Flexible external gear, strain wave reducer, and robot

Abstract

To more smoothly engage a flexible external gear and an internal gear of a wave motion reduction gear.SOLUTION: A flexible external gear includes a cylindrical body part and a diaphragm part. The body part extends to a direction including a component in the central axis direction. The diaphragm part extends from one end part in the axial direction of the body part to a direction including a component in the radial direction. The body part includes a first body part and a second body part. The first body part is disposed on one side in the axial direction in the body part and has flexibility. The second body part is disposed on the other side in the axial direction of the first body part. The second body part includes a plurality of external teeth. Each of the plurality of external teeth projects outwardly in the radial direction and is arranged in the peripheral direction. A maximum value of the thickness of the diaphragm part is equal to or less than twice the length from a radial outer end of the outer tooth to a radial inner side surface of the second body part. A minimum value of the thickness of the first body part is equal to or less than a half of the maximum value of the thickness of the diaphragm part. Due to this structure, while rigidity of the diaphragm part and the second body part is secured, successful bending in the radial direction of the first body part is enabled.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a flexible external gear, a strain wave reducer, and a robot. [Background technology]

[0002] BACKGROUND ART A wave gear device including a flexible external gear and an internal gear has been known in the past. This type of wave gear device is mainly used as a reducer (Patent Document 1). [Patent Document 1] Japanese Patent Application Publication No. 02-283941 Summary of the Invention [Problem to be solved by the invention]

[0003] The distortion wave gear device of Patent Document 1 includes a cup-shaped distortion gear (10) with external teeth (20), a ring gear (14) with internal teeth (22), and a wave generator (12) that generates relative rotation between the distortion gear (10) and the ring gear (14). The distortion gear (10) is formed from a distortion gear blank with a uniform thickness of 0.015D to 0.03D (D: inner diameter of the distortion gear). The distortion gear (10) also has a cylindrical portion with the external teeth (20) formed around its open end, and an end portion consisting of a diaphragm (35) with a thickness half the thickness of the cylindrical portion.

[0004] Furthermore, the open end of the distortion gear 10 comes into contact with the wave generator 12 and deforms into an ellipse. As a result, the external teeth 20 of the distortion gear 10 engage with the internal teeth 22 of the ring gear 14 along each side of the major axis of the ellipse. Here, the number of external teeth 20 of the distortion gear 10 is different from the number of internal teeth 22 of the ring gear 14. As a result, the distortion gear 10 and the ring gear 14 move relative to each other as the wave generator 12 rotates. However, as mentioned above, the cylindrical portion of the distortion gear 10 is thicker than the diaphragm 35, and is therefore less likely to bend.

[0005] An object of the present invention is to provide a technology that allows a flexible external gear to bend better, thereby enabling the external teeth and the internal teeth of an internal gear to mesh more smoothly. [Means for solving the problem]

[0006] The present invention is a flexible externally toothed gear having a cylindrical body portion extending in a direction including a component in the direction of a central axis, and a diaphragm portion extending from one axial end of the body portion in a direction including a component in the radial direction, the body portion having a first body portion arranged on one axial side and having flexibility, and a second body portion arranged on the other axial side of the first body portion, the second body portion having a plurality of external teeth protruding radially outward and arranged circumferentially, the maximum thickness of the diaphragm portion being no more than twice the length from the radial outer ends of the external teeth to the radial inner surface of the second body portion, and the minimum thickness of the first body portion being no more than half the maximum thickness of the diaphragm portion. [Effects of the Invention]

[0007] According to the present invention, the entire body portion including the first body portion can be bent satisfactorily. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 1 is a schematic diagram of the robot. [Figure 2] FIG. 2 is a vertical cross-sectional view of the wave reducer. [Figure 3] FIG. 3 is a cross-sectional view of the wave reducer. [Figure 4] FIG. 4 is a partial vertical cross-sectional view of a flexible external gear. [Figure 5] FIG. 5 is a partial vertical cross-sectional view of a flexible external gear according to a modified example. [Figure 6] FIG. 6 is an enlarged view of a part of FIG. DETAILED DESCRIPTION OF THE INVENTION

[0009] Hereinafter, exemplary embodiments of the present application will be described with reference to the drawings.

[0010] <1. About the robot> FIG. 1 is a schematic diagram of a robot 100 equipped with a wave reducer 1 according to one embodiment. The robot 100 is a so-called industrial robot that performs tasks such as transporting, processing, and assembling parts on an industrial product manufacturing line, for example. As shown in FIG. 1, the robot 100 has a wave reducer 1. In this embodiment, the robot 100 has a base frame 101, an arm 102, a motor 103, and the wave reducer 1. As a result, in the wave reducer 1 equipped on the robot 100, the entire body 21, including a first body 211 described below, can be deflected well.

[0011] The arm 102 is rotatably supported relative to the base frame 101. The motor 103 and the wave reducer 1 are incorporated into a joint between the base frame 101 and the arm 102. When a drive current is supplied to the motor 103, a rotational motion is output from the motor 103. The rotational motion output from the motor 103 is slowed down by the wave reducer 1 and transmitted to the arm 102. As a result, the arm 102 rotates relative to the base frame 101 at the slower speed.

[0012] <2. Structure of the wave reducer> <2-1. Overall structure of the wave reducer> Next, the overall structure of the wave reducer 1 will be described.

[0013] In the following, the direction parallel to the central axis 9 of the wave reducer 1 will be referred to as the "axial direction," the direction perpendicular to the central axis 9 of the wave reducer 1 will be referred to as the "radial direction," and the direction along the arc centered on the central axis 9 of the wave reducer 1 will be referred to as the "circumferential direction." However, the above "parallel direction" also includes a direction that is approximately parallel. Furthermore, the above "perpendicular direction" also includes a direction that is approximately perpendicular. Furthermore, in this application, in Figures 2, 4, and 5 (described later), the axial direction will be defined as the left-right direction, the left side will be defined as "one axial side," and the right side will be defined as "the other axial side," and the shapes and positional relationships of each part will be described.

[0014] FIG. 2 is a longitudinal sectional view of a wave reducer 1 according to one embodiment. FIG. 3 is a transverse sectional view of the wave reducer 1 as seen from position AA in FIG. 2. To avoid complicating the drawing, hatching indicating cross sections has been omitted from FIG. 3. As described above, the wave reducer 1 is mounted on a joint of the robot 100, and reduces the speed of rotational motion input from the motor 103 before outputting it. More specifically, the wave reducer 1 is a device that uses the differential between the internal gear 10 and the flexible external gear 20, which will be described later, to reduce the rotational motion of a first rotational speed obtained from the motor 103 to a second rotational speed that is lower than the first rotational speed.

[0015] 2 and 3, the wave reducer 1 has an internal gear 10, a flexible external gear 20, and a wave generator 30. The wave reducer 1 of this embodiment also has an outer ring 151, an inner ring 152, and an output section 40.

[0016] The wave reducer 1 is also provided with an input member 104 for receiving power from the motor 103. The input member 104 extends axially in a cylindrical shape around the central axis 9. The output shaft of the motor 103 is inserted radially inward of the input member 104. The input member 104 is also fixed to the output shaft of the motor 103 so that they cannot rotate relative to each other. As a result, the input member 104 rotates at a first rotational speed around the central axis 9 together with the rotating part of the motor 103. The input member 104 may be the same member as the output shaft.

[0017] The internal gear 10 is an annular gear centered on a central axis 9. The internal gear 10 is fixed to a base frame 101 of the robot 100. The internal gear 10 is arranged coaxially with the central axis 9. As will be described later, the flexible external gear 20 has a second body portion 212. The internal gear 10 is arranged radially outward from the second body portion 212. The rigidity of the internal gear 10 is sufficiently higher than the rigidity of a body portion 21 of the flexible external gear 20, which will be described later. Therefore, the internal gear 10 can be considered to be a substantially rigid body. The internal gear 10 has a plurality of internal teeth 11. The plurality of internal teeth 11 protrude radially inward from the radially inner surface of the internal gear 10. The plurality of internal teeth 11 are arranged at a constant pitch circumferentially on the inner surface of the internal gear 10.

[0018] The internal gear 10 is provided with a plurality of through holes 110. In this embodiment, the number of through holes 110 is eight. Each of the eight through holes 110 passes through the internal gear 10 in the axial direction. The eight through holes 110 are arranged at equal intervals in the circumferential direction around the central axis 9. The internal gear 10 is fixed to the base frame 101 of the robot 100 by fastening screws (not shown) that pass through each of the eight through holes 110 to the base frame 101. The internal gear 10 is also provided with a plurality of screw holes 111. Each of the screw holes 111 is recessed from one axial end face of the internal gear 10 toward the other axial end. The screw holes 111 may be through holes.

[0019] The flexible external gear 20 is a bottomed annular gear that is flexible and deformable. As will be described later, the flexible external gear 20 is fixed to the arm 102 of the robot 100 via the output section 40 and an inner ring 152. The flexible external gear 20 is supported so as to be rotatable about a central axis 9. FIG. 4 is a partial vertical cross-sectional view enlarging a portion of the flexible external gear 20. As shown in FIGS. 2 to 4, the flexible external gear 20 has a cylindrical body section 21 and a diaphragm section 22.

[0020] The body portion 21 extends in a direction that includes a component in the direction of the central axis 9. In this embodiment, the body portion 21 extends in a cylindrical shape in the axial direction centered on the central axis 9. The body portion 21 is also flexible and can bend radially. In particular, the end portion on the other axial side of the body portion 21 (hereinafter referred to as the "other axial end portion") is a free end, and therefore can be displaced radially more than other portions. The other axial end portion of the body portion 21 is located radially outside the wave generator 30 and radially inside the internal gear 10.

[0021] The body portion 21 has a first body portion 211 and a second body portion 212. The first body portion 211 is disposed on one axial side of the body portion 21 and is flexible. The first body portion 211 is a cylindrical portion that is flexible in the radial direction.

[0022] The second body portion 212 is disposed on the other axial side of the first body portion 211. The second body portion 212 is located radially inward of the internal gear 10. The second body portion 212 has a plurality of external teeth 23. The plurality of external teeth 23 are arranged in the circumferential direction. Each of the plurality of external teeth 23 protrudes radially outward. The plurality of external teeth 23 are arranged at a constant pitch along the circumferential direction. As will be described in detail below, the outer ring 323 of the flexible bearing 32 comes into contact with the inner circumferential surface of the second body portion 212. This causes some of the plurality of external teeth 23 to mesh with some of the plurality of internal teeth 11. In other words, when the body portion 21 is pushed from the radially inner side by the wave generator 30, some of the plurality of external teeth 23 and some of the plurality of internal teeth 11 of the internal gear 10 mesh with each other. The number of internal teeth 11 that the internal gear 10 has and the number of external teeth 23 that the flexible external gear 20 has are slightly different.

[0023] The diaphragm portion 22 is a portion that extends from one axial end of the body portion 21 (hereinafter referred to as "one axial end") in a direction that includes a radial component. In other words, the diaphragm portion 22 extends in a direction that includes a radial component from one axial end of the body portion 21. In this embodiment, the diaphragm portion 22 expands radially inward from one axial end of the body portion 21. The diaphragm portion 22 also expands in an annular shape around the central axis 9. The diaphragm portion 22 is a flat portion that is less flexible than the body portion 21. Because the diaphragm portion 22 has such a structure, the flexible external gear 20 can be made smaller in the radial direction. A plurality of through holes 220 are formed in the diaphragm portion 22. Each of the plurality of through holes 220 penetrates the diaphragm portion 22 in the axial direction. Note that the diaphragm portion 22 may expand radially outward from one axial end of the body portion 21.

[0024] The thickness t(a) of the diaphragm portion 22 is approximately constant from the radially inner end to the radially outer end of the diaphragm portion 22. In this embodiment, the thickness t(a) of the diaphragm portion 22 is the width in the axial direction. This makes it easier to manufacture the diaphragm portion 22 when manufacturing the flexible external gear 20 compared to when the thickness t(a) of the diaphragm portion 22 is not constant.

[0025] However, the thickness t(a) of the diaphragm portion 22 does not have to be constant from the radially inner end to the radially outer end of the diaphragm portion 22. For example, as shown in a modified example in FIG. 5 , a thick portion 25 having a larger axial thickness than the diaphragm portion 22 may be formed radially inside the diaphragm portion 22. Furthermore, the axial thickness of the diaphragm portion 22 may gradually increase toward the thick portion 25. The plurality of through holes 220 may be provided in the thick portion 25.

[0026] The body portion 21 further has a connecting portion 24. The connecting portion 24 extends in a direction having both axial and radial components. The connecting portion 24 connects one axial end portion of the first body portion 211 and the radial end portion of the diaphragm portion 22. In this embodiment, the connecting portion 24 connects one axial end portion of the first body portion 211 and the radially outer end portion of the diaphragm portion 22.

[0027] The structure of the flexible external gear 20 will be described in more detail later.

[0028] The wave generator 30 is a mechanism that generates periodic flexible deformation in the body portion 21. The wave generator 30 is disposed radially inside the second body portion 212. The wave generator 30 of this embodiment has a cam 31 and a flexible bearing 32. The cam 31 and the flexible bearing 32 each extend in an annular shape centered on the central axis 9. The cam 31 is fixed to the outer surface of the input member 104 so as not to rotate relative to each other, and is supported rotatably about the central axis 9. The cam 31 of this embodiment has an elliptical cam profile. That is, the radially outer surface of the cam 31 is elliptical when viewed in the axial direction, and has an outer diameter that varies depending on the circumferential position. The flexible bearing 32 is a flexible bearing. The flexible bearing 32 is disposed between the radially outer surface of the cam 31 and the radially inner surface of the body portion 21 of the flexible external gear 20. Therefore, the cam 31 and the body 21 can rotate at different rotational speeds.

[0029] The flexible bearing 32 has an inner ring 321, multiple balls 322, and an elastically deformable outer ring 323. The inner ring 321 contacts the radially outer surface of the cam 31. The multiple balls 322 are interposed between the inner ring 321 and the outer ring 323 and are arranged circumferentially. The outer ring 323 elastically deforms (flexibly deforms) via the inner ring 321 and the balls 322 along the cam profile of the rotating cam 31. The outer ring 323 also contacts the radially inner surface of the body portion 21 of the flexible external gear 20. As a result, the body portion 21 deforms into an elliptical shape that follows the radially outer surface of the cam 31. As a result, the external teeth 23 of the flexible external gear 20 mesh with the internal teeth 11 of the internal gear 10 at two locations corresponding to both ends of the major axis of the ellipse. However, the external teeth 23 do not mesh with the internal teeth 11 at other circumferential positions. In this manner, a ball bearing is used as the flexible bearing 32 in this embodiment. However, other types of bearings such as a roller bearing may be used instead of a ball bearing.

[0030] When the motor 103 is driven, the cam 31 rotates around the central axis 9 together with the rotating portion of the motor 103 and the input member 104 at a first rotational speed. As a result, the major axis of the ellipse of the flexible external gear 20 also rotates at the first rotational speed. As a result, the meshing position between the external teeth 23 and the internal teeth 11 also changes circumferentially at the first rotational speed. Also, as described above, the number of internal teeth 11 of the internal gear 10 is slightly different from the number of external teeth 23 of the flexible external gear 20. Due to this difference in the number of teeth, the meshing combination between the external teeth 23 and the internal teeth 11 changes slightly circumferentially with each rotation of the cam 31. Here, as described above, the internal gear 10 is fixed to the base frame 101 of the robot 100 and does not rotate. As a result, the flexible external gear 20 rotates relative to the internal gear 10 and the base frame 101 around the central axis 9 at a second rotation speed lower than the first rotation speed.

[0031] The outer ring 151 is a member that expands in an annular shape centered on the central axis 9. Both the outer ring 151 and the inner ring 152 have high rigidity. The outer ring 151 is provided with a plurality of through holes 153. Each of the plurality of through holes 153 passes through the outer ring 151 in the axial direction. The outer ring 151 is fixed to the internal gear 10 by fastening a plurality of screws 154 that pass through each of the plurality of through holes 153 into a plurality of screw holes 111 in the internal gear 10 that are adjacent to the other axial side of the outer ring 151.

[0032] An inner ring 152 is disposed radially inside the outer ring 151. The inner ring 152 is a member that expands in an annular shape centered on the central axis 9. The arm 102 of the robot 100 is fixed to the inner ring 152. The inner ring 152 has an outer diameter that is slightly smaller than the inner diameter of the outer ring 151. The inner ring 152 is provided with a plurality of screw holes 155. The plurality of screw holes 155 are each formed from an end face of the inner ring 152 on the other axial side toward one axial side.

[0033] The inner ring 152 is rotatably connected to the outer ring 151 via a bearing 16. In this embodiment, a cross roller bearing is used as the bearing 16. As shown in FIG. 2 , the bearing 16 has multiple cylindrical rollers 161 between the inner peripheral surface of the outer ring 151 and the outer peripheral surface of the inner ring 152. The multiple cylindrical rollers 161 are arranged with their orientations alternating between an annular V-groove provided on the inner peripheral surface of the outer ring 151 and an annular V-groove provided on the outer peripheral surface of the inner ring 152. This allows the outer ring 151 and the inner ring 152 to be connected with high rigidity while allowing rotation of the inner ring 152 relative to the outer ring 151. Such cross roller bearings can achieve sufficient rigidity in the axial and radial directions without being used in pairs like ball bearings. In other words, using cross roller bearings allows the number of bearings provided in the wave reducer 1 to be reduced. This reduces the weight of the bearing 16 and limits the axial dimension of the bearing 16.

[0034] Output portion 40 is a member for extracting power after deceleration. Output portion 40 extends cylindrically along central axis 9. As shown in FIG. 2, an output flange portion 401 that expands radially outward is formed at the other axial end of output portion 40. Furthermore, output flange portion 401 is provided with a plurality of through holes 400. Each of the plurality of through holes 400 passes through output flange portion 401 in the axial direction.

[0035] As shown in FIG. 2, the diaphragm portion 22 of the flexible external gear 20 is disposed on one axial side of the output flange portion 401. A washer 17 is interposed on one axial side of the diaphragm portion 22, and an inner ring 152 is also disposed thereon. The number of washers 17 disposed may be one or more. Furthermore, the washer 17 does not necessarily have to be disposed. This makes it possible to easily adjust the axial positions of the flexible external gear 20 and the output portion 40 relative to the inner ring 152.

[0036] The washer 17 is also provided with a plurality of through holes 170. Each of the plurality of through holes 170 passes through the washer 17 in the axial direction. The flexible external gear 20 and the output section 40 are fixed to the inner ring 152 in the axial direction by fastening a plurality of screws 156, which pass through the plurality of through holes 220 of the flexible external gear 20 and the plurality of through holes 400 of the output section 40, into a plurality of screw holes 155 of the inner ring 152 via the plurality of through holes 170 of the washer 17. This connects the inner ring 152, the flexible external gear 20, and the output section 40 so that they cannot rotate relative to one another.

[0037] As described above, the inner ring 152 is rotatably supported relative to the outer ring 151 and the internal gear 10 via the bearings 16. This allows the flexible external gear 20 fixed to the inner ring 152, the output unit 40, and the arm 102 of the robot 100 to rotate about the central axis 9 relative to the base frame 101 to which the internal gear 10 is fixed. As a result, when the motor 103 is driven, the flexible external gear 20 and the arm 102 rotate about the central axis 9 at a second rotational speed that is lower than the first rotational speed that is the output of the motor 103.

[0038] <2-2. Detailed structure of flexible external gear> Next, a more detailed description will be given of the structure of the flexible external gear 20. In the following description, the thickness of the body portion 21 including the first body portion 211 and the second body portion 212 refers to the thickness in the normal direction to the extension direction of the body portion 21 when the body portion 21 is inclined with respect to the central axis 9, and refers to the thickness in the radial direction when the body portion 21 is parallel to the central axis 9.

[0039] The flexible external gear 20 can be formed, for example, by pressing a plate-shaped material to create a cylindrical intermediate member, and then by drawing or cutting to form the final shape. The external teeth 23 can be formed by rolling a roller against the intermediate member. In this embodiment, the external teeth 23 are formed with teeth that extend along the axial direction, like a spur gear. The length t(d) from the radially outer end to the radially inner end of the external teeth 23 may vary depending on the axial and circumferential positions. The length t(c) from the radially outer end of the external teeth 23 to the radially inner surface of the second body portion 212 may also vary depending on the axial and circumferential positions.

[0040] In addition, stainless steel is used as the material for the flexible external gear 20 of this embodiment. However, the material for the flexible external gear 20 may also be steel with a relatively low carbon content, aluminum, or the like.

[0041] Fig. 6 is an enlarged view of a portion of Fig. 3. As shown in Fig. 6, hereinafter, two external teeth 23 adjacent in the circumferential direction of the flexible external gear 20 will be referred to as "external tooth 23k" and "external tooth 23(k+1)," respectively. The circumferential center of the "external tooth 23k" will be referred to as "circumferential center 23o," and the circumferential center of the "external tooth 23(k+1)" will be referred to as "circumferential center 23(o+1)." In this embodiment, the circumferential distance between the circumferential center 23o and the circumferential center 23(o+1), i.e., the circumferential interval cp, is greater than twice the value of the radially thinnest portion of the thickness t(b) of the first trunk portion 211 shown in Figs. 4 and 5. That is, for the external teeth 23k, 23(k+1) that are circumferentially adjacent, the circumferential spacing cp between the circumferential centers 23o, 23(o+1) of each external tooth 23k, 23(k+1) is greater than twice the minimum value min{t(b)} of the thickness t(b) of the first trunk portion 211. In this way, in this embodiment, the circumferential pitch between adjacent external teeth 23k, 23(k+1) is longer, which makes it easier to mold the external teeth 23.

[0042] Furthermore, in this embodiment, the circumferential distance between the circumferential center 23o and the circumferential center 23(o+1), i.e., the circumferential interval cp, is greater than the value of the axially thinnest portion of the thickness t(a) of the diaphragm portion 22 shown in Figures 4 and 5. That is, for circumferentially adjacent external teeth 23k, 23(k+1), the circumferential interval cp between the circumferential centers 23o, 23(o+1) of each external tooth 23k, 23(k+1) is greater than the minimum value min{t(a)} of the thickness t(a) of the diaphragm portion 22. Thus, in this embodiment, the circumferential pitch between adjacent external teeth 23k, 23(k+1) is longer, which makes it easier to mold the external teeth 23.

[0043] Furthermore, in this embodiment, the maximum value max{t(d)} of the length t(d) from the radial outer end to the radial inner end of the external teeth 23 is greater than the minimum value min{t(b)} of the thickness t(b) of the first trunk portion 211. In this way, by making the maximum value max{t(d)} of the length t(d) from the radial outer end to the radial inner end of the external teeth 23 greater than the minimum value min{t(b)} of the thickness t(b) of the first trunk portion 211, in other words, by providing the external teeth 23 with a certain degree of radial length, the external teeth 23 and the internal teeth 11 of the internal gear 10 mesh well. This allows the wave reducer 1 to transmit torque with greater precision.

[0044] In addition, in this embodiment, the maximum value max{ct} of the tooth thickness ct of the external teeth 23 at the radial midpoint cm between the radial outer end and the radial inner end of the external teeth 23 is smaller than the minimum value min{t(b)} of the thickness t(b) of the first trunk portion 211. In this way, by reducing the tooth thickness ct of the external teeth 23, the degree of freedom in molding the external teeth 23 can be improved. Furthermore, the meshing between the external teeth 23 and the internal teeth 11 of the internal gear 10 is further improved. Note that the tooth thickness ct may vary depending on the axial direction. It is sufficient that the maximum value max{ct} of the tooth thickness ct in the region where the tooth thickness ct is maximum in the axial direction is smaller than the minimum value min{t(b)} of the thickness t(b) of the first trunk portion 211.

[0045] Furthermore, in this embodiment, the maximum value max{t(c)} of the length t(c) from the radial outer end of the external teeth 23 to the radial inner surface of the second trunk portion 212 is greater than the minimum value min{t(b)} of the thickness t(b) of the first trunk portion 211, and is smaller than twice the minimum value min{t(b)} of the thickness t(b) of the first trunk portion 211. In this way, by making the maximum value max{t(c)} of the length t(c) from the radial outer end of the external teeth 23 to the radial inner surface of the second trunk portion 212 greater than the minimum value min{t(b)} of the thickness t(b) of the first trunk portion 211, it is possible to ensure a certain degree of radial length of the external teeth 23 for good meshing with the internal teeth 11 of the internal gear 10, while by making the maximum value max{t(c)} smaller than twice the minimum value min{t(b)} of the thickness t(b) of the first trunk portion 211, it is possible to prevent the external teeth 23 from becoming excessively long in the radial direction. As a result, it is possible to improve the rigidity of the external teeth 23. Note that the length t(c) from the radial outer end of the external teeth 23 to the radial inner surface of the second body portion 212 and the thickness t(b) of the first body portion 211 may each have a different value depending on the axial position. In this case, it is sufficient to compare the values in the regions where the length t(c) from the radial outer end of the external teeth 23 to the radial inner surface of the second body portion 212 and the thickness t(b) of the first body portion 211 are maximum or minimum.

[0046] 4, in this embodiment, the thickness t(a) of the diaphragm portion 22 is approximately the same as the length t(c) from the radial outer ends of the external teeth 23 to the radial inner surface of the second trunk portion 212. This makes it easier to manufacture the flexible externally toothed gear 20 compared to when the thickness t(a) of the diaphragm portion 22 and the length t(c) from the radial outer ends of the external teeth 23 to the radial inner surface of the second trunk portion 212 are different.

[0047] In the present embodiment, the thickness t(a) of the diaphragm portion 22 at its thickest point in the axial direction is equal to or less than twice the length t(c) from the radially outer end of the external teeth 23 to the radially inner surface of the second body portion 212. That is, the maximum value max{t(a)} of the thickness t(a) of the diaphragm portion 22 is equal to or less than twice the length t(c) from the radially outer end of the external teeth 23 to the radially inner surface of the second body portion 212. In addition, in the cylindrical body portion 21 of the flexible external gear 20, the thickness t(b) of the first body portion 211 located on the diaphragm portion 22 side is equal to or less than half the thickness t(a) of the diaphragm portion 22 at its thickest point in the axial direction. That is, the minimum value min{t(b)} of the thickness t(b) of the first body portion 211 is equal to or less than half the maximum value max{t(a)} of the thickness t(a) of the diaphragm portion 22. In this way, by suppressing the thickness t(b) of the first body portion 211, the first body portion 211 can be deflected favorably in the radial direction while ensuring the rigidity of the diaphragm portion 22 and the second body portion 212. As a result, the entire body portion 21, including the first body portion 211, can be deflected favorably. Furthermore, by having the flexible external gear 20 in the wave reducer 1, a wave reducer 1 can be realized in which the first body portion 211 can be deflected favorably.

[0048] Moreover, in this embodiment, the minimum value min{t(b)} of the thickness t(b) of the first body portion 211 is less than half the maximum value max{t(a)} of the thickness t(a) of the diaphragm portion 22. This allows the first body portion 211 to bend more satisfactorily in the radial direction while ensuring the rigidity of the diaphragm portion 22 and the second body portion 212. Furthermore, in this embodiment, the minimum value min{t(b)} of the thickness t(b) of the first body portion 211 is equal to or less than half the minimum value min{t(a)} of the thickness t(a) of the diaphragm portion 22. As a result, the first body portion 211 can bend more satisfactorily in the radial direction while ensuring the rigidity of the diaphragm portion 22 and the second body portion 212.

[0049] As described above, the flexible external gear 20 of this embodiment further includes a connecting portion 24 between the first body portion 211 and the diaphragm portion 22. The connecting portion 24 connects one axial end of the first body portion 211 and the radially outer end of the diaphragm portion 22, and extends in a direction having both axial and radial components. This allows the first body portion 211 and the diaphragm portion 22 to be firmly connected together while maintaining both the flexibility of the first body portion 211 and the rigidity of the diaphragm portion 22.

[0050] Furthermore, in a cross section taken along the central axis 9, the connection portion 24 has an arcuate shape that curves in a direction having both axial and radial components. As shown in FIGS. 2, 4, and 5, in this embodiment, the connection portion 24 curves in an arcuate shape in a direction having both axial and radial components in a longitudinal cross section taken along the central axis 9. The maximum value of the radius of curvature of the connection portion 24 is 10 times or less the thickness t(b) of the first body portion 211. By providing the connection portion 24 that curves with a high curvature in this manner, stress concentration at the connection portion 24 can be alleviated while ensuring the flexibility of the body portion 21. In other words, by having the above-described configuration of the connection portion 24, stress concentration at the connection portion 24 can be alleviated compared to, for example, when the first body portion 211 and the diaphragm portion 22 are connected at a right angle.

[0051] <3. Modifications> Although exemplary embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments. The configurations of the respective members and parts may be appropriately combined or substituted within the scope of the gist of the present invention.

[0052] Furthermore, the detailed shapes of the flexible external gear, the strain wave reducer, and the robot may differ from the shapes shown in the drawings of the above-described embodiment. [Industrial Applicability]

[0053] The present application can be used for a flexible external gear, a strain wave reducer, and a robot. [Explanation of symbols]

[0054] 1 Wave reducer 9 Center axis 10 Internal gear 11 Inner teeth 20 Flexible external gear 21 Torso 22 Diaphragm part 23,23k,23(k+1) external teeth 23o,23(o+1) Circumferential center 24 Connection 30 Wave Generator 31 Cam 32 Flexible bearing 40 Output section 100 robots 101 base frame 102 Arm 103 Motor 211 First body 212 Second body

Claims

1. a cylindrical body portion extending in a direction including a component in the direction of the central axis; a diaphragm portion extending in a direction including a radial component from one axial end portion of the body portion; and The body portion is a first body portion disposed on one axial side and having flexibility; a second body portion disposed on the other axial side of the first body portion; and the second body portion has a plurality of external teeth that protrude radially outward and are arranged in a circumferential direction, a maximum value of the thickness of the diaphragm portion is equal to or less than twice the length from the radial outer end of the external tooth to the radial inner surface of the second body portion, A flexible external gear, wherein the minimum value of the thickness of the first body portion is equal to or less than half the maximum value of the thickness of the diaphragm portion.

2. 2. The flexible external gear according to claim 1, A flexible external gear, wherein the thickness of the diaphragm portion is substantially constant from the radially inner end to the radially outer end of the diaphragm portion.

3. 3. The flexible external gear according to claim 2, a thickness of the diaphragm portion being approximately the same as a length from a radially outer end of the external teeth to a radially inner surface of the second body portion;

4. A flexible external gear according to any one of claims 1 to 3, A flexible external gear, wherein the minimum value of the thickness of the first body portion is equal to or less than half the minimum value of the thickness of the diaphragm portion.

5. A flexible external gear according to any one of claims 1 to 4, a maximum value of a length from a radially outer end of the external teeth to a radially inner surface of the second body portion is greater than a minimum value of a thickness of the first body portion and is smaller than twice the minimum value of the thickness of the first body portion.

6. A flexible external gear according to any one of claims 1 to 5, A flexible externally toothed gear, wherein a maximum value of a length from a radial outer end to a radial inner end of the external teeth is greater than a minimum value of a thickness of the first body portion.

7. A flexible external gear according to any one of claims 1 to 6, A flexible external gear, wherein the circumferential distance between the circumferential centers of the external teeth adjacent in the circumferential direction is greater than twice the minimum value of the thickness of the first body portion.

8. A flexible external gear according to any one of claims 1 to 7, A flexible external gear, wherein the circumferential distance between the circumferential centers of the external teeth adjacent in the circumferential direction is greater than the minimum value of the thickness of the diaphragm portion.

9. A flexible external gear according to any one of claims 1 to 8, A flexible externally toothed gear, wherein a maximum value of the tooth thickness of the external teeth at a radial midpoint between a radial outer end and a radial inner end of the external teeth is smaller than a minimum value of the thickness of the first body portion.

10. A flexible external gear according to any one of claims 1 to 9, the body portion has a connection portion that connects one axial end portion of the first body portion and a radial end portion of the diaphragm portion, The flexible external gear, wherein the connection portion extends in a direction having both axial and radial components.

11. A flexible external gear according to claim 10, the connecting portion has an arc shape curved in a direction having both axial and radial components in a cross section taken along the central axis, A flexible external gear, wherein the maximum value of the radius of curvature of the connection portion is 10 times or less the thickness of the first body portion.

12. A flexible external gear according to any one of claims 1 to 11, A flexible external gear, wherein the minimum value of the thickness of the first body portion is less than half the maximum value of the thickness of the diaphragm portion.

13. The flexible external gear according to any one of claims 1 to 12; a wave generator disposed radially inside the second body portion; an internal gear disposed radially outside the second body portion; A wave reducer having the internal gear has a plurality of internal teeth protruding radially inward from a radially inner surface, A wave reducer in which a portion of the plurality of external teeth mesh with a portion of the plurality of internal teeth.

14. A robot comprising the wave reducer of claim 13.

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