Flexspline and harmonic reducer

Abstract

The present application provides a flexible wheel and a harmonic wave reducer. The flexible wheel has a bowl-shaped structure, and the flexible wheel includes a straight cylinder section (1), a contraction section (2) and a bottom flange (3). The contraction section (2) includes a third arc section (6), a first arc section (4) and a second arc section (5) arranged in sequence along the axial direction of the straight cylinder section (1). The second arc section (5) and the third arc section (6) are both convex arcs. The third arc section (6) is connected to the straight cylinder section (1). The bottom flange (3) is arranged at the end of the second arc section (5). According to the flexible wheel of the present application, the stress concentration phenomenon at the bottom of the flexible wheel can be effectively improved, the fatigue resistance can be improved, and the load-bearing capacity of the flexible wheel can be improved.

Description

Technical Field

[0001] The present application relates to the technical field of speed reducers, and in particular to a flexible wheel speed reducer. Background Art

[0002] A harmonic reducer is a type of gear reducer. It consists of three essential components: a rigid wheel, a flexspline, and a wave generator. The wave generator consists of a cam and a flexible rolling bearing, and the cam hub is an elliptical curve. Due to its unique structure, compared to conventional gear reducers, harmonic reducers offer a wide range of transmission ratios, a large number of meshing teeth, a high load capacity, a simple structure, a compact size, a light weight, smooth and impact-free transmission, high transmission efficiency, and high transmission precision. Therefore, they are widely used in industries such as aerospace, biomimetic machinery, and precision transmission.

[0003] As the weakest and most fatigue-prone component in the harmonic reducer, the flexspline's structural form has a great influence on its load-bearing and lifespan. As an elastic deformable body, the flexspline is in an alternating stress state under the forced deformation force of the cam hub, and is prone to stress concentration in the transition area of ​​the deformation zone, and uneven load stress distribution. The fatigue failure of the flexspline is mainly due to bending stress, which is related to the working principle of the cyclic deformation of the flexspline. Common structures of flexsplines include cup-shaped, top-hat-shaped, and cylindrical. Among them, the cup-shaped flexspline has the most complex structure and suffers from severe stress concentration, which makes the flexspline extremely prone to fatigue failure. At present, the commonly used cylinder structure of the cup-shaped flexspline is a straight cylinder. Although a circular arc transition is used in the cylinder and the bottom of the cylinder, stress concentration still exists. Summary of the Invention

[0004] Therefore, the technical problem to be solved by the present application is to provide a flexible pulley and harmonic reducer, which can effectively improve the stress concentration phenomenon at the bottom of the flexible pulley, improve fatigue resistance, and improve the load-bearing capacity of the flexible pulley.

[0005] In order to solve the above problems, the present application provides a flexible wheel, which has a bowl-shaped structure. The flexible wheel includes a straight cylinder section, a contraction section and a bottom flange. The contraction section includes a third arc section, a first arc section and a second arc section arranged in sequence along the axial direction of the straight cylinder section. The second arc section and the third arc section are both outward convex arcs. The third arc section is connected to the straight cylinder section, and the bottom flange is arranged at the end of the second arc section.

[0006] Preferably, the first arc segment is an inwardly concave arc or an outwardly convex arc.

[0007] Preferably, flexible teeth are provided on the outer circumference of the straight section, and the wall thickness of the straight section is S=25×(3+0.01×Z)×d1×10^-4, where Z is the number of flexible teeth and d1 is the pitch circle diameter of the flexible teeth.

[0008] Preferably, the wall thickness of the contraction section is S1, and the wall thickness of the straight section is S, where S1 = (0.65-0.95) × S.

[0009] Preferably, the radius of the first arc segment is greater than the radii of the second arc segment and the third arc segment, and the radii of the second arc segment and the third arc segment are equal.

[0010] Preferably, the radius of the first arc segment R1 = (0.2-0.4) × d, the radius of the second arc segment R2 = (0.1-0.15) × d, and the radius of the third arc segment R3 = (0.1-0.15) × d, where d is the inner hole diameter of the straight cylinder segment.

[0011] Preferably, the radius of the first arc segment is R1, the radius of the second arc segment is R2, and R1 = (2-2.8) × R2.

[0012] Preferably, in the cross section passing through the central axis of the flexible wheel, the distance between the center of the third arc segment and the end face of the straight tube segment away from the contraction section is L3, and the distance between the center of the third arc segment and the end face of the bottom flange facing the straight tube segment is L4, where L3 = (1.0-1.25) × L4.

[0013] Preferably, in a cross section passing through the central axis of the flexible wheel, a line connecting an inner side wall endpoint where the third arc segment is connected to the straight cylinder segment and an inner side wall endpoint where the second arc segment is connected to the bottom flange is a first line, and an angle between the first line and the end face of the bottom flange is in a range of 45° to 65°.

[0014] Preferably, the third arc segment and the straight cylinder segment are transitionally connected through a first transition portion, and the second arc segment and the bottom flange are transitionally connected through a second transition portion. The thickness of the first transition portion decreases along the direction approaching the third arc segment, and the thickness of the second transition portion increases along the direction away from the second arc segment.

[0015] Preferably, flexible teeth are provided on the outer circumference of the straight cylinder section, the first transition portion includes a first transition arc located on the outer circumference, the second transition portion includes a second transition arc located on the outer circumference and / or inner circumference, the third arc segment and the outer circumferential wall of the flexible teeth are transitionally connected through the first transition arc, and the second arc segment and the bottom flange are transitionally connected through the second transition arc.

[0016] Preferably, the radius of the first transition arc is R4, the radius of the second transition arc is R5, and R4>R5.

[0017] Preferably, the radius of the second arc segment is R2, R4 = (1.6-2.0) × R2, and R5 = (0.25-0.5) × R2.

[0018] Preferably, the bottom flange comprises an axial flange, which at least partially protrudes toward the end where the straight cylindrical section is located.

[0019] According to another aspect of the present application, a harmonic reducer is provided, including a flexspline, which is the flexspline described above.

[0020] The flexible wheel provided by the present application has a bowl-shaped structure. The flexible wheel includes a straight cylinder section, a contraction section and a bottom flange. The contraction section includes a third arc section, a first arc section and a second arc section arranged in sequence along the axial direction of the straight cylinder section. The second arc section and the third arc section are both convex arcs. The third arc section is connected to the straight cylinder section. The bottom flange is arranged at the end of the second arc section. The flexible wheel has a bowl-shaped structure. The bowl end is straight cylinder-shaped. The contraction section at the bottom end of the bowl includes a plurality of arc sections connected in sequence, so that the contraction section as a whole presents a contraction-shaped structure. The adjacent arc sections adopt a tangent structure to form a good connection performance, reduce the influence of forced deformation at the flexible wheel cylinder, and utilize the arc connection structure formed by the connection between the arc section and the bottom flange to reduce the stress concentration at the junction of the cylinder and the bottom flange, improve the bearing capacity of the cylinder to resist bending, reduce bending stress, improve the rigidity of the flexible wheel cylinder, reduce the displacement and strain value of the flexible wheel deformation, improve the fatigue strength of the flexible wheel, increase the fatigue life of the flexible wheel, and improve the bearing capacity of the harmonic reducer. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a schematic diagram of the structural dimensions of a flexible pulley according to an embodiment of the present application;

[0022] Figure 2 This is a schematic structural diagram of a flexible pulley according to an embodiment of the present application;

[0023] Figure 3 This is a schematic structural diagram of a flexible pulley according to an embodiment of the present application;

[0024] Figure 4 This is a schematic structural diagram of a flexible pulley according to an embodiment of the present application;

[0025] Figure 5 This is a schematic structural diagram of a flexible pulley according to an embodiment of the present application;

[0026] Figure 6 This is a side structural diagram of a flexible pulley according to an embodiment of the present application;

[0027] Figure 7 This is a side structural diagram of a flexible pulley according to an embodiment of the present application;

[0028] Figure 8 This is a stress distribution diagram of a flexible spline according to an embodiment of the present application;

[0029] Figure 9 The stress distribution diagram of the flexible wheel in the related art;

[0030] Figure 10 This is a displacement simulation diagram of a flexible pulley according to an embodiment of the present application;

[0031] Figure 11 A displacement simulation diagram of a flexible pulley in related art;

[0032] Figure 12 This is a strain simulation diagram of a flexspline according to an embodiment of the present application;

[0033] Figure 13 This is a strain simulation diagram of a flexible pulley in related technology.

[0034] The reference numerals indicate:

[0035] 1. Straight section; 2. Contraction section; 3. Bottom flange; 4. First arc section; 5. Second arc section; 6. Third arc section; 7. Flexible teeth; 8. First transition section; 9. Second transition section; 10. Axial flange. DETAILED DESCRIPTION

[0036] See also Figures 1 to 7 As shown, according to an embodiment of the present application, the flexible wheel has a bowl-shaped structure, and the flexible wheel includes a straight cylinder section 1, a contraction section 2 and a bottom flange 3. The contraction section 2 includes a third arc section 6, a first arc section 4 and a second arc section 5 arranged in sequence along the axial direction of the straight cylinder section 1. The second arc section 5 and the third arc section 6 are both outward convex arcs. The third arc section 6 is connected to the straight cylinder section 1, and the bottom flange 3 is arranged at the end of the second arc section 5.

[0037] The flexible wheel has a bowl-shaped structure, and the bowl end is in the shape of a straight cylinder. The contraction section 2 located at the bottom end of the bowl includes a plurality of arc segments connected in sequence, so that the contraction section 2 presents a contraction-shaped structure as a whole, and the adjacent arc segments adopt a tangent structure to form a good connection performance, reduce the influence of forced deformation at the flexible wheel cylinder, and utilize the arc connection structure formed by connecting the arc segment and the bottom flange 3 to reduce the stress concentration at the intersection of the cylinder and the bottom flange 3, improve the bearing capacity of the cylinder to resist bending, reduce bending stress, improve the rigidity of the flexible wheel cylinder, reduce the displacement and strain value of the flexible wheel deformation, improve the fatigue strength of the flexible wheel, increase the fatigue life of the flexible wheel, and improve the bearing capacity of the harmonic reducer.

[0038] The above-mentioned barrel portion includes a straight barrel section 1 and a contraction section 2, and a bottom flange 3 is arranged at the bottom of the barrel portion.

[0039] The simulation data of the flexible pulley with the bowl-shaped structure of the present application and the flexible pulley in the related art are shown in the following table:

[0040] SOLIDWORKS simulation analysis data for the same wall thickness and the same working conditions

[0041] structure Stress value MPa) Displacement value mm Strain value mm Bowl-shaped flexible pulley 1.632e+02 4.238e-02 6.828e-04 Traditional structure flexible pulley 2.128e+02 2.376e-01 7.666e-04 Optimization percentage 23.3％ 82.2％ 10.9％

[0042] From the comparison of the above data, it can be seen that the bowl-shaped flexspline of the embodiment of the present application has a stress value of 163.2 MPa, which is 23.3% lower than the traditional structure value of 212.8 MPa; the displacement value and deformation value are 0.04238 mm, which is 82.3% lower than the traditional structure value of 0.2376 mm; the strain value is 0.0006828 mm, which is 10.9% lower than the traditional structure value of 0.0007666 mm; the overall deformation and stress of the flexspline cylinder are significantly improved, and the load-bearing capacity is significantly improved.

[0043] In this embodiment, the contraction section 2, the straight cylinder section 1 and the bottom flange 3 are all connected by a smooth curved surface transition at the connection position. The multiple arc segments of the contraction section 2 itself are tangent to each other at the connection position to form a smooth transition curved surface, making the side wall structure of the cylinder smoother and less stressful.

[0044] In one embodiment, the first arc segment 4 is an inwardly concave arc or an outwardly convex arc.

[0045] In one embodiment, the outer circumference of the straight-tube section 1 is provided with flexible teeth 7, and the wall thickness S of the straight-tube section 1 is 25×(3+0.01×Z)×d1×10^-4, where Z is the number of flexible teeth 7 and d1 is the pitch circle diameter of the flexible teeth 7. This allows the wall thickness of the straight-tube section 1 to be adjusted, resulting in improved structural strength and reduced stress.

[0046] In one embodiment, the wall thickness of the contraction section 2 is S1, where S1 = (0.65-0.95) × S.

[0047] In one embodiment, the radius of the first arc segment 4 is greater than the radii of the second arc segment 5 and the third arc segment 6, and the radii of the second arc segment 5 and the third arc segment 6 are equal, so that the contraction section 2 can be more symmetrical and uniform in structure, and the formed bowl bottom structure has moderate strength, which is more suitable for the structural deformation of the flexible wheel.

[0048] In one embodiment, the radius R1 of the first arc segment 4 is (0.2-0.4) × d, the radius R2 of the second arc segment 5 is (0.1-0.15) × d, and the radius R3 of the third arc segment 6 is (0.1-0.15) × d, where d is the inner hole diameter of the straight cylinder segment 1. This can reasonably limit the value range of the bowl bottom structure, reduce the fluctuation range of the value, improve the uniformity of the bowl bottom structure, improve the deformation ability of the flexible wheel, and reduce the deformation stress.

[0049] In one embodiment, the radius of the first arc segment 4 is R1, the radius of the second arc segment 5 is R2, and R1 = (2-2.8) × R2.

[0050] In one embodiment, in a cross section passing through the central axis of the flexible wheel, the distance between the center of the third arc segment 6 and the end surface of the straight cylindrical section 1 away from the contraction section 2 is L3, and the distance between the center of the third arc segment 6 and the end surface of the bottom flange 3 facing the straight cylindrical section 1 is L4, where L3 = (1.0-1.25) × L4.

[0051] In one embodiment, within a cross section passing through the central axis of the flexspline, the line connecting the inner sidewall endpoint where the third arc segment 6 connects to the straight cylindrical segment 1 and the inner sidewall endpoint where the second arc segment 5 connects to the bottom flange 3 is a first line, and the angle between the first line and the end face of the bottom flange 3 ranges from 45° to 65°. Preferably, the angle between the first line and the end face of the bottom flange 3 is 55°. If this angle is too large, the flexible tooth portion may be shortened, resulting in insufficient flexible tooth performance. If this angle is too small, the bowl portion may be shortened, resulting in poor deformation capability, and failing to meet the deformation capability requirements during flexspline operation.

[0052] In one embodiment, the third arc segment 6 is transitionally connected to the straight-tube segment 1 via a first transition portion 8, and the second arc segment 5 is transitionally connected to the bottom flange 3 via a second transition portion 9. The thickness of the first transition portion 8 decreases along the direction approaching the third arc segment 6, and the wall thickness is the same as that of the third arc segment 6 at the connection position with the third arc segment 6. The thickness of the second transition portion 9 increases along the direction away from the second arc segment 5, and the wall thickness is the same as that of the bottom flange 3 at the connection position with the bottom flange 3. Since the thickness of the contraction section 2 is different from that of the straight-tube segment 1, and the thickness of the contraction section 2 is also different from that of the bottom flange 3, if the contraction section 2 is directly connected to the straight-tube segment 1 or the contraction section 2 is directly connected to the bottom flange 3, stress concentration is likely to occur at the connection position due to the thickness difference. When a transition section with varying thickness is used to achieve a smooth transition connection at the connection position, this problem can be effectively solved and stress concentration can be avoided.

[0053] In one embodiment, the bottom flange 3 includes an axial flange 10, which at least partially protrudes toward the end where the straight cylindrical section 1 is located. In this structure, at least a portion of the axial flange 10 is located inside the cylindrical portion. While the axial length of the bottom flange 3 remains unchanged, the overall axial length of the flexspline can be reduced, thereby reducing the overall axial length of the harmonic reducer.

[0054] In one embodiment, the axial flange 10 entirely protrudes toward the end where the straight tube section 1 is located.

[0055] In one embodiment, a portion of the axial flange 10 protrudes toward the end where the straight tube section 1 is located, and another portion protrudes toward an end away from the straight tube section 1, so that a portion of the axial flange 10 is located inside the tube portion, and another portion is located outside the tube portion.

[0056] In one embodiment, flexible teeth 7 are provided on the outer periphery of the straight cylinder section 1, the first transition portion 8 includes a first transition arc located on the outer periphery, the second transition portion 9 includes a second transition arc located on the outer periphery and / or the inner periphery, the third arc segment 6 and the outer peripheral wall of the flexible teeth 7 are transitionally connected through the first transition arc, and the second arc segment 5 and the bottom flange 3 are transitionally connected through the second transition arc.

[0057] In this embodiment, since the inner circumferential walls of the straight-tube section 1 and the contraction section 2 are coplanar structures, there is no need to consider the connection problem here. The outer wall of the straight-tube section 1 and the outer wall of the contraction section 2 are not located at the same height. Therefore, it is only necessary to achieve a smooth transition connection between the outer wall of the straight-tube section 1 and the outer wall of the contraction section 2 to solve the stress concentration problem at the connection position between the straight-tube section 1 and the contraction section 2.

[0058] As for the connection position between the contraction section 2 and the bottom flange 3, the location of the axial flange 10 of the bottom flange 3 determines the transitional connection relationship between the contraction section 2 and the axial flange 10 of the bottom flange 3. For example, when the axial flange 10 completely protrudes toward the inside of the cylinder, the second transition arc is located on the inner circumference of the second transition portion 9; when the axial flange 10 completely protrudes toward the outside of the cylinder, the second transition arc is located on the outer circumference of the second transition portion 9; when the axial flange 10 protrudes toward both the outside and inside of the cylinder, the second transition arc is located on both the inner and outer circumferences of the second transition portion 9.

[0059] In one embodiment, the first arc segment 4 is concave, and the center of the first arc segment 4 is located on the extension line of the tangent of the end point of the second arc segment 5 .

[0060] In one embodiment, the radius of the first transition arc is R4, and the radius of the second transition arc is R5, where R4>R5. Because the stress at the junction between the tooth end and the flexspline cylinder is greater than the stress at the junction between the contraction section 2 and the bottom flange 3, making the radius of the first transition arc larger than the radius of the second transition arc can better adapt the arc radius and improve structural stress.

[0061] In one embodiment, the radius of the second arc segment 5 is R2, R4 = (1.6-2.0) × R2, and R5 = (0.25-0.5) × R2. In this embodiment, R4 is the transition arc segment between the end of the tooth portion and the flexspline cylinder, which can effectively improve the stress of the structure at this location, avoid stress concentration caused by sharp corners, and improve fatigue resistance. R5 is the transition arc segment between the cylinder portion and the bottom of the flange, which can effectively improve the stress of the structure at this location, avoid stress concentration caused by sharp corners, and improve fatigue resistance.

[0062] In one embodiment, a through hole is provided in the middle of the bottom flange 3 , the through hole is connected to the output component, and connecting holes are provided around the through hole, and the connecting holes are evenly distributed around the through hole.

[0063] In one embodiment, the central through hole of the bottom flange 3 is a regular polygonal structure or a spline structure, which can facilitate the rotational drive connection with the output member.

[0064] In one embodiment, in a cross section passing through the central axis of the flexible wheel, with the intersection of the bowl end surface and the central axis as the center, the first arc segment 4 is concave, and the center coordinates of the first arc segment 4 are (L-L2+S1, 1.25×d1 / 2).

[0065] In one embodiment, the effective length of the bowl-shaped flexible tooth is L1 = (0.3-0.4) × L, and the axial length of the bottom flange 3 is L2 = (0.06-0.1) × L, where L is the total axial length of the bowl-shaped flexible wheel.

[0066] See also Figures 8 to 13 As shown, there are stress comparison diagrams, displacement comparison diagrams, and strain comparison diagrams of the flexible pulley in the embodiment of the present application and the flexible pulley in the related art. It can be seen from the diagram that, compared with the flexible pulley in the related art, the flexible pulley in the embodiment of the present application can effectively reduce the bending stress of the flexible pulley, reduce the displacement and strain values ​​of the flexible pulley deformation, improve the fatigue strength of the flexible pulley, increase the fatigue life of the flexible pulley, and improve the load-bearing capacity of the harmonic reducer.

[0067] According to an embodiment of the present application, the harmonic reducer includes a flexspline, which is the flexspline described above.

[0068] It is easy for those skilled in the art to understand that, under the premise of no conflict, the above-mentioned advantageous methods can be freely combined and superimposed.

[0069] The above are merely preferred embodiments of the present application and are not intended to limit the present application. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present application shall be included within the scope of protection of the present application. The above are merely preferred embodiments of the present application. It should be noted that those skilled in the art may make various improvements and variations without departing from the technical principles of the present application, and such improvements and variations shall also be considered within the scope of protection of the present application.

Claims

1. A flexible pulley, characterized in that: The flexible wheel has a bowl-shaped structure, and includes a straight cylinder section (1), a contraction section (2) and a bottom flange (3). The contraction section (2) includes a third arc section (6), a first arc section (4) and a second arc section (5) arranged in sequence along the axial direction of the straight cylinder section (1). The second arc section (5) and the third arc section (6) are both outward convex arcs. The third arc section (6) is connected to the straight cylinder section (1). The bottom flange (3) is arranged at the end of the second arc section (5); the third arc section (6) is transitionally connected to the straight cylinder section (1) through a first transition section (8), and the second arc section (5) is transitionally connected to the bottom flange (3) through a second transition section (9). The thickness of the first transition section (8) decreases along the direction approaching the third arc section (6), and the thickness of the second transition section (9) increases along the direction away from the second arc section (5); The outer circumference of the straight tube section (1) is provided with flexible teeth (7), the first transition portion (8) includes a first transition arc located on the outer circumference, the second transition portion (9) includes a second transition arc located on the outer circumference and / or inner circumference, the third arc section (6) and the outer circumferential wall of the flexible teeth (7) are transitionally connected via the first transition arc, and the second arc section (5) and the bottom flange (3) are transitionally connected via the second transition arc; the inner circumferential wall of the straight tube section (1) and the contraction section (2) are coplanar structures; The first arc segment (4) is concave, and the center of the first arc segment (4) is located on the extension line of the tangent of the end point of the second arc segment (5); A through hole is provided in the middle of the bottom flange (3), the through hole is connected to the output component, and connecting holes are provided around the through hole, and the connecting holes are evenly distributed around the through hole.

2. The flexible spline according to claim 1, characterized in that: The first arc segment (4) is an inwardly concave arc or an outwardly convex arc.

3. The flexible spline according to claim 1, wherein: Flexible teeth (7) are provided on the outer periphery of the straight tube section (1), and the wall thickness of the straight tube section (1) is S=25×(3+0.01×Z)×d1×10^-4, wherein Z is the number of teeth of the flexible teeth (7), and d1 is the pitch circle diameter of the flexible teeth (7).

4. The flexible spline according to claim 1, characterized in that: The wall thickness of the contraction section (2) is S1, and the wall thickness of the straight section (1) is S, where S1 = (0.65-0.95) × S.

5. The flexible spline according to claim 1, characterized in that: The radius of the first circular arc segment (4) is greater than the radii of the second circular arc segment (5) and the third circular arc segment (6), and the radii of the second circular arc segment (5) and the third circular arc segment (6) are equal.

6. The flexible spline according to claim 5, characterized in that: The radius R1 of the first circular arc segment (4) is (0.2-0.4)×d, the radius R2 of the second circular arc segment (5) is (0.1-0.15)×d, and the radius R3 of the third circular arc segment (6) is (0.1-0.15)×d, wherein d is the inner hole diameter of the straight cylinder segment (1).

7. The flexible spline according to claim 1, characterized in that: The radius of the first arc segment (4) is R1, and the radius of the second arc segment (5) is R2, where R1 = (2 to 2.8) × R2.

8. The flexible spline according to claim 1, characterized in that: In a cross section passing through the central axis of the flexible wheel, the distance between the center of the third arc segment (6) and the end face of the straight tube segment (1) away from the contraction section (2) is L3, and the distance between the center of the third arc segment (6) and the end face of the bottom flange (3) facing the straight tube segment (1) is L4, where L3 = (1.0-1.25) × L4.

9. The flexible spline according to claim 1, characterized in that: In a cross section passing through the central axis of the flexible wheel, a line connecting an inner side wall endpoint where the third arc segment (6) is connected to the straight cylinder segment (1) and an inner side wall endpoint where the second arc segment (5) is connected to the bottom flange (3) is a first line, and an angle between the first line and the end face of the bottom flange (3) is in the range of 45° to 65°.

10. The flexible spline according to claim 1, wherein: The radius of the first transition arc is R4, the radius of the second transition arc is R5, and R4>R5.

11. The flexible spline according to claim 10, characterized in that: The radius of the second arc segment (5) is R2, R4 = (1.6-2.0) × R2, and R5 = (0.25-0.5) × R2.

12. The flexible spline according to claim 1, wherein: The bottom flange (3) comprises an axial flange (10), and the axial flange (10) at least partially protrudes toward the end where the straight cylinder section (1) is located.

13. A harmonic reducer, comprising a flexible pulley, characterized in that: The flexible spline is the flexible spline according to any one of claims 1 to 12.

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