5). It is a figure which shows the gear train of the quantity F = 0 made to deform | transform at equal intervals with the number of external gear teeth number of 10 and the number of external gear teeth number of 15. It is a figure which shows the gear train of the external gear tooth number 10 pieces (amount F = -0.1 deformed at equal intervals ) and the external gear tooth number 15 pieces (offset amount F = -0.1). It is a figure which shows the gear train of the number of external gear teeth 10 (amount F = 0.8 deformed at equal intervals ) and the number of 15 external gear teeth (amount F deformed at equal intervals = −0.8).

a Center distance at the time of gear meshing d1 External gear pitch circle diameter d2 Internal gear pitch circle diameter d3 External gear pitch circle diameter d4 in FIG. 9 External gear pitch circle diameter in FIG. 9 external gear tooth tip circle diameter df Internal gear The diameter of the root circle D The pitch circle diameter of the gear deformed at equal intervals Da The diameter of the tip circle of the gear deformed at equal intervals Df The diameter of the root circle of the gear deformed at equal intervals e Eccentricity F Value to be deformed at equal intervals o1 Circumferential gear center point R Arc radius R1 Arc radius of figure deformed at equal intervals r Radius of circle tangent 3 in Fig. S Confinement area of internal gear pump in Figs. 3 and 4 α1 Division number of teeth of outer gear α2 Number of teeth division angle of internal gear

Claims (2)

The size of the tooth of the gear is defined by an arc radius R having a center on the reference pitch line, and the tooth profile of the gear is an arc radius R created around a division point obtained by equally dividing the reference pitch line by the number of gear teeth Z. Based on a tooth profile formed by a three-tangent arc in which the two arcs adjacent to the arc and the reference pitch line are circumscribed, and based on the center of the arc radius R and the center of the three-tangent arc A gear having a tooth profile deformed at equal intervals and having a tooth profile curve connected so that each of the deformed tooth profiles contacts.   A gear transmission device comprising a plurality of gears including the gear according to claim 1.