JP5475153B2 - Bending gear system - Google Patents

Description

The present invention relates to a deflection meshing type gear equipment.

  A flexure meshing gear device shown in Patent Document 1 includes a vibrating body and a cylindrical external tooth that is arranged on the outer periphery of the vibrating body and has the flexibility to bend and deform by the rotation of the vibrating body. A gear, a first internal gear having rigidity with which the external gear internally meshes, and a first internal gear axially arranged on the first internal gear and having rigidity to internally mesh with the external gear. 2 internal gears.

  For this reason, when the first internal gear is fixed to the casing, the external gear flexed and deformed by the rotation of the vibration generator is in meshed with the first internal gear, and the first internal gear and The external gear is decelerated based on the difference in the number of teeth. And the output of the decelerated external gear can be taken out from the second internal gear.

JP 2006-29508 A

  However, in the flexure meshing gear device as shown in Patent Document 1, it is necessary to realize the meshing with the internal gear by bending the external gear, and further, the cylindrical external gear. In this case, it is difficult to theoretically mesh the two internal gears with the external gear because the meshing with the two internal gears must be considered at the same time. The number of theoretical meshes as a gear was very small. For this reason, the conventional flexure-mesh type gear device using a cylindrical external gear has low impact resistance, low transmission torque, and low transmission efficiency.

The present invention, which solve such the problems, to provide impact resistance is improved, the deflection meshing type gear equipment capable more increase transmission torque and transmission efficiency Let it be an issue.

The present invention relates to a vibrating body, a cylindrical external gear that is disposed on the outer periphery of the vibrating body and is flexible and deformed by the rotation of the vibrating body, and the external gear A first internal gear having rigidity for intermeshing engagement; and a second internal gear having rigidity for intermeshing engagement with the external gear, which is arranged in parallel in the axial direction on the first internal gear. In the flexure meshing gear device, the vibration exciter has an arc portion whose outer shape is an arc shape in a meshing range in which the external gear is engaged with the first internal gear and the second internal gear. and a first straight line passing through the eccentric shaft is the center of the circular arc portion and the rotation axis of the force isolator, the external gear and the common normal line of the contact point caused by engagement between the first Uchihaha wheel If the intersection of the first pitch point, and the first straight line, the external gear and the common normal and, the intersection of the second pitch of the contact points caused by engagement between the second internal gear And then, when the virtual pin when or cylindrical and pin cylindrical external teeth of the external gear, the center of the pin corresponding to the outer teeth, between the first pitch point and the second pitch point arranged, when virtual pin when or cylindrical and pin internal teeth cylindrical shape of the internal gear, the center of the pin corresponding to the inner tooth, the first pitch point and the second pitch point by being placed between the Rukoto is obtained by solving the above problems. When the internal teeth of the first internal gear or the second internal gear are assumed to be a cylindrical pin, specifically, the external teeth are obtained based on the virtual pins, and the first internal teeth are calculated based on the external teeth. The internal teeth of the gear and the second internal gear are formed as an envelope.

  In the present invention, when the external tooth of the external gear is a cylindrical pin between the two pitch points, the center of the pin or the internal tooth of the first internal gear or the second internal gear is cylindrical. When imagining a pin having a shape, the center of the pin is arranged. Therefore, the load applied to the external teeth of the cylindrical external gear when meshed with the first internal gear and the load applied to the external teeth of the cylindrical external gear when engaged with the second internal gear In addition to having components opposite to each other, the two load regions applied to the external gear can be brought close to each other in the circumferential direction of the external gear. In other words, when viewed from the axial direction, the two internal gears can sandwich only a small number of external teeth during the meshing operation. For this reason, the phenomenon (ratcheting phenomenon) that the meshing of the external gear and the internal gear is shifted by excessive torque can be particularly prevented. In other words, the present invention makes it possible to increase the allowable transmission torque and increase the transmission efficiency, particularly focusing on improving the ratchetability.

  According to the present invention, impact resistance is improved, and transmission torque and transmission efficiency can be increased.

The disassembled perspective view which shows an example of the whole structure of the bending meshing type gear apparatus which concerns on 1st Embodiment of this invention. Similarly sectional drawing which shows an example of whole composition The figure which also shows a vibration body The figure which also shows a vibration body Schematic diagram of a combination of a vibrator and a vibrator bearing Similarly, meshing diagram of external gear and internal gear Similarly, an enlarged view of the meshing of the external gear, the internal gear for reduction, and the internal gear for output The figure which similarly shows the position of the entity of the tooth profile of the external gear, the internal gear for reduction, and the internal gear for output The figure which defines the tooth profile of the external gear The figure which similarly defines the tooth profile of the internal gear for reduction and the internal gear for output The figure which similarly defines the tooth profile of the internal gear for reduction and the internal gear for output The figure which similarly defines the tooth profile of the internal gear for reduction and the internal gear for output Similarly, a table showing the relationship between the peripheral length, number of teeth, and pitch of the internal gear for reduction, the internal gear for output, and the external gear The figure which similarly shows the relationship between a pitch point and the position of the entity of an external gear The figure which similarly shows the relationship between a pitch point and the position of the entity of an external gear The figure which similarly shows the correction of the tooth profile of the internal gear for reduction and the internal gear for output A table showing the number of simultaneous meshes in the internal gear for reduction when the reduction ratio and the diameter of the internal gear are changed in the first embodiment. Table showing the number of simultaneous meshes in the internal gear for output when the reduction ratio and the diameter of the internal gear are changed in the first embodiment The figure which shows the relationship between the position of the entity of the external gear in 1st Embodiment, and a pitch point. The disassembled perspective view which shows an example of the whole structure of the bending meshing type gear apparatus which concerns on 2nd Embodiment of this invention. Similarly sectional drawing which shows an example of whole composition The figure which defines the tooth profile of the external gear The figure which similarly defines the tooth profile of the internal gear for reduction and the internal gear for output The figure which similarly shows the relationship between a pitch point and the position of the entity of an internal gear The figure which similarly shows the relationship between a pitch point and the position of the entity of an internal gear Table showing the number of simultaneous meshes in the internal gear for reduction when the reduction ratio and the diameter of the internal gear are changed in the second embodiment Table showing the number of simultaneous meshes in the internal gear for output when the reduction ratio and the diameter of the internal gear are changed in the second embodiment The figure which shows the relationship between the position of the entity of the internal gear in 2nd Embodiment, and a pitch point. The figure which shows the ratcheting prevention effect in 2nd Embodiment. The figure for calculating | requiring the contact line of the external gear in 1st Embodiment, the internal gear for reduction, and the internal gear for output Figure showing the contact line

  Hereinafter, an example of an embodiment of the present invention will be described in detail with reference to the drawings.

<< First Embodiment >>
<Configuration>
First, the overall configuration of the present embodiment will be schematically described mainly with reference to FIGS. 1 and 2.

  The flexure meshing gear device 100 is arranged on the outer periphery of the vibrating body 104 and the vibrating body 104 and has flexible external gears 120A and 120B (simply simply deformed by the rotation of the vibrating body 104). , External gear 120), and a reduction internal gear 130 </ b> A that is a first internal gear having rigidity with which the external gear 120 internally meshes, and an output internal gear that is a second internal gear. 130B. Hereinafter, the internal gear 130A for reduction and the internal gear 130B for output are collectively referred to simply as the internal gear 130.

  Hereinafter, each component will be described in detail.

  As shown in FIGS. 3 (A) and 3 (B), the vibrator 104 has a column shape, and an input shaft hole 106 into which an input shaft (not shown) is inserted is formed at the center. A keyway 108 is provided in the input shaft hole 106 so that the vibrator 104 rotates integrally with the input shaft when the input shaft is inserted and rotated.

  As shown in FIGS. 3 and 4, the vibrator 104 is formed in a shape (two arc shapes) obtained by connecting two arc portions (first arc portion FA, second arc portion SA). The first arc portion FA is an arc having a radius of curvature r1 centered on a point B (referred to as an eccentric shaft), and an arc portion (also referred to as a meshing range) for meshing the external gear 120 and the internal gear 130. ). The second arc portion SA is an arc having a radius of curvature r2 centered on the point C, and constitutes an arc portion (also referred to as a non-meshing range) in a range where the external gear 120 and the internal gear 130 do not mesh with each other. Yes. The length of the first arc portion FA is determined by a meshing angle θ that is an angle formed between the major axis x and the normal line N at the point A.

  At this time, as shown in FIG. 4, if the radius of the major axis x of the vibrating body 104 is r, the eccentric amount is L and the curvature radius r1 of the first arc part FA is expressed by equation (1). .

  r1 = r−L (1)

  Further, as shown in FIG. 4, the tangent line T (normal line N) is common to the connecting portion A between the first arc portion FA and the second arc portion SA. For this reason, the radius of curvature r2 of the second arc portion SA is (the radius of curvature r1 + the length BC), and therefore is expressed by Expression (2).

r2 = r1 + length BC
= R1 + L / cos θ (2)

  The vibration body bearing 110A is a bearing disposed between the outside of the vibration body 104 and the inside of the external gear 120A. As shown in FIGS. 2 and 5, the inner ring 112, the cage 114A, and the rolling element. As a roller 116A and an outer ring 118A. The inner side of the inner ring 112 abuts on the vibrating body 104, and the inner ring 112 rotates while deforming integrally with the vibrating body 104. The roller 116A has a cylindrical shape (including a needle). For this reason, compared with the case where a rolling element is a ball | bowl, since the part to which the roller 116A contacts the inner ring | wheel 112 and the outer ring | wheel 118A is increased, load capacity can be enlarged. That is, by using the rollers 116A, the transmission torque of the vibration body bearing 110A can be increased and the life can be extended. The outer ring 118A is disposed outside the roller 116A. The outer ring 118 </ b> A is bent and deformed by the rotation of the vibrating body 104, and deforms the external gear 120 </ b> A disposed outside the outer ring 118 </ b> A.

  As shown in FIG. 2, the vibration body bearing 110B includes an inner ring 112, a retainer 114B, rollers 116B, and an outer ring 118B, similarly to the vibration body bearing 110A. The vibration body 104 and the inner ring 112 are common to the vibration body bearings 110A and 110B. The retainer 114B, the roller 116B, and the outer ring 118B are the same as the retainer 114A, the roller 116A, and the outer ring 118A as a single member (component).

  As shown in FIG. 2, the external gear 120A is in mesh with the internal gear 130A for reduction. The external gear 120A includes a base member 122 and external teeth 124A. The base member 122 is a flexible cylindrical member that supports the external teeth 124 </ b> A, and is disposed outside the vibration body bearing 110 </ b> A. The external teeth 124A are cylindrical pins having a radius ρ1 (for this reason, the external teeth 124A (124B), the external gear 120A (120B), and the flexibly meshing gear device 100 of this embodiment are simply pin types. Called). The external teeth 124A are held on the base member 122 by a ring member 126A.

  As shown in FIG. 2, the external gear 120B is in mesh with the output internal gear 130B. And the external gear 120B is comprised from the base member 122 and the external tooth 124B similarly to the external gear 120A. The external teeth 124B have the same number as the external teeth 124A and are configured by the same cylindrical pin, and are held by the base member 122 by the ring member 126B. That is, the base member 122 supports the external teeth 124A and the external teeth 124B in common. That is, the external gears 120A and 120B have the same shape. The eccentric amount L of the vibrator 104 is transmitted to the external teeth 124A and the external teeth 124B in the same phase. Hereinafter, the external teeth 124A and 124B are collectively referred to as external teeth 124.

  The reduction internal gear 130A is formed of a rigid member, as shown in FIG. The internal gear 130A for reduction has a number of teeth that is a multiple of two than the number of teeth 124A of the external gear 120A (the number of teeth will be described in detail later). A casing (not shown) is fixed to the reduction internal gear 130A via a bolt hole 132A. And the internal gear 130A for deceleration contributes to the deceleration of rotation of the vibration body 104 by meshing with the external gear 120A. FIG. 6A shows how the external gear 120A meshes with the reduction internal gear 130A, and FIG. 7A shows the appearance of the external teeth 124A and the internal teeth 128A on the x-axis.

  On the other hand, the output internal gear 130B is also formed of a rigid member, like the reduction internal gear 130A. The output internal gear 130B has the same number of teeth of the internal teeth 128B as the number of teeth of the external teeth 124B of the external gear 120B (constant speed transmission). Note that an output shaft (not shown) is attached to the output internal gear 130B via a bolt hole 132B, and the same rotation as the rotation of the external gear 120B is output to the outside. FIG. 6B shows how the external gear 120B meshes with the output internal gear 130B, and FIG. 7B shows the appearance of the external teeth 124B and internal teeth 128B on the x-axis. Hereinafter, the inner teeth 128A and 128B are collectively referred to as the inner teeth 128.

  In the present embodiment, the simultaneous meshing number Nph of the external gear 120A and the reduction internal gear 130A and the simultaneous meshing number Npl of the external gear 120B and the output internal gear 130B are both set to 2 or more and The meshing is the theoretical meshing. For this reason, torque transmission efficiency is not lowered, smooth torque transmission can be realized, and transmission torque can be increased.

<Determination method of tooth profile>
A method for determining the tooth profile of the external gear 120, the reduction internal gear 130A, and the output internal gear 130B will be described.

  First, an outline of how to obtain the tooth profile will be described below.

  First, the tooth profile of the external gear 120 is defined. Next, the locus of the tooth profile of the external gear 120 is represented by a trochoid curve equation, and the tooth profile of the internal gear 130 is defined using the trochoid curve equation. Next, a plurality of parameters defining the tooth shapes of the external gear 120 and the internal gear 130 are associated with each other from the size and the number of teeth of the external gear 120 and the internal gear 130. Next, the correction range of the tooth tip and the tooth root of the tooth profile of the internal gear 130 is determined. Next, the tooth profile portion outside the correction range is obtained using the associated parameters, and the number of simultaneous meshes is obtained from the tooth shape portion. Then, optimal parameters are determined so that the number of simultaneous meshes is 2 or more. In determining the parameters, trial and error are performed so that the target values such as the torque, the allowable surface pressure of the tooth surface, the main stress of each portion, and the bearing life are satisfied at the same time.

  Details will be described below.

  First, the tooth profile of the external gear 120 is defined.

  When the external tooth 124 is a cylindrical pin having a radius ρ1, a distance R1 from the eccentric shaft B to the center position (ρ1 = 0) of the pin serving as the external tooth 124 in the meshing range of the external gear 120 is defined as an external tooth. This is referred to as the radius of the tooth profile in the meshing range of the gear 120. Further, when the internal tooth 128 of the internal gear 130 is a cylindrical pin having a radius ρ2 (including a case where the internal tooth 128 is simply assumed in design), the internal tooth is determined from the rotation axis Fc (point on the axial direction O) of the vibration generator 104. The distance R to 128 (including imaginary) pin center position (ρ2 = 0) is referred to as the radius of the tooth profile of the internal gear 130. Then, as shown in FIG. 8, the relationship between the radius R and the radius R1 is expressed by Expression (3).

  R1 = RL (3)

  In the present embodiment, the external gear 120 is disposed on the outer periphery of the vibration generator 104 via the vibration generator bearing 110. The radial thicknesses of the vibrator bearing 110 and the external gear 120 are both constant. For this reason, since the vibrating body 104 has a two-arc shape, the external gear 120 also has a two-arc shape. The radius of the entity of the tooth profile in the meshing range of the external gear 120 corresponding to the curvature radius r1 of the meshing range of the oscillator 104 is R1. For this reason, when the radius of the entity of the tooth profile in the non-meshing range of the external gear 120 corresponding to the radius of curvature r2 of the non-meshing range of the vibrating body 104 is R2, Equations (2) and (3) are used. The radius R2 can be expressed by the equation (4).

  R2 = R1−L / cos θ (4)

  As shown in FIG. 9, the external tooth 124 is a cylindrical pin having a radius ρ1 on the circumference of the radius R1 (= RL) from the eccentric shaft B in the meshing range (for this reason, the eccentric shaft B is the center of the meshing radius of the external gear 120 when the external gear 120 and the internal gear 130 mesh).

  Therefore, the tooth profile of the external gear 120 is defined by the radius ρ1, the eccentric amount L, the radius R, and the meshing angle θ.

  Next, the tooth profile of the internal gear 130 is defined. The locus of the position of the tooth profile of the external gear 120 (the position of the radius ρ1 = 0) is obtained, and then moved inward by the radius ρ1 as the tooth profile of the internal gear 130. More specific description will be given below. The reduction gear ratio when the external gear 120 is a circular gear (referred to as a virtual gear) having a tooth profile entity radius R1 is referred to as a virtual reduction ratio n.

As shown in FIG. 10, the external gear 120 is revolved by an angle α around the rotation axis Fc of the vibration body 104. That is, the eccentric shaft B rotates α. At that time, the coordinate (x1, y1) of the position of the tooth profile of the external gear 120 rotates in the opposite direction by the angle α / n by the virtual reduction ratio n and moves to the coordinate (x2, y2). . For this reason, the coordinates (x _pfc , y _pfc ) indicating the locus of the position of the tooth profile of the external gear 120 are expressed by equations (5) and (6).

Here, since the tooth profile of the internal gear 130 is theoretically engaged with the external gear 120 as shown in FIG. 11, the coordinate of the position of the tooth profile of the internal gear 130 is expressed by an internal trochoid curve equation (hypotrochoid). (Curve formula). That is, the radius b1 of the base circle BA fixed around the rotation axis Fc, the radius a1 of the rolling circle AA that rotates without sliding along the circumference of the base circle BA, the radius L1 of the drawing point, and the rotation angle β1. When used, the coordinates (x _pfc , y _pfc ) of the position of the tooth profile of the internal gear 130 are expressed by equations (7) and (8).

  Here, if the relationship of Formula (9)-(11) is used, the relationship of Formula (12) and Formula (13) will be calculated | required.

In addition, since Formula (5) and Formula (12) (Formula (6) and Formula (13)) have shown the same coordinate ( _xpfc , _ypfc ), Formula (14) is calculated _| required.

  α = n * β (14)

Next, as shown in FIG. 12, the position coordinates (x _pfc , y _pfc ) of the tooth profile of the internal gear 130 are moved inward (on the internal gear 130 side) by the radius ρ1 of the external tooth 124. Therefore, the coordinates (x _fc , y _fc ) of the tooth profile of the internal gear 130 can be expressed by equations (15) to (17).

That is, radius R, ρ1, eccentricity L, virtual reduction ratio n (virtual reduction ratio n _h for making the tooth profile of the internal gear 130A for reduction, virtual reduction ratio n for making the tooth shape of the internal gear 130B for output By substituting _l ) and changing the angle β, the coordinates (x _fc , y _fc ) of the tooth profiles of the reduction internal gear 130A and the output internal gear 130B can be obtained.

  Next, parameters defining the external gear 120 and the internal gear 130 are associated with each other.

  As described above, the shape of the external gear 120 is a two-arc shape defined by the radii R1 and R2. Therefore, the parameter k (2 or more) indicating the difference in the number of teeth between the external gear 120A and the reduction internal gear 130A and the parameter i for deriving the reduction ratio N (i = 1 for the reduction internal gear 130A). , I = 0 when the output internal gear 130B is used, and the sizes of the external gear 120 and the internal gear 130 shown in FIG. 13 (peripheral lengths obtained from the radii R and R1 of the tooth profile) The table shows LC (circumference length) and the pitch P (the circumferential length of one tooth period) when using the virtual gear reduction ratio n and the number of teeth NT. Can do. Here, since the pitch P by the virtual gear and the pitch by the external gear 120 (= LC / NT) are equal, the relationship of the formula (18) exists.

  NT = LC / P (18)

  When Expression (18) is used, Expression (19) and Expression (20) can be derived from the table of FIG.

  Next, a parameter Gp (referred to as a pin type pitch coefficient) is introduced. Here, an intersection of a straight line passing through the eccentric shaft B and the rotation shaft Fc and a common normal of a contact point generated by meshing of the external gear 120 (external teeth 124) and the internal gear 130 (internal teeth 128) is defined. The pitch point is defined by the external gear 120 and the internal gear 130. The pin type pitch coefficient Gp can easily grasp the relative positional relationship between the positions of the tooth forms of the external gear 120 and the internal gear and the pitch points, and can easily adjust the parameters. It was introduced as follows. Specifically, as shown in Expression (21), the pin type pitch coefficient Gp is determined by the radius R1 (= RL) and the distance n from the eccentric shaft B to the pitch point by the external gear 120 and the internal gear 130. * Expressed as a ratio to L.

If the point _{P h} indicates pitch point by the external gear 120A and the decelerating internal gear 130A, 14 tooth entity of the external gear 120 radially (R-L) and the virtual reduction ratio _{n h} Show the relationship. A pin type pitch coefficient Gph (referred to as a pin type deceleration-side pitch coefficient) obtained at this time is defined in Expression (22) based on Expression (21). When formula (19) is rearranged with formula (19) and formula (20) and parameter i = 1, formula (23) is obtained.

When the point P ₁ indicates the pitch point by the external gear 120B and the output internal gear 130B, FIG. 15 shows the relationship between the radius (RL) of the tooth profile of the external gear 120 and the virtual reduction ratio n ₁ . Show the relationship. A pin type pitch coefficient Gpl (referred to as a pin type output side pitch coefficient) obtained at this time is defined in Expression (24) based on Expression (21). When Expression (24) is rearranged with Expression (19) and Expression (20) with parameter i = 0, Expression (25) is obtained.

Therefore, when the radius R, the reduction ratio N, the pin type deceleration side pitch coefficient Gph, and the meshing angle θ are given, the virtual reduction ratio n _h and the eccentricity L are determined, and then the pin type output side pitch coefficient Gpl, the virtual reduction ratio n _l can be determined.

In the present embodiment, as shown in FIGS. 14 and 15, the value of the pin type output side pitch coefficient Gpl> 1 is obtained by substituting the pin type deceleration side pitch coefficient Gph <1. In the present embodiment, when the meshing angle θ is 40 to 65 degrees and the value of cos ⁻¹ of the pin type deceleration side pitch coefficient Gph is 15 to 30 degrees, the result of obtaining each tooth profile is as follows. Is a more preferable condition.

  Next, the correction range of the tooth profile of the internal gear 130 is determined.

  As shown in FIG. 16, an angle when an angle β formed by a straight line connecting the coordinates of the inner teeth 128 and the center Oc of the outer teeth 124 (pins) and the x axis is about 45 degrees is βs. Then, when the angle β is from 0 to βs, there is a possibility of interference with the external teeth 124 of the external gear 120, and therefore, correction is performed on the root of the internal teeth 128 of the internal gear 130 within that range. Further, the angle β when the distance δ between the tooth tip of the outer tooth 124 and the tooth tip of the inner tooth 128 is about 15% of the radius ρ1 of the pin is defined as an angle βf. When the angle β is from βf to π, there is a possibility that a high surface pressure may occur during the interference with the external teeth 124 of the external gear 120 and the engagement with the external teeth 124 of the external gear 120. Correction is made to the tooth tips of the 130 internal teeth 128. That is, the angles βs to βf where the tooth profile is not corrected (the region of the tooth profile that is not corrected) are effective ranges in which the theoretical meshing is performed.

  Next, the simultaneous meshing numbers Nph and Npl are obtained.

  The simultaneous meshing numbers Nph and Npl can be obtained by dividing the effective range determined by the rotation angle α of the external gear 120 by the pitch angle (a value obtained by dividing 2π by the number of teeth NT). Here, the angles βfh and βsh are angles in the deceleration internal gear 130A, and the angles βfl and βsl are angles in the output internal gear 130B. The rotation angles determined by the angles βfh, βsh, βfl, βsl from the relationship of the equation (14) are αfh, αsh, αfl, αsl, respectively. That is, by using the equation (14), the simultaneous meshing number Nph of the reduction internal gear 130A is obtained by the equation (26), and the simultaneous meshing number Npl of the output internal gear 130B is obtained by the equation (27). .

  The number of simultaneous meshes is obtained along the equations (26) and (27). FIG. 17 shows the simultaneous meshing number Nph of the reduction internal gear 130A obtained when k = 2, and FIG. 18 shows the simultaneous meshing number Npl of the output internal gear 130B.

  The tooth profile of the internal gear 130 in the present embodiment is determined by the conditions of the diameter (2 * R) and the reduction ratio (1 / N) that achieve both of these simultaneous meshing numbers Nph and Npl of 2 or more. That is, when the difference in the number of teeth is 2 (k = 2), the reduction ratio (1 / N) is 1/20, and the tooth profile of the present embodiment is not obtained, and 1/30 or less (decelerated more than 1/30). The reduction gear ratio of the internal gear 130 of this embodiment is determined.

<Operation>
The operation of the flexure meshing gear device 100 will be described mainly with reference to FIG.

  When the vibration generator 104 is rotated by rotation of an input shaft (not shown), the external gear 120A is bent and deformed via the vibration generator bearing 110A according to the rotation state. At this time, the external gear 120B is also bent and deformed in the same phase as the external gear 120A via the vibration body bearing 110B.

  The bending deformation of the external gear 120 is made according to the shape of the radius of curvature r1 of the vibrator 104. Since the curvature is constant at the position of the first arc portion FA of the vibrating body 104 shown in FIG. 4, the bending stress is constant. Since the tangent line T is the same at the position of the first arc part FA and the second arc part SA in the connecting part A, sudden deformation at the connecting part is prevented. At the same time, since there is no abrupt position change of the rollers 116A and 116B in the connecting portion A, the rollers 116A and 116B are less slipped and torque transmission loss is small.

  When the external gear 120 is bent and deformed by the vibrator 104, the external teeth 124 move radially outward in the first arc portion FA (meshing range), and the internal teeth of the internal gear 130 are moved. 128. Since the external teeth 124 are rotatable pins when meshing, the external teeth 124 move close to rolling on the meshing surface, and the external teeth 124 slide on the base member 122 side where the surface pressure is lower than the meshing surface. . For this reason, there is little loss of transmission efficiency. The tooth shape of the inner tooth 128 is a tooth shape based on a trochoid curve with respect to the outer tooth 124 which is a cylindrical pin. For this reason, since the external teeth 124 and the internal teeth 128 are perfectly meshed with each other, loss can be reduced and high torque transmission efficiency can be realized.

  At the time of meshing, a load (direction and size) different from that of the external teeth 124B is applied to the external teeth 124A (differing from the external gear 120 of the present embodiment, but see FIG. 29). However, the vibrator bearings 110A and 110B, except for the inner ring 112, in the axial direction O are in relation to the external teeth 124A meshing with the reduction internal gear 130A and the external teeth 124B meshing with the output internal gear 130B. Separated into parts. For this reason, each of the skew of the roller 116B caused by the meshing between the reduction internal gear 130A and the external tooth 124A, and the skew of the roller 116A caused by the meshing between the output internal gear 130B and the external tooth 124B, respectively. It is prevented.

  Since the rollers 116A and 116B have a cylindrical shape, the load capacity is large and there are many portions that come into contact with the inner ring 112 and the outer rings 118A and 118B with respect to ball bearings having the same size ball. Can be bigger.

  Further, in the axial direction O, the external teeth 124 are divided into a portion (external teeth 124A) with which the reduction internal gear 130A meshes and a portion (external teeth 124B) with which the output internal gear 130B meshes. Therefore, when the external gear 120A meshes with the reduction internal gear 130A, even if the external teeth 124B are deformed, the deformation does not cause the external teeth 124A to be deformed. Similarly, when the external gear 120B meshes with the output internal gear 130B, even if the external teeth 124A are deformed, the external teeth 124B are not deformed by the deformation. That is, by dividing the external teeth 124, it is possible to prevent a decrease in transmission torque such that the deformation of one external tooth 124A (124B) causes the other external tooth 124B (124A) to deform and deteriorate the meshing relationship. Can do.

  The meshing position of the external gear 120 </ b> A and the reduction internal gear 130 </ b> A rotates as the vibration body 104 moves in the major axis direction x. Here, when the vibrating body 104 rotates once, the rotation phase of the external gear 120A is delayed by a difference in the number of teeth from the internal gear 130A for deceleration. In other words, the reduction ratio by the reduction internal gear 130A is ((the number of teeth of the external gear 120A (N * k) −the number of teeth of the reduction internal gear 130A ((N + 1) * k)) / the external gear 120A. The number of teeth (N * k)) =-1 / N.

  Since both the external gear 120B and the output internal gear 130B have the same number of teeth (N * k), the external gear 120B and the output internal gear 130B are engaged with each other without moving. The same teeth are meshed with each other. For this reason, the same rotation as the rotation of the external gear 120B is output from the output internal gear 130B. As a result, an output obtained by reducing the rotation of the vibrating body 104 based on the reduction ratio 1 / N by the reduction internal gear 130A can be extracted from the output internal gear 130B.

  The present embodiment includes, as its basic configuration, a configuration in which the cylindrical external gear 120 is engaged with two internal gears 130 having a rigidity (a reduction internal gear 130A and an output internal gear 130B), and The external gear 120 and the internal gear 130 are configured so that the external gear 120 and the internal gear 130 have tooth shapes in which the simultaneous meshing numbers Nph and Npl are both 2 or more, and a trochoid curve is used. So, the theoretical engagement is realized. For this reason, the impact resistance is improved, the surface pressure applied to the meshing tooth surfaces is dispersed, and a large torque can be transmitted, and the local stress generated in the external gear 120 is particularly affected by the conventional general cup. Compared to the type of flexure meshing gear device, the number can be significantly reduced. That is, in the flexibly meshing gear device according to the present embodiment, the conical area is increased and the surface is not constricted due to the bending of the vibration generating body, and there is no stress concentration at the bottom of the cup. Since the pressure can be dispersed, the load capacity can be greatly increased.

In this embodiment, as shown in FIGS. 14, 15, and 19, since the pin type deceleration side pitch coefficient Gph <1 and the pin type output side pitch coefficient Gpl> 1, the expression (28) is established. Yes. That is, as shown in equation (29), in the present embodiment, the distance to the pitch point _{P h} by a gear 130A in the deceleration and the external gear 120A and _(n h * L) from the eccentric shaft B from the eccentric axis B The position of the pin center of the external gear 120 (substance of the tooth profile) from the eccentric shaft B to the distance (n _l * L) from the external gear 120B to the output internal gear 130B to the pitch point P ₁ Is arranged.

  Therefore, the load applied to the external teeth 124A of the external gear 120A when meshing with the internal gear 130A for reduction and the load applied to the external teeth 124B of the external gear 120B when meshing with the internal gear 130B for output are: The two load regions applied to the external gear 120 can be brought close to each other in the circumferential direction of the external gear 120 while having components opposite to each other. That is, when viewed from the axial direction O, the two internal gears 130 can sandwich only a small number of external teeth 124 during the meshing operation. For this reason, the phenomenon (ratcheting phenomenon) that the engagement between the external gear 120 and the internal gear 130 is shifted by excessive torque can be prevented. That is, the ratcheting resistance can be improved.

  Deflection mesh gear device using cup-type external gears that are actually commercialized (with the internal gear tooth shape having a radius of about 26 mm and a reduction ratio of 1/50 (referred to as a comparative example)) In the flexibly meshing gear device 100 according to the present embodiment having the same size and the same reduction ratio, the ratchet resistance is greatly improved (approximately 4 times or more) from the actual measurement value of the comparative example. It has been confirmed that. At the same time, it can be confirmed by theoretical calculation and tests that the rated torque is 3.3 kgfm in the comparative example, whereas the rated torque is 6.6 kgfm in the flexure meshing gear device 100 of the present embodiment. It was. That is, it can be confirmed by theoretical calculation that the rated torque is about twice, and it can be confirmed by a test.

  Thus, in this embodiment, it is possible to increase the transmission torque and increase the transmission efficiency. Instead of improving the transmission torque, the flexure meshing gear device 100 can be made more compact.

  Further, in the present embodiment, the tooth shape of the external gear 120 is the same at the portions that mesh with the reduction internal gear 130A and the output internal gear 130B, respectively, so that the processing of the external gear 120 is easy. The processing cost can be kept low and the shape can be processed with high accuracy.

  That is, according to the present invention, it is possible to increase the transmission torque and the transmission efficiency by increasing the number of simultaneous meshes Nph and Npl of the external gear 120 and the internal gear 130.

<< Second Embodiment >>
An example of the second embodiment according to the present invention will be described in detail with reference to FIGS. In this embodiment, instead of the cylindrical pin of the first embodiment, a tooth shape based on a trochoid curve is adopted for the external gear, and the external teeth of the external gear are formed integrally with the base member (solid Called type). In addition, if the definition is the same as the parameter used in the first embodiment, the sign of the parameter used in the present embodiment is also the same.

  The configuration different from the first embodiment and the method for determining the tooth profile will be described, and the other portions will be denoted by the same reference numerals in the last two digits, and redundant description will be omitted.

<Configuration>
As shown in FIGS. 20 and 21, the external gear 220 </ b> A meshes internally with the reduction internal gear 230 </ b> A. The external gear 220A includes a base member 222 and external teeth 224A. The base member 122 is a flexible cylindrical member, is disposed outside the vibration body bearing 210A, and is integrally formed with the external teeth 224A. For this reason, the external teeth 224A can be made small and highly accurate processing can be performed. That is, the external gear 220A of this embodiment is suitable for a small flexure meshing gear device with a small load capacity. The external teeth 224A are formed based on a trochoid curve.

  As shown in FIGS. 20 and 21, the external gear 220 </ b> B meshes internally with the output internal gear 230 </ b> A. And the external gear 220B is comprised from the base member 222 and the external tooth 224B similarly to the external gear 220A. The external teeth 224B are formed in the same number and shape as the external teeth 224A. Here, as shown in FIG. 20, the external teeth 224A and the external teeth 224B are divided in the axial direction, but the base member 222 is common. That is, the external gears 220A and 220B have the same shape. The eccentric amount L of the vibrator 204 is transmitted to the external teeth 224A and the external teeth 224B in the same phase. Hereinafter, the external teeth 224A and 224B are collectively referred to as external teeth 224.

<Determination method of tooth profile>
A method for determining the tooth shapes of the external gear 220, the internal gear 230A for reduction, and the internal gear 230B for output will be described.

  First, an outline of how to obtain the tooth profile will be described below.

  First, the internal tooth of the internal gear is assumed to be a cylindrical pin, and the locus of the position of the tooth shape of the internal gear when the pin radius is set to ρ2 = 0 is represented by a trochoid curve equation. This is used to define the tooth profile of the external gear 220. Next, the locus of the position of the tooth profile of the external gear is obtained, and the tooth profile of the internal gear is defined from the locus. Next, a plurality of parameters defining the tooth shapes of the external gear 220 and the internal gear 230 are associated with each other based on the size and the number of teeth of the external gear 220 and the internal gear 230. Next, the correction range of the tooth tip and the tooth root of the tooth profile of the internal gear 230 is determined. Next, the tooth profile portion outside the correction range is obtained using the associated parameters, and the number of simultaneous meshes is obtained from the tooth shape portion. Then, optimal parameters are determined so that the number of simultaneous meshes is 2 or more. In determining the parameters, trial and error are performed so that the target values such as the torque, the allowable surface pressure of the tooth surface, the main stress of each portion, and the bearing life are satisfied at the same time.

  Details will be described below.

  First, the tooth profile of the external gear 220 is defined.

A cylindrical pin having a radius ρ2 is virtually arranged as the internal tooth 228A of the reduction internal gear 230A (for convenience, the reduction internal gear 230A is provided, but it may be arranged on the output internal gear 230B. ), The locus of the position of the tooth profile of the internal gear 230A for reduction with the pin radius ρ2 = 0 (synonymous with the center of the pin). Then, the tooth profile of the external gear 220 is moved to the inside (external gear 220 side) by the pin radius ρ2. More specific description will be given below. The virtual reduction ratio n (n _h , n _l ) has the same definition as in the first embodiment.

  As in the first embodiment, the external gear 220 has a two-arc shape, and the relationship between the radii R1 and R2 is expressed by Expressions (3) and (4).

The external gear 220 theoretically meshes with a reduction internal gear 230A that virtually includes a pin. For this reason, as shown in FIG. 22, the locus drawn when the center of the pin of the deceleration internal gear 230A moves from the coordinate (x4, y4) to the coordinate (x5, y5) in a static space centered on the eccentric shaft B. (X _p , y _p ) are expressed by an external trochoid curve equation (epitrochoid curve equation) as the coordinates of the position of the tooth profile of the external gear 220. That is, the radius b2 of the base circle BB fixed around the eccentric axis B, the radius a2 of the rolling circle AB that rotates without sliding along the circumference of the base circle BB, the radius L2 of the drawing point, and the rotation angle β2 When used, the coordinates (x _p , y _p ) of the position of the tooth profile entity of the external gear 220 are expressed by equations (30) and (31).

  Here, if the relationship of Formula (32)-(34) is used, the relationship of Formula (35) and Formula (36) will be calculated | required.

Next, the coordinates (x _p , y _p ) of the position of the tooth profile of the external gear 220 are moved inward (external gear 220 side) by the internal tooth 228 and a virtual pin radius ρ2. Then, the coordinates (x _kfc , y _kfc ) of the tooth profile of the external gear 220 with the rotation axis Fc as the origin can be expressed by equations (37) to (39).

That is, the coordinates (x _kfc , y _kfc ) of the external gear 220 can be obtained by changing the angle β by substituting the radius R, ρ2, the eccentricity L, and the virtual reduction ratio n _h .

Next, the tooth profile of the internal gear 230 is defined. The envelope of the coordinate (x _p , y _p ) of the position of the tooth profile of the external gear 220 is obtained, and the envelope is moved inward (internal gear 230 side) by a radius ρ2 to determine the tooth profile of the internal gear 230. The trajectory of That is, the tooth profile of the internal gear 230A for reduction is obtained again. More specific description will be given below.

The locus Q of the tooth profile of the external gear 220 on the xd-yd coordinate centered on the eccentric axis B of the external gear 220 (two broken line portions shown in FIG. 23) is as shown in FIG. Draw an envelope (solid line portion shown in FIG. 23). For this reason, the coordinates (x _pfc , y _pfc ) of the position of the tooth profile of the internal gear 230 with the rotation axis Fc as the origin are expressed by the equations (40), (41) using the equations (30), (31). It is represented by Here, the relationship between the angles α and β is expressed by the equation (43) by using the equation (42) which is a conditional expression of the envelope.

Next, the coordinates (x _pfc , y _pfc ) of the position of the tooth profile of the internal gear 230 are moved inward (internal gear 230 side) by the radius ρ 2 of the virtual tooth 228 and the virtual pin. Coordinates (x _fc , y _fc ) of the tooth profile of the internal gear 230 with the axis Fc as the origin can be obtained by equations (44) and (45).

That is, by changing the angle β by substituting the radius R, ρ2, the eccentricity L, and the virtual reduction ratios n _h , n _l , the respective coordinates of the tooth profiles of the reduction internal gear 230A and the output internal gear 230B (X _fc , y _fc ) can be obtained.

  Next, parameters defining the external gear 220 and the internal gear 230 are associated with each other.

  As described above, as in the first embodiment, the shape of the external gear 220 is a two-arc shape defined by the radii R1 and R2. That is, also in this embodiment, the relationship of Formula (19) and Formula (20) is established.

  Next, a parameter Gs (referred to as a solid type pitch coefficient) is introduced. Here, an intersection of a straight line passing through the eccentric shaft B and the rotation shaft Fc and a common normal of a contact point generated by meshing of the external gear 220 (external teeth 224) and the internal gear 230 (internal teeth 228) is obtained. The pitch point is defined by the external gear 220 and the internal gear 230 (that is, the definition of the pitch point is the same as in the first embodiment). As with the pin type pitch coefficient Gp, the solid type pitch coefficient Gs can easily grasp the relative positional relationship between the positions of the tooth forms of the external gear 220 and the internal gear 230 and the pitch points, and These parameters are introduced so as to facilitate the adjustment of these parameters. Specifically, as shown by the equation (46), the solid type pitch coefficient Gs is calculated from the radius R and the distance (n + 1) * L from the rotation axis Fc to the pitch point between the external gear 220 and the internal gear 230. It is expressed as a ratio.

Figure 24 and the radius R of the tooth profile of the entity of the internal gear 230 showing the relationship between the virtual reduction ratio n _h. The solid type pitch coefficient Gsh (referred to as a solid type deceleration side pitch coefficient) obtained at this time is defined in Expression (47) based on Expression (46). When the equation (47) is rearranged with the parameter i = 1 in the equations (19) and (20), the equation (48) is obtained.

FIG. 25 shows the relationship between the radius R of the tooth profile of the internal gear 230 and the virtual reduction ratio n ₁ . The solid type pitch coefficient Gsl (referred to as a solid type output side pitch coefficient) obtained at this time is defined in Expression (49) based on Expression (46). When formula (49) is rearranged with formula (19) and formula (20) and parameter i = 0, formula (50) and formula (51) can be obtained.

Therefore, when the radius R, the reduction ratio N, the solid type deceleration side pitch coefficient Gsh, and the meshing angle θ are given, the virtual reduction ratio n _h and the eccentricity L are determined, followed by the solid type output side pitch coefficient Gsl, the virtual reduction ratio. n _l can be determined.

Similarly to the first embodiment, the present embodiment substitutes the solid type deceleration side pitch coefficient Gsh <1 to obtain the value of the solid type output side pitch coefficient Gsl> 1, as shown in FIGS. Yes. Similarly to the first embodiment, the present embodiment may further include a case where the meshing angle θ is 40 to 65 degrees and the value of cos ⁻¹ of the solid type deceleration side pitch coefficient Gsh is 15 to 30 degrees. It is a more preferable condition from the result of obtaining each tooth profile.

  Next, the correction range of the tooth profile of the internal gear 230 is determined.

  Similar to the first embodiment, the tooth tip and tooth base of the internal tooth 228 are corrected. For this reason, the angles βs to βf in which the tooth profile has not been corrected (the region of the tooth profile that has not been corrected) are the effective range in which the theoretical meshing is performed.

  Next, the simultaneous meshing numbers Nsh and Nsl are obtained.

  Similar to the first embodiment, the simultaneous meshing numbers Nsh and Nsl can be obtained by dividing the effective range determined by the rotation angle α of the external gear 220 by the pitch angle. That is, using the relationship of the equation (43), the simultaneous meshing number Nsh of the reduction internal gear 230A is obtained by the equation (52), and the simultaneous meshing number Nsl of the output internal gear 230B is obtained by the equation (53). It is done.

  The number of simultaneous meshes is obtained along the equations (52) and (53). FIG. 26 shows the simultaneous meshing number Nsh of the reduction internal gear 230A obtained when k = 2, and FIG. 27 shows the simultaneous meshing number Nsl of the output internal gear 230B.

  The tooth profile of the internal gear 230 in the present embodiment is determined by the condition of the diameter (2 * R) and the reduction ratio (1 / N) that realize both of these simultaneous meshing numbers Nsh and Nsl are 2 or more. In other words, when the difference in the number of teeth is 2 (k = 2), the reduction ratio (1 / N) is 1/30, which is not the tooth profile of the present embodiment, and is reduced to 1/50 or less (greater than 1/50). The reduction gear ratio) determines the tooth profile of the internal gear of this embodiment.

  In the present embodiment, since the external teeth 224 are formed integrally with the base member 222, the external gear 220 can be easily processed and the processing can be performed with high accuracy.

  In other respects, the present embodiment can obtain substantially the same operational effects as the first embodiment.

For example, as in the first embodiment, in this embodiment, as shown in FIGS. 24, 25 and 28, the solid type deceleration side pitch coefficient Gsh <1 and the solid type output side pitch coefficient Gsl> 1 are set. Formula (54) is materialized. That is, as shown in equation (55), the distance from the axis of rotation Fc until the pitch point _{P h} by a gear 230A in the deceleration and the external gear _{220A ((n h +1) *} L) and the external teeth from the rotation axis Fc The center of the pin when the internal tooth 228 of the internal gear 230 is virtually assumed to be a pin between the distance ((n ₁ +1) * L) to the pitch point P ₁ by the gear 220B and the output internal gear 230B ( The position of the tooth profile entity) is arranged.

  For this reason, the load Fd applied to the external teeth 224A of the external gear 220A when meshing with the internal gear 230A for reduction and the load Fo applied to the external teeth 224B of the external gear 220B when meshing with the internal gear 230B for output. Can have components opposite to each other and can bring the regions of the two loads Fd and Fo applied to the external gear 220 close to each other in the circumferential direction of the external gear 220. That is, as shown in FIG. 29, when viewed from the axial direction O, the two internal gears 230 have only a small number of external teeth 224 while the regions of the load Fd and the load Fo are brought close to each other during the meshing operation. It can be set as the aspect inserted. For this reason, the ratcheting resistance can be improved as in the first embodiment.

  In addition, both Formula (29) and Formula (55) can be transformed into Formula (56).

That is, in the above-described embodiment, it is an intersection of a straight line passing through the rotation shaft Fc and the eccentric shaft B and a common normal of each contact point generated by the meshing of the external gears 120 and 220 and the internal gears 130 and 230. When the external tooth 124 of the external gear 120 is a cylindrical pin between the pitch points P _h and P ₁ , when the center of the pin or the internal tooth 228 of the internal gear 230 is a cylindrical pin (virtual) Since the center R of the pin is disposed, ratcheting resistance can be improved.

  Although the present invention has been described with reference to the above embodiment, the present invention is not limited to the above embodiment. That is, it goes without saying that improvements and design changes can be made without departing from the scope of the present invention.

  For example, in the above embodiment, when the simultaneous meshing number Nph, Npl, Nsh, Nsl is set to 2 or more, the tooth profile of the external gear or the internal gear is obtained based on the trochoid curve. Is not limited to this. For example, the contact line that is the locus of the contact point generated by the meshing of the external gear and the internal gear can be uniquely determined from the coordinates of the tooth profile of the internal gear that is obtained, so that it can also be used. . Hereinafter, the unique relationship between the coordinates of the tooth profile of the internal gear 130 and the contact line in the case of the first embodiment will be specifically described.

The contact line CL is a locus viewed from the XY coordinate system shown in FIG. 30 in which the coordinates of the tooth profile (x _fc , y _fc ) of the internal gear 130 are rotated by an angle α. Therefore, the coordinates (x _cfc , y _cfc ) of the contact line are given by the equations (57) and (58) obtained by rotating the tooth shape coordinates (x _fc , y _fc ) of the internal gear 130 by an angle α.

  The contact line CL obtained by the above equation is shown in FIG. The contact line CL is drawn between a plurality of tooth tips and tooth roots of the external gear 120 and the internal gear 130, and it can be seen that a plurality of simultaneous meshing numbers Nph and Npl can be secured.

  For this reason, the tooth profile of the internal gear may be obtained from a contact line that can secure a plurality of simultaneous meshing numbers Nph and Npl by using this.

  In the above embodiment, the deceleration side pitch coefficients Gph and Gsh are smaller than 1 and the output side pitch coefficients Gpl and Gsl are larger than 1. However, the present invention is not necessarily limited to such a relationship. For example, the deceleration side pitch coefficients Gph and Gsh may be larger than 1 and the output side pitch coefficients Gpl and Gsl may be smaller than 1. Further, the case where any pitch coefficient is larger than 1 or any pitch coefficient is smaller than 1 is not denied. This is because the tooth profiles of the external gear and the internal gear can be obtained by determining not only the parameters that define the pitch coefficient but also the adjustment of many parameters through trial and error.

  The flexure meshing gear device of the present invention can be used for various applications, but can be suitably used for precision control applications such as an industrial robot joint (wrist) drive device and a machine tool.

DESCRIPTION OF SYMBOLS 100, 200 ... Flexure meshing gear apparatus 104, 204 ... Exciter 110A, 110B, 210A, 210B ... Exciter bearing 114A, 114B, 214A, 214B ... Cage 116A, 116B, 216A, 216B ... Roller 120, 120A, 120B, 220, 220A, 220B ... external gears 122, 222 ... base members 124, 124A, 124B, 224, 224A, 224B ... external teeth 128, 128A, 128B, 228, 228A, 228B ... internal teeth 130, 130A , 130B, 230, 230A, 230B ... internal gears a1, a2 ... radius of rolling circle AA, AB ... rolling circle B ... eccentric shaft b1, b2 ... radius of base circle BA, BB ... base circle CL ... contact line FA ... First arc part (meshing range)
Fc ... rotating shaft Fd, Fo ... load Gp, Gph, Gpl, Gs, Gsh, Gsl ... pitch coefficient L ... eccentricity _n, n _h, n l _... virtual reduction ratio (reciprocal of)
N: Reduction ratio (reciprocal of)
Nph, Npl, Nsh, Nsl ... Simultaneous meshing number O ... Axial direction Oc ... Pin center Ph, Pl ... Pitch point R ... Radius of tooth profile of internal gear R1 ... Tooth profile of meshing range of external gear Radius of entity R2 ... Radius of entity of tooth profile in non-engagement range of external gear SA ... Second arc portion (non-engagement range)
ρ1, ρ2 ... Radius of cylindrical pin

Claims (1)

A vibrating body, a cylindrical external gear that is arranged on the outer periphery of the vibrating body and is flexibly deformed by the rotation of the vibrating body, and a rigidity with which the external gear meshes inwardly And a second internal gear having a rigidity that is provided in parallel with the first internal gear in the axial direction and has a rigidity to internally mesh with the external gear. In the gear device,
The vibrator has an arc portion whose outer shape is an arc shape in a meshing range in which the external gear and the first internal gear and the second internal gear mesh.
A first straight line passing through the center and is eccentric axis of the circular arc portion and the rotation axis of the force isolator, a common normal of the contact point caused by engagement between the external gear and the first Uchihaha wheel, Is the first pitch point ,
The intersection of the first straight line and the common normal of the contact point generated by the meshing of the external gear and the second internal gear is a second pitch point,
When the external tooth of the external gear is a cylindrical pin or when it is assumed to be a cylindrical pin, the center of the pin corresponding to the external tooth is arranged between the first pitch point and the second pitch point. It is,
When the internal tooth of the internal gear is a cylindrical pin or when it is assumed to be a cylindrical pin, the center of the pin corresponding to the internal tooth is arranged between the first pitch point and the second pitch point. meshing type gear device deflection, characterized in that that will be.