TWI811833B - Harmonic speed reducer - Google Patents

Abstract

The present invention discloses a harmonic deceleration device, which includes a wave generator, a flexspline, a first rigid wheel and a second rigid wheel. The wave generator can be driven to rotate around the central axis. The periphery of the flexspline is provided with a plurality of first external tooth-like structures, a grooves and a plurality of second external tooth-like structures. The first rigid wheel includes a plurality of first internal tooth structures for meshing with the plurality of first external tooth structures. The second rigid wheel includes a plurality of second internal tooth structures for meshing with the plurality of second external tooth structures. The angle between the first top surface of each first internal tooth structure and the first intersection line of the cross-section and the horizontal line is between 0.1 and 5 degrees. In the cross section, the distance between the first intersection line and the central axis gradually decreases from the inner side to the outer side of the first rigid wheel, the normal line of the cross section and the central axis are perpendicular to each other, and the central axis passes through the cross section.

Description

Harmonic reduction device

The invention relates to a deceleration device, in particular to a harmonic deceleration device with two rigid wheels.

Please refer to Figure 1, which shows a partial cross-sectional schematic diagram of a conventional double rigid wheel harmonic reduction device. After the flexspline F of the conventional double rigid wheel harmonic reduction device is installed on the periphery of the wave generator WG, the external tooth-shaped structure F1 of the flexspline F will be deformed, and the deformed external tooth-shaped structure F1 is connected with the two The inner sides of the internal tooth structures R11 and R21 of the rigid sprockets R1 and R2 respectively will cause interference (i.e. the circled area A in Figure 1). This will lead to the meshing of the flex spline F with the two rigid sprockets R1 and R2. The efficiency is reduced, which in turn will lead to a reduction in the service life of the double rigid wheel harmonic reduction device.

The invention discloses a harmonic deceleration device, which is mainly used to improve the problems of poor meshing efficiency and low service life of the conventional double rigid wheel harmonic deceleration device.

One embodiment of the present invention discloses a harmonic deceleration device including: a wave generator, a flexspline and two rigid splines. The wave generator is used to connect to a driving unit. The wave generator can be driven by the driving unit and rotate around a central axis. The flexspline is connected to the periphery of the wave generator. The periphery of the flexspline has a plurality of first external teeth. structure, a plurality of second external tooth-shaped structures and a separation groove, the separation groove is located between each first external tooth-shaped structure and each second external tooth-shaped structure; the two rigid wheels are respectively defined as a first rigid wheel and a first Two rigid wheels, the first rigid wheel includes a plurality of first internal tooth-shaped structures, the second rigid wheel includes a plurality of second internal tooth-shaped structures, and the plurality of first internal tooth-shaped structures are used to communicate with the plurality of first external tooth-shaped structures. Structural meshing, a plurality of second internal tooth-like structures are used to mesh with a plurality of second external tooth-like structures; the number of the plurality of first internal tooth-like structures included in the first rigid wheel is equal to the number of the plurality of first internal tooth-like structures included in the flexspline. The number of external tooth-like structures is the same, and the number of multiple second internal tooth-like structures included in the second rigid wheel is greater than the number of multiple second external tooth-like structures included in the flexspline; the two opposite sides of the first rigid wheel are opposite to each other. The sides are respectively defined as an inner side and an outer side, the opposite sides of the second rigid wheel are respectively defined as an inner side and an outer side, the first rigid wheel and the second rigid wheel are arranged adjacent to each other, and the first rigid wheel The inner side and the inner side of the second rigid wheel are arranged facing each other; each first internal tooth structure of the first rigid wheel includes a first top surface and four first connecting surfaces, and the four first connecting surfaces are connected to the first The four sides of the top surface are connected; a first intersection between each first top surface and a cross section and a first horizontal line parallel to the central axis range from 0.1 to 5 degrees, and in the cross section, The straight-line distance between the first intersection line and the central axis gradually decreases from the inside of the first rigid wheel to the outside of the first rigid wheel, a normal direction of the section is perpendicular to the central axis, and the central axis passes through the section; where , each second internal tooth-like structure of the second rigid wheel includes a second top surface and four second connection surfaces, and the four second connection surfaces are opposite to the four sides of the second top surface. Connection; a second intersection line of each second top surface and the cross section, and a second included angle between a second horizontal line parallel to the central axis, ranging from 0.1 to 5 degrees, and in the cross section , the linear distance between the second intersection line and the central axis gradually becomes smaller from the inner side of the second rigid wheel toward the outer side of the second rigid wheel. Among them, the maximum radial dimension of the flexspline driven by the wave generator and deformed is defined as a flexspline long axis, the minimum radial dimension of the flexspline driven by the wave generator is defined as a flexspline short axis, and the flexspline long axis is defined as C _L , the minor axis of the flexspline is defined as _CS , a first tooth surface width of each first internal tooth-like structure is defined as L ₁ , a first included angle is defined as θ ₁ , a first tooth surface width of each second internal tooth-like structure is defined as θ 1 The second tooth surface width is defined as L ₂ , and the second included angle is defined as θ ₂ ; among them, C _L , C _S , L ₁ , and θ ₁ comply with θ ₁ =C ₁ *tan ^-1 ((C _L -C _S )/ (4*L ₁ )), and 0.08≦C ₁ ≦0.45; or, C _L , C _S , L ₂ , θ ₂ are consistent with θ ₂ =C ₂ *tan ^-1 ((C _L -C _S ) /(4*L ₂ )), and 0.08≦C ₂ ≦0.45.

To sum up, the harmonic deceleration device of the present invention can effectively improve the first external tooth structure of the flexspline and the first internal tooth structure of the first rigid sprocket through the design of the first included angle, the second included angle and the separation groove. The meshing efficiency of the structure, as well as the meshing efficiency of the second external tooth-shaped structure of the flexspline and the second internal tooth-shaped structure of the second rigid wheel, can thereby increase the service life of the harmonic reduction device.

In order to further understand the characteristics and technical content of the present invention, please refer to the following detailed description and drawings of the present invention. However, these descriptions and drawings are only used to illustrate the present invention and do not make any reference to the protection scope of the present invention. limit.

Common knowledge:

Q: Harmonic reduction device

F:flexspline

F1: External tooth-like structure

WG: Wave Generator

R1, R2: rigid wheel

R11, R21: Internal tooth-like structure

A: Circle selection place

The present invention:

100: Harmonic reduction device

1: Wave generator

2: Flexspline

2A: Ring body

2A1: First ring part

2A2: Second ring part

2A3: Connecting ring part

2B: Separation tank

21: First external tooth-like structure

22: Second external tooth-like structure

3: The first round

3A:Inside

3B: Outside

31: First internal tooth-like structure

311:Top surface

3111: Intersection

312:Connection surface

4: The second round

4A:Inside

4B:Outside

41: Second internal tooth-like structure

411:Top surface

4111: Intersection

412:Connection surface

CP: central axis

S: Section

N: normal direction

H1: first horizontal line

H2: The second horizontal line

θ1: the first included angle

θ2: The second included angle

D1: Straight line distance

D2: Straight line distance

C _L : Long axis of flexspline

C _S : Flexspline short shaft

D _b : inner diameter of flexspline

D _a1 : Tip circle diameter of the first external tooth structure

D _f1 : Root circle diameter of the first external tooth structure

D _a2 : Tip circle diameter of the second external tooth structure

D _f2 : Root circle diameter of the second external tooth-like structure

L ₁ : First tooth surface width

L ₂ : Second tooth surface width

t ₁ :Thickness of the first annular part

t ₂ : Thickness of the second annular part

_t3 :Thickness of connecting ring part

W _G : Width of dividing groove

Figure 1 is a partial cross-sectional schematic diagram of a conventional double rigid wheel harmonic reduction device.

Figure 2 is a schematic diagram of the harmonic reduction device of the present invention.

Figure 3 is a schematic cross-sectional view of the harmonic reduction device of the present invention.

Figure 4 is an exploded schematic diagram of the harmonic reduction device of the present invention.

FIG. 5 is a schematic cross-sectional view along the cross-section line V-V in FIG. 2 .

FIG. 6 is a partially enlarged schematic diagram of FIG. 5 .

Figure 7 is a partial cross-sectional schematic view of the first rigid wheel and the second rigid wheel of the harmonic reduction device of the present invention.

Figure 8 is a partial cross-sectional schematic view of the first rigid wheel of the harmonic reduction device of the present invention.

Figure 9 is a partial cross-sectional schematic view of the second rigid wheel of the harmonic reduction device of the present invention.

Figure 10 is a partial cross-sectional schematic view of the flexspline of the harmonic reduction device of the present invention.

Figure 11 is a schematic diagram of the flexspline before and after deformation of the harmonic reduction device of the present invention.

Figure 12 is a partial cross-sectional schematic view of the flexspline of the harmonic reduction device of the present invention.

Figure 13 is a schematic cross-sectional view of the flexspline of the harmonic reduction device of the present invention.

In the following description, if it is pointed out that please refer to a specific diagram or as shown in a specific diagram, it is only used to emphasize that in the subsequent explanation, most of the relevant content mentioned appears in the specific diagram. However, this is not limited to the specific drawings that can only be referred to in the subsequent description.

Please refer to Figures 2 to 6 together. The harmonic deceleration device 100 of the present invention includes a wave generator 1, a flexspline 2 and two rigid splines. A flexspline 2 is arranged on the periphery of the wave generator 1, and two rigid splines are arranged on the periphery of the flexspline 2. For the convenience of explanation, in the following description, the two rigid wheels are respectively defined as a first rigid wheel 3 and a second rigid wheel 4, and the plurality of internal toothed structures included in the first rigid wheel 3 and the second rigid wheel 4 are respectively defined as the first internal toothed structure 31 and the second internal toothed structure 41 .

The wave generator (Wave Generator) 1 is used to connect a driving unit (such as a motor shaft, a motor rotor, etc.). The Wave Generator 1 can be driven by the driving unit and rotate around a central axis CP.

The flexspline 2 is connected to the periphery of the wave generator 1. The flexspline 2 defines an annular body 2A. Each first external tooth-shaped structure 21 is formed on the periphery of the annular body 2A. Each second external tooth-shaped structure 22 is Formed on the periphery of the annular body 2A, a separation groove 2B is formed between the plurality of first external tooth-shaped structures 21 and the plurality of second external tooth-shaped structures 22.

In one embodiment, the appearance of each first external tooth-like structure 21 may be exactly the same as the appearance of each second external tooth-like structure 22 , and all the first external tooth-like structures 21 included in the flexspline 2 The number and the number of all the second external tooth-like structures 22 included in the flexspline 2 may be exactly the same, but are not limited to this. In different embodiments, the appearance of each first external tooth-like structure 21 may also be different from the appearance of each second external tooth-like structure 22. For example, a plurality of first external tooth-like structures 21 It may be a straight tooth design, and the plurality of second external tooth-like structures 22 may be a non-straight tooth design.

The first rigid sprocket 3 includes a plurality of first internal tooth-like structures 31 . The plurality of first internal tooth-like structures 31 included in the first rigid spline 3 are used to interact with the plurality of first external tooth-like structures 21 of the flexspline 2 . Engagement. The second rigid sprocket 4 includes a plurality of second internal tooth-like structures 41 . The plurality of second internal tooth-like structures 41 included in the second rigid spline 4 are used to interact with the plurality of second external tooth-like structures 22 of the flexspline 2 . Engagement. In practical applications, the second rigid wheel 4 may be connected to an external output component. For example, the second rigid wheel 4 may be directly or indirectly connected to wheels, arms, and other components.

The first rigid wheel 3 and the second rigid wheel 4 are arranged adjacently, and the two opposite sides of the first rigid wheel 3 are respectively defined as an inner side 3A and an outer side 3B. The two opposite sides of the second rigid wheel 4 are respectively defined as an inner side 3A and an outer side 3B. The sides are respectively defined as an inner side 4A and an outer side 4B, and the inner side 3A of the first rigid wheel 3 and the inner side 4A of the second rigid wheel 4 are arranged facing each other.

As mentioned above, in one specific application, the number of the plurality of first external tooth-like structures 21 included in the flexspline 2 may be equal to the number of the plurality of second external tooth-like structures 22 included in the flexspline 2 . The number of the plurality of first internal tooth-like structures 31 included in the first rigid spline 3 may be the same as the number of the plurality of first external tooth-like structures 21 of the flexspline 2 , and the number of the plurality of first internal tooth-like structures 31 included in the first rigid spline 3 can be the same. The number of the plurality of second internal tooth-like structures 41 included is greater than the number of the plurality of second external tooth-like structures 22 included in the flexspline 2 .

Following the above, when the driving unit drives the wave generator 1 to operate, the wave generator 1 will drive the flexspline 2 to repeatedly flexibly deform, and a part of the plurality of first external tooth-shaped structures 21 of the flexspline 2 will interact with the first rigid structure. Parts of the plurality of first internal toothed structures 31 of the wheel 3 mesh with each other. Since the number of the first internal toothed structures 31 included in the first rigid wheel 3 is different from the number of the first external toothed structures 21 included in the flexspline 2 The number is the same. Therefore, when the flexspline 2 is repeatedly flexibly deformed, the flexspline 2 will not rotate relative to the first rigid spline 3, but part of the second external tooth-like structure 22 of the flexspline 2 that is repeatedly flexibly deformed will It meshes with part of the second internal tooth-like structure 41 of the second rigid wheel 4, because the number of the second external tooth-like structures 22 contained in the flexspline 2 is equal to the number of the second internal tooth-like structures 41 of the second rigid wheel 4. Therefore, the second rigid wheel 4 will be driven to rotate by the repeatedly flexibly deformed flexspline 2. In this way, the high-speed power input by the driving unit will be output by the second rigid wheel 4 at a relatively low speed.

Please refer to Figures 4 to 8 together. Each first internal tooth structure 31 of the first rigid wheel 3 includes a top surface 311 and four connecting surfaces 312. The four connecting surfaces 312 are connected to the four sides of the top surface 311. . An intersection line 3111 of each top surface 311 and a cross-section S has a first angle θ1 between 0.1 and 5 degrees with a first horizontal line H1 parallel to the central axis CP, and the intersection line 3111 in the cross-section S and the central axis The linear distance between CPs gradually decreases from the inner side 3A to the outer side 3B; a normal direction N of the cross-section S is perpendicular to the central axis CP, and the central axis CP passes through the cross-section S.

Similarly, each second internal tooth structure 41 of the second rigid wheel 4 includes a top surface 411 and four connecting surfaces 412 , and the four connecting surfaces 412 are connected to the four sides of the top surface 411 . An intersection line 4111 of each top surface 411 and the cross-section S is a second included angle with a second horizontal line H2 parallel to the central axis CP. θ2 ranges from 0.1 to 5 degrees, and the straight-line distance D2 between the intersection line 4111 and the central axis CP in the cross-section S gradually becomes smaller from the inner side 4A to the outer side 4B.

As mentioned above, through the design of the first included angle θ1, the second included angle θ2 and the separation groove 2B, the axial positioning of the flexspline 2 can be maintained, and the meshing efficiency between the flexspline 2 and the two rigid sprockets can be effectively improved ( Mesh Efficiency) and the carrying capacity of the harmonic reduction device 100, and can further extend the overall service life of the harmonic reduction device 100.

As shown in Figures 1, 2, 4 and 5, in the conventional harmonic reduction device Q, the periphery of the flexspline F does not have the separation groove 2B that the flexspline 2 of the present invention has, but the conventional harmonic reduction device Q When the flexspline F is installed on the periphery of the wave generator WG, the external tooth structure F1 of the flexspline F will undergo relatively obvious deformation, and after the two rigid splines R1, R2 and the flexspline F are combined with each other, because the flexspline F The external toothed structure F1 of the wheel F has been deformed, so the flexspline F is prone to axial displacement. For this reason, the internal toothed structures R11 and R21 of the two rigid wheels R1 and R2 will be combined with the external toothed structure F1 of the flexspline F. The problem of poor meshing efficiency may lead to a decrease in the overall service life of the harmonic reduction device Q.

In addition, the external tooth-like structure F1 of the flexspline F of the conventional harmonic reduction device Q is relatively significantly deformed. Therefore, when the conventional harmonic reduction device Q is operating, the flexspline F will easily shake left and right. problem. On the other hand, the harmonic reduction device 100 of the present invention is designed such that the flexspline 2 has a separation groove 2B, a first included angle θ1 (shown in Figure 8) and a second included angle θ2 (shown in Figure 9). When the deceleration device 100 is in operation, the flexspline 2 is relatively less likely to shake left and right.

Please refer to Figures 7 to 12 together. In the preferred embodiment, the maximum radial dimension of the flexspline 2 when driven by the wave generator is defined as the long axis of the flexspline. The flexspline 2 is driven by the wave generator and deformed. The minimum radial dimension of the deformation is defined as a minor axis of the flexspline; assuming that the major axis of the flexspline is defined as _CL and the minor axis of the flexspline is defined as _CS , a first tooth surface width of each first internal tooth structure 31 is defined as L ₁ , the first included angle is defined as θ ₁ , a second tooth surface width of each second internal tooth structure 41 is defined as L ₂ , and the second included angle is defined as θ ₂ , then C _L , _CS , L ₁ , θ ₁ is consistent with the relationship formula θ ₁ =C ₁ *tan ^-1 ((C _L -C _S )/(4*L ₁ )), where 0.08≦C ₁ ≦0.45; C _L , C _S , L ₂ , θ ₂ is consistent with the relationship formula θ ₂ =C ₂ *tan ^-1 ((C _L -C _S )/(4*L ₂ )), where 0.08 ≦C ₂ ≦0.45. In this way, the flexspline 2 and the first The rigid wheel 3 and the second rigid wheel 4 can achieve relatively good meshing efficiency.

，3.5≦R≦20.8；其中，在D_f1>D_f2時，D_f2、D_a1、W_G符合以下關係式：

，3.5≦R≦20.8；其中，第一環狀部2A1的厚度定義為t₁，第二環狀部2A2的厚度定義為t₂，連接環狀部2A3的厚度定義為t₃，柔輪2的內徑定義為D_b；其中，t₁=(D_f1-D_b)/2，t₂=(D_f2-D_b)/2；當t₁<t₂時，則t₁≦t₃≦t₂；當t₁>t₂時，t₂≦t₃≦t₁。 Please refer to Figures 7 to 13 together. In a preferred embodiment, the annular body 2A of the flexspline 2 can be defined with a first annular portion 2A1, a second annular portion 2A2 and a connecting annular portion 2A3. , one side of the first annular portion 2A1 is connected to the connecting annular portion 2A3, and the other side of the connecting annular portion 2A3 is connected to the second annular portion 2A2. A plurality of first external tooth-like structures 21 are formed on the first annular portion 2A1. On the periphery of an annular portion 2A1, a plurality of second external tooth-like structures 22 are formed on the periphery of the second annular portion 2A2, connecting the periphery of the annular portion 2A3, a plurality of first external tooth-like structures 21 and a plurality of second The external tooth structures 22 together form the dividing groove 2B. The diameter of the addendum circle of the first external tooth-like structure 21 is defined as D _a1 , the diameter of the addendum circle of the first external tooth-like structure 21 is defined as D _f1 , and the diameter of the addendum circle of the first external tooth-like structure 21 is defined as D f1 . The diameter of the addendum circle is defined as D _a2 , the diameter of the addendum circle of the second external tooth structure 22 is defined as D _f2 , and the width of the separation groove 2B is defined as W _G ; where, when D _f1 < When D _f2 , D _f1 , D _a2 and W _G conform to the following relationship:

, 3.5≦R≦20.8; among them, when D _f1 >D _f2 , D _f2 , D _a1 , and W _G conform to the following relationship:

, 3.5≦R≦20.8; where, the thickness of the first annular part 2A1 is defined as t ₁ , the thickness of the second annular part 2A2 is defined as t ₂ , the thickness of the connecting annular part 2A3 is defined as t ₃ , and the flexspline 2 The inner diameter of is defined as D _b ; among them, t ₁ =(D _f1 -D _b )/2, t ₂ =(D _f2 -D _b )/2; when t ₁ <t ₂ , then t ₁ ≦t ₃ ≦t ₂ ; when t ₁ >t ₂ , t ₂ ≦t ₃ ≦t ₁ .

As mentioned above, through the above design, the flexspline 2, the first rigid sprocket 3 and the second rigid sprocket 4 can achieve relatively good meshing efficiency.

To sum up, the harmonic deceleration device of the present invention can effectively improve the first external tooth structure of the flexspline and the first internal tooth structure of the first rigid wheel through the design of the first included angle, the second included angle and the separation groove. The meshing efficiency of the structure, as well as the second external tooth structure of the flexspline and the second internal tooth of the second rigid sprocket The meshing efficiency of the harmonic reduction device can be improved, thereby improving the service life of the harmonic reduction device. In addition, by making the first included angle, the second included angle and the flexspline conform to the above relational expression, the meshing efficiency of the flexspline and the first rigid spline, and the meshing efficiency of the flexspline and the second rigid spline can be further improved.

The above are only the best possible embodiments of the present invention, and do not limit the patent scope of the present invention. Therefore, all equivalent technical changes made by using the description and drawings of the present invention are included in the protection scope of the present invention.

1: Wave generator

2: Flexspline

2A: Ring body

2B: Separation tank

21: First external tooth-like structure

22: Second external tooth-like structure

3: The first round

3A:Inside

3B: Outside

31: First internal tooth-like structure

3111: Intersection

4: The second round

4A:Inside

4B:Outside

41: Second internal tooth-like structure

4111: Intersection

Claims (8)

A harmonic deceleration device, which includes: a wave generator, which is used to connect to a driving unit, and the wave generator can be driven by the driving unit to rotate around a central axis; a flexspline, which is connected to a driving unit. The periphery of the wave generator is connected. The periphery of the flexspline has a plurality of first external tooth-shaped structures, a plurality of second external tooth-shaped structures and a separation groove. The separation groove is located at each first external tooth-shaped structure. between the structure and each second external toothed structure; two rigid wheels, which are respectively defined as a first rigid wheel and a second rigid wheel, the first rigid wheel includes a plurality of first internal toothed structures, the The second rigid wheel includes a plurality of second internal tooth-shaped structures, a plurality of first internal tooth-shaped structures for meshing with a plurality of first external tooth-shaped structures, and a plurality of second internal tooth-shaped structures for engaging with the plurality of first external tooth-shaped structures. To mesh with a plurality of the second external tooth-like structures; the number of the plurality of first internal tooth-like structures included in the first rigid wheel is equal to the number of the plurality of first external teeth included in the flexspline. The number of the plurality of second internal tooth-like structures included in the second rigid spline is greater than the number of the plurality of second external tooth-like structures included in the flexspline; The opposite sides of a rigid wheel are respectively defined as an inner side and an outer side. The opposite sides of the second rigid wheel are respectively defined as an inner side and an outer side. The first rigid wheel and the second rigid wheel are respectively defined as an inner side and an outer side. The rigid wheels are arranged adjacent to each other, and the inner side of the first rigid wheel and the inner side of the second rigid wheel are arranged facing each other; each of the first inner sides of the first rigid wheel The tooth structure includes a first top surface and four first connection surfaces. The four first connection surfaces are connected to the four sides of the first top surface; each of the first top surfaces is connected to a cross-section. A first angle between the first intersection line and a first horizontal line parallel to the central axis is between 0.1 and 5 degrees, and in the cross-section, the angle between the first intersection line and the central axis is The linear distance gradually decreases from the inner side of the first rigid wheel to the outer side of the first rigid wheel, a normal direction of the cross section is perpendicular to the central axis, and the central axis Through the cross section; wherein, each of the second internal tooth-like structures of the second rigid wheel includes a second top surface and four second connecting surfaces, and the four second connecting surfaces are connected to the second The four sides of the top surface are connected; a second intersection line of each second top surface and the cross section has a second angle between 0.1 and 5 degrees with a second horizontal line parallel to the central axis, And in the cross section, the linear distance between the second intersection line and the central axis gradually becomes smaller from the inside of the second rigid wheel to the outside of the second rigid wheel; Wherein, the maximum radial dimension of the flexspline driven by the wave generator and deformed is defined as a long axis of the flexspline, and the minimum radial dimension of the flexspline driven by the wave generator and deformed is defined as a flexspline. The minor axis of the flexspline, the major axis of the flexspline is defined as _CL , the minor axis of the flexspline is defined as _CS , a first tooth surface width of each of the first internal tooth-like structures is defined as _L1 , the third An included angle is defined as θ ₁ , a second tooth surface width of each second internal tooth-like structure is defined as L ₂ , and the second included angle is defined as θ ₂ ; where, C _L , _CS , L ₁ , θ ₁ is consistent with the relationship expression θ ₁ =C ₁ *tan ^-1 ((C _L -C _S )/(4*L ₁ )), and 0.08≦C ₁ ≦0.45; or, C _L , C _S , L ₂ , θ ₂ conforms to the relational expression θ ₂ =C ₂ *tan ^-1 ((C _L -C _S )/(4*L ₂ )), and 0.08≦C ₂ ≦0.45. The harmonic deceleration device of claim 1, wherein the flexspline defines an annular body, each of the first external tooth-like structures is formed on the periphery of the annular body, and each of the second external tooth structures is formed on the periphery of the annular body. The tooth-like structure is formed on the periphery of the annular body, and the separation grooves are formed between the plurality of first external tooth-like structures and the plurality of second external tooth-like structures. The harmonic reduction device according to claim 2, wherein the diameter of the Dedendum Circle of the first external tooth-like structure is defined as D _f1 , and the diameter of the Dedendum Circle of the second external tooth-like structure is Circle) diameter is defined as D _a2 , the diameter of the dedendum circle of the second external tooth-like structure is defined as D _f2 , and the width of the separation groove is defined as W _G ; where, when D _f1 <D _f2 , D _f1 , D _a2 , W _G conform to the following relationship:

,3.5≦R≦20.8. The harmonic reduction device according to claim 2, wherein the diameter of the addendum circle of the first external tooth-shaped structure is defined as D a1 , and the diameter of the addendum circle of the first external tooth-shaped structure is defined as D _a1 . Circle) diameter is defined as D _f1 , the diameter of the dedendum circle of the second external tooth-like structure is defined as D _f2 , and the width of the separation groove is defined as W _G ; wherein, when D _f1 >D _f2 , D _a1 , D _f2 , W _G conform to the following relationship:

,3.5≦R≦20.8. The harmonic reduction device according to claim 4, wherein the diameter of the Dedendum Circle of the first external tooth-like structure is defined as D _f1 , and the diameter of the Dedendum Circle of the second external tooth-like structure is Circle) diameter is defined as D _f2 , wherein the flexspline defines a first annular part, a second annular part and a connecting annular part, one side of the first annular part is connected to the connecting ring The other side of the connecting annular part is connected to the second annular part, a plurality of first external tooth-like structures are formed on the periphery of the first annular part, and a plurality of first external tooth-like structures are formed on the periphery of the first annular part. The second external tooth-like structure is formed on the periphery of the second annular portion, connecting the periphery of the annular portion, the plurality of first external tooth-like structures and the plurality of second external tooth-like structures. The separation groove is jointly formed; wherein the thickness of the first annular portion is defined as t ₁ , the thickness of the second annular portion is defined as t ₂ , and the thickness of the connecting annular portion is defined as t ₃ , The inner diameter of the flexspline is defined as D _b ; among them, t ₁ =(D _f1 -D _b )/2, t ₂ =(D _f2 -D _b )/2; when t ₁ <t ₂ , then t ₁ ≦t ₃ ≦t ₂ . The harmonic reduction device according to claim 4, wherein the diameter of the Dedendum Circle of the first external tooth-like structure is defined as D _f1 , and the diameter of the Dedendum Circle of the second external tooth-like structure is Circle) diameter is defined as D _f2 . The flexspline defines a first annular part, a second annular part and a connecting annular part. One side of the first annular part is connected to the connecting annular part. are connected, the other side of the connecting annular part is connected to the second annular part, a plurality of the first external tooth-like structures are formed on the periphery of the first annular part, and a plurality of the A second external tooth-like structure is formed on the periphery of the second annular portion. The periphery of the connecting annular portion, the plurality of first external tooth-like structures and the plurality of second external tooth-like structures jointly form The separation groove; wherein, the thickness of the first annular portion is defined as t ₁ , the thickness of the second annular portion is defined as t ₂ , the thickness of the connecting annular portion is defined as t ₃ , and the thickness of the first annular portion is defined as t 1 The inner diameter of the flexspline is defined as D _b ; among them, t ₁ =(D _f1 -D _b )/2, t ₂ =(D _f2 -D _b )/2; when t ₁ >t ₂ , t ₂ ≦t ₃ ≦ _t1 . The harmonic reduction device according to claim 1, wherein each of the first external tooth-shaped structures and each of the second external tooth-shaped structures have the same appearance. The harmonic reduction device according to claim 1, wherein each of the first external tooth-shaped structures and each of the second external tooth-shaped structures have different shapes, and each of the first external tooth-shaped structures or Each of the second external tooth-like structures is a straight tooth structure.

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