Spherical Gear Rotating System

Abstract

To provide a spherical type gear rotation system that enables driving with three degrees of freedom of rotation with a small number of drive means and can be constituted relatively easily at low cost.SOLUTION: A spherical gear 11 has a part provided with only a first gear structure 21 and a part provided with only a second gear structure 22. A first gear 13 is provided to mesh with respective teeth of the first gear structure 21, and rotate the spherical gear 11 in a first direction. A second gear 14 is provided to mesh with respective teeth of the second gear structure 22 and rotate the spherical gear 11 in a second direction. First drive means 15 rotates the first gear 13 and second drive means 16 rotates the second gear 14. Third drive means 17 rotates the spherical gear 11 on an axis orthogonal to the axis of rotation of the first gear 13 together with the first gear 13. Center axes of rotations of the spherical gear 11 by the first drive means 15, second drive means 16 and third drive means 17 do not overlap with one another.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a spherical gear rotating system. [Background technology]

[0002] In recent years, the development of mechanisms and actuators with multiple degrees of freedom has been progressing for the purpose of application to robots and mechatronics systems. For example, if it is possible to realize a system that can drive multiple rotational degrees of freedom with one joint, it will be possible to reduce the size of the system and increase its functionality.

[0003] Conventionally, the present inventors have developed a spherical gear mechanism that uses spherical gears to achieve three rotational degrees of freedom (3-RDoF) as a mechanism with multiple rotational degrees of freedom (see, for example, Non-Patent Document 1). As shown in FIG. 6, this spherical gear mechanism comprises an intersecting spherical gear 51 having two tooth structures formed by forming a plurality of grooves around two perpendicular axes (axes A3 and B3 in FIG. 6(b)) on the entire surface of a sphere, two saddle-shaped gears 52 having special tooth surfaces that mesh with each of the tooth structures and each of which is provided to rotate the intersecting spherical gear 51, a pair of first motors 53 that rotate each of the saddle-shaped gears 52 around its rotation axis (axes A2 and B2 in FIG. 6(b)), a pair of second motors 54 that rotate each of the saddle-shaped gears 52 around axes (axes A1 and B1 in FIG. 6(b)) that pass through the center of the intersecting spherical gear 51 and are perpendicular to the rotation axis of each of the saddle-shaped gears 52, and a support 55 that supports the intersecting spherical gear 51 on its surface. This spherical gear mechanism can achieve three degrees of rotational freedom for driving the intersecting type spherical gear 51 provided with the output shaft 56 by driving the motors 53, 54. Also, in principle, this has the characteristic that there is no limit to the movable range of the intersecting type spherical gear 51.

[0004] Incidentally, a toothed structure on the surface of a sphere has been proposed as a configuration for a universal joint, and examples include a toothed structure consisting of a plurality of grooves formed around a predetermined axis on the entire surface of a sphere (see, for example, Patent Document 1), and a transmission mechanism consisting of a gear having a convex portion on the inside of a lattice provided on the entire surface of a hemisphere, and a gear having a concave portion on the inside of a lattice provided on the entire surface of the hemisphere, meshed with each other (see, for example, Patent Document 2). [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Kazuki Abe, Kenjiro Tadakuma, and Riichiro Tadakuma, “ABENICS: Active Ball Joint Mechanism With Three-DoF Based on Spherical Gear Meshings”, IEEE Transactions on Robotics, [online], April 2021, [Retrieved August 7, 2021], Internet〈URL: https: / / www.researchgate.net / publication / 351357682〉, DOI: 10.1109 / TRO.2021.3070124 [Patent documents]

[0006] [Patent Document 1] U.S. Pat. No. 5,533,418 [Patent Document 2] US Patent Application Publication No. 2015 / 0128734 Summary of the Invention [Problem to be solved by the invention]

[0007] The spherical gear mechanism described in Non-Patent Document 1, as shown in FIG. 6, uses four drive means (motors 53, 54) to achieve three degrees of rotational freedom for the intersecting spherical gear 51. This makes the drive structure complicated and increases costs such as material costs.

[0008] The present invention has been made with attention to these problems, and aims to provide a spherical gear rotation system that can achieve three rotational degrees of freedom with a small number of drive means and can be constructed relatively simply and inexpensively. [Means for solving the problem]

[0009] The spherical gear rotation system according to the present invention comprises a spherical gear having a first tooth structure having a plurality of teeth arranged in a first direction along a surface of a sphere, and a second tooth structure having a plurality of teeth arranged in a second direction intersecting the first direction, the spherical gear having a portion on the surface of the sphere where only the first tooth structure is provided and a portion on the surface of the sphere where only the second tooth structure is provided, a support that supports the spherical gear rotatably along the surface of the sphere, and a first gear that is rotatable in the first direction by meshing with the teeth of the first tooth structure and rotating the spherical gear around a first rotation axis, and a second gear that is rotatable in the first direction by meshing with the teeth of the second tooth structure and rotating the spherical gear around a second rotation axis. The present invention is characterized in that the spherical gear has a second gear arranged to rotate in the second direction, a first driving means for rotating the first gear about the first rotation axis, a second driving means for rotating the second gear about the second rotation axis, and a third driving means for rotating the first gear about a third axis that passes through the center of the sphere and is perpendicular to the first rotation axis, and by rotating the first gear with the third driving means, the spherical gear is also rotated together with the first gear, and the central axes of rotation of the spherical gear by the first driving means, the second driving means and the third driving means do not overlap with each other.

[0010] The spherical gear rotation system according to the present invention is configured so that the central axes of rotation of the spherical gears by the first drive means, second drive means, and third drive means do not overlap with one another, and therefore it is possible to realize three rotational degrees of freedom drive of the spherical gear with just these three drive means. In this way, compared to the conventional spherical gear mechanism that uses four drive means (motors 53, 54) shown in Fig. 6, the spherical gear rotation system according to the present invention can realize three rotational degrees of freedom drive with fewer drive means and can be configured simply and inexpensively.

[0011] In the spherical gear rotation system according to the present invention, the spherical gear has a portion where only the first tooth structure is provided and a portion where only the second tooth structure is provided, and therefore, unlike the conventional intersecting type spherical gear 51 as shown in Fig. 6, the movable range is in principle limited even when the saddle gears 52 and motors 53, 54 are used. However, since the movable range of the intersecting type spherical gear 51 is practically limited by supports and the like even in the conventional spherical gear mechanism, by appropriately setting the arrangement of the first tooth structure and the second tooth structure, and the arrangement of each gear and each motor, it is possible to set the movable range of the spherical gear of the spherical gear rotation system according to the present invention to a range that does not cause practical problems while ensuring drive with three rotational degrees of freedom.

[0012] In the spherical gear rotation system according to the present invention, the spherical gear has a portion along the surface of the sphere where only a first tooth structure having a plurality of teeth arranged in a first direction is provided, and the tip surface of the tooth tip in this portion forms a long and thin line shape. Similarly, along the surface of the sphere, there is a portion where only a second tooth structure having a plurality of teeth arranged in a second direction intersecting with the first direction is provided, and the tip surface of the tooth tip in this portion also forms a long and thin line shape. In these portions, the area of ​​the tip surface of the tooth tip that comes into contact with the support is larger than that of a conventional intersecting spherical gear 51 that has a shape formed by the intersection of two orthogonal tooth structures as shown in FIG. 6, so that damage and wear due to the load between the support and the spherical gear can be suppressed.

[0013] INDUSTRIAL APPLICABILITY The spherical gear rotation system according to the present invention can be used in devices that are driven with three rotational degrees of freedom, such as the joints of a robot arm or an omnidirectional wheel.

[0014] In the spherical gear rotation system according to the present invention, the spherical gear may have any configuration as long as the teeth of the first tooth structure are arranged in a first direction and the teeth of the second tooth structure are arranged in a second direction. Also, as long as the first direction and the second direction are not parallel and intersect with each other, they may intersect at any angle. For example, in a spherical gear, the first tooth structure may be formed by forming a plurality of grooves along a line where a plurality of planes perpendicular to a first axis passing through the center of the sphere intersect with the surface of the sphere, and the second tooth structure may be formed by forming a plurality of grooves along a line where a plurality of planes perpendicular to a second axis passing through the center of the sphere intersect with the first axis and the surface of the sphere. In this case, the teeth can be regularly arranged along the surface of the sphere, and the sphere can be smoothly rotated in the first direction and the second direction. Furthermore, in order to easily expand the range of motion, the first axis and the second axis may be perpendicular to each other.

[0015] More specifically, in this case, the first tooth structure may be provided on the surface of the sphere on one side of a plane including the first axis, and the second tooth structure may be provided on the surface of the sphere on one side of a plane including the second axis. The first tooth structure may be provided on the surface of the sphere on one side of a plane including the first axis, and the second tooth structure may be provided on the surface of the sphere on the other side of the plane including the first axis. The first tooth structure may be provided on the surface of the sphere on one side of a plane including the first axis and the second axis, and the second tooth structure may be provided on the surface of the sphere on the other side of the plane including the first axis and the second axis. In these cases, the movable range in three degrees of freedom of rotation can be expanded while suppressing damage and wear due to the load between the support body.

[0016] In the spherical gear rotation system according to the present invention, the spherical gear may have a portion on the surface of the sphere where the first tooth structure and the second tooth structure are provided overlapping each other. In this case, by configuring the portion other than the portion where the first tooth structure and the second tooth structure are overlapping to be supported by a support body, it is possible to suppress damage and wear due to the load between the support body and the spherical gear. In addition, in the spherical gear rotation system according to the present invention, the spherical gear may have a portion on the surface of the sphere where the first tooth structure and the second tooth structure are not provided. In this case, the portion where the first tooth structure and the second tooth structure are not provided can be configured to be supported by a support body in rolling contact, which can further reduce friction.

[0017] In the spherical gear rotation system according to the present invention, the spherical gear may be provided such that the tips of the teeth of the first tooth structure and the second tooth structure extend perpendicularly to the surface of the sphere. Also, in the spherical gear rotation system according to the present invention, the first tooth structure and the second tooth structure of the spherical gear may be provided such that the intervals between adjacent teeth are equal along the surface of the sphere. In these cases, the teeth can be regularly arranged along the surface of the sphere, allowing smooth rotation in the first and second directions. Effect of the Invention

[0018] According to the present invention, it is possible to provide a spherical gear rotation system that can realize drive with three rotational degrees of freedom using a small number of drive means and can be constructed relatively simply and inexpensively. [Brief description of the drawings]

[0019] [Figure 1] FIG. 2 is an enlarged perspective view of a spherical gear and its surroundings, showing a spherical gear rotation system according to an embodiment of the present invention. [Diagram 2] FIG. 2A is a perspective view of a spherical gear in a spherical gear rotation system according to an embodiment of the present invention, and FIG. 2B is a transparent perspective view showing the arrangement of each tooth structure. [Diagram 3]FIG. 2A is a perspective view showing a first modified example of a spherical gear in a spherical gear rotation system according to an embodiment of the present invention, and FIG. 2B is a see-through perspective view showing the arrangement of each tooth structure. [Figure 4] FIG. 11 is a perspective view showing a second modified example of the spherical gear in the spherical gear rotation system according to the embodiment of the present invention. [Diagram 5] FIG. 1 is a three-dimensional plot diagram showing changes in attitude of a spherical gear during a drive test of a spherical gear rotation system according to an embodiment of the present invention. [Figure 6] FIG. 1A is a partially exploded perspective view showing the overall configuration of a conventional spherical gear mechanism, and FIG. 1B is a perspective view showing the rotation principle of a spherical gear. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. 1 to 5 show a spherical gear rotating system according to an embodiment of the present invention. As shown in FIG. 1, the spherical gear rotation system 10 includes a spherical gear 11, a support 12, a first gear 13, a second gear 14, a first drive means 15, a second drive means 16, a third drive means 17, and an output shaft 18.

[0021] As shown in FIG. 2, the spherical gear 11 has a first tooth structure 21 having a plurality of teeth arranged in a first direction along the surface of the sphere, and a second tooth structure 22 having a plurality of teeth arranged in a second direction intersecting with the first direction. The first tooth structure 21 is formed by forming a plurality of grooves along a line where a plurality of planes perpendicular to a first axis 23 passing through the center of the sphere intersect with the surface of the sphere. The second tooth structure 22 is formed by forming a plurality of grooves along a line where a plurality of planes perpendicular to a second axis 24 passing through the center of the sphere intersect with the first axis 23 intersect with the surface of the sphere. The first tooth structure 21 and the second tooth structure 22 are provided so that the tips of the teeth extend in a direction perpendicular to the surface of the sphere. The first tooth structure 21 and the second tooth structure 22 are provided so that the intervals between adjacent teeth are equal along the surface of the sphere. The spherical gear 11 has, on the surface of the sphere, a portion where only the first tooth structure 21 is provided and a portion where only the second tooth structure 22 is provided.

[0022] In addition, as long as the first direction and the second direction of the spherical gear 11 are not parallel and intersect with each other, they may intersect at any angle. In other words, it is sufficient that the first axis 23 and the second axis 24 intersect. In the specific example shown in Fig. 2, the first axis 23 and the second axis 24 of the spherical gear 11 are perpendicular to each other, and the first direction and the second direction are perpendicular to each other on the spherical surface.

[0023] The spherical gear 11 may have a portion on the surface of the sphere where only the first tooth structure 21 is provided and a portion on the surface of the sphere where only the second tooth structure 22 is provided, and may have a portion on the surface of the sphere where the first tooth structure 21 and the second tooth structure 22 are provided overlapping each other, or a portion on the surface of the sphere where the first tooth structure 21 and the second tooth structure 22 are not provided. In a specific example shown in FIG. 2, the first tooth structure 21 is provided on the entire surface of the sphere (surface of the hemisphere) on one side of a plane including the first axis 23 and the second axis 24, and the second tooth structure 22 is provided on the entire surface of the sphere (surface of the opposite hemisphere) on the other side of the plane including the first axis 23 and the second axis 24. The spherical gear 11 shown in FIG. 2 does not have a portion on the surface of the sphere where the first tooth structure 21 and the second tooth structure 22 are provided overlapping each other, or a portion on the surface of the sphere where the first tooth structure 21 and the second tooth structure 22 are not provided.

[0024] The spherical gear 11 may have a configuration as shown in Fig. 3 or 4, for example, other than the configuration shown in Fig. 2. That is, as shown in Fig. 3, the first tooth structure 21 may be provided on a spherical surface (hemisphere surface) on one side of a plane that includes the first axis 23 and does not include the second axis 24, and the second tooth structure 22 may be provided on a spherical surface (hemisphere surface) on one side of a plane that includes the second axis 24 and does not include the first axis 23. In this case, the spherical gear 11 has, on the surface of the sphere, a portion 25 where the first tooth structure 21 and the second tooth structure 22 are provided overlapping each other, and a portion 26 where the first tooth structure 21 and the second tooth structure 22 are not provided. 4, the first tooth structure 21 may be provided on a spherical surface (hemisphere surface) on one side of a plane that includes the first axis 23 and is perpendicular to the second axis 24, and the second tooth structure 22 may be provided on a spherical surface (hemisphere surface) on the other side of the plane. Note that a conventional intersecting type spherical gear 51 shown in FIG. 6 has the first tooth structure 21 and the second tooth structure 22 each provided on the entire spherical surface.

[0025] 1, the support 12 is configured to rotatably support the spherical gear 11 along the surface of a sphere. The support 12 rotatably supports a portion of the surface of the spherical gear 11 through sliding contact.

[0026] The first gear 13 has teeth on the side of a cylinder of a predetermined thickness, and is configured to mesh with each tooth of the first tooth structure 21. The first gear 13 is disposed on the hemisphere side of the spherical gear 11 supported by the support 12, on which the first tooth structure 21 is formed, so as to mesh with each tooth of the first tooth structure 21. The first gear 13 is attached to the support 12, and is provided so as to be able to rotate (pitch) the spherical gear 11 in a first direction by rotating the first gear 13 about a first rotation axis that is a central axis. In addition, the first gear 13 is provided so as to be able to rotate together with the spherical gear 11 about a third axis that passes through the center of the sphere and is perpendicular to the first rotation axis, while meshing with the spherical gear 11. In the specific example shown in FIG. 1, the first gear 13 is made of a saddle gear 52 shown in FIG. 6, but may be made of any material as long as it can rotate the spherical gear 11 by meshing with each tooth of the first tooth structure 21.

[0027] The second gear 14 has teeth on the side of a cylinder of a predetermined thickness, and is configured to mesh with each tooth of the second tooth structure 22. The second gear 14 is disposed on the hemisphere side of the spherical gear 11 supported by the support 12 where the second tooth structure 22 is formed, i.e., on the opposite side of the spherical gear 11 from the first gear 13, so as to mesh with each tooth of the second tooth structure 22. The second gear 14 is attached to the support 12, and is provided so as to be able to rotate (yaw) the spherical gear 11 in a second direction by rotating it about a second rotation axis that is the central axis. In addition, the second gear 14 is provided so as to be able to rotate together with the spherical gear 11 about a fourth axis that passes through the center of the sphere and is perpendicular to the second rotation axis while meshing with the spherical gear 11. In the specific example shown in FIG. 1, the second gear 14 is made of a saddle gear 52 shown in FIG. 6, but it may be made of anything that can mesh with each tooth of the second tooth structure 22 and rotate the spherical gear 11.

[0028] The first driving means 15 has a motor and is attached to the support 12 so as to rotate the first gear 13 around the first rotation axis. The second driving means 16 has a motor and is attached to the support 12 so as to rotate the second gear 14 around the second rotation axis. The third driving means 17 has a motor and is attached to the support 12 so as to rotate the first gear 13 around a third axis that passes through the center of the sphere and is perpendicular to the first rotation axis. The spherical gear rotation system 10 is configured so that the spherical gear 11 can rotate (roll) together with the first gear 13 by rotating the first gear 13 with the third driving means 17. At this time, the second gear 14 also rotates together with the spherical gear 11. The spherical gear rotation system 10 is configured so that the central axes of rotation of the spherical gear 11 by the first driving means 15, the second driving means 16, and the third driving means 17 do not overlap with each other, and in the specific example shown in FIG. 1, they are configured to be perpendicular to each other.

[0029] The output shaft 18 is provided on the surface of the spherical gear 11 so as to be able to transmit the rotational motion of the spherical gear 11 to the outside. In the specific example shown in Fig. 1, the spherical gear rotation system 10 has a rolling rotation angle of ±90 degrees, a pitching rotation angle of ±45 degrees, and a yawing rotation angle of ±45 degrees of the spherical gear 11. Note that the spherical gear rotation system 10 does not need to have the output shaft 18 in cases where the spherical gear 11 is used as an omnidirectional wheel, for example.

[0030] Next, the operation will be described. In the spherical gear rotation system 10, the spherical gear 11 has a portion provided with only the first tooth structure 21 and a portion provided with only the second tooth structure 22, and since the tooth structures do not intersect, the tip surfaces of the teeth in these portions form an uninterrupted, elongated line shape. In these portions, the area of ​​the tip surfaces of the teeth that come into contact with the support body 12 is larger than in a conventional intersecting-type spherical gear 51 as shown in Fig. 6, so damage and wear due to the load between the support body 12 can be suppressed. In addition, the spherical gear 11 can be manufactured more easily than the conventional intersecting-type spherical gear 51, and manufacturing costs can be reduced.

[0031] In the spherical gear rotation system 10, the central axes of rotation of the spherical gear 11 by the first driving means 15, second driving means 16, and third driving means 17 are perpendicular to each other and do not overlap, so these three driving means alone can achieve three degrees of rotational freedom of the spherical gear 11. In this way, the spherical gear rotation system 10 can be constructed more simply and inexpensively than a conventional spherical gear mechanism that uses four driving means (motors 53, 54) as shown in Figure 6.

[0032] In addition, the spherical gear rotation system 10 has a spherical gear 11 with a portion having only the first tooth structure 21 and a portion having only the second tooth structure 22, so that the movable range is more limited than that of a conventional intersecting type spherical gear 51 as shown in FIG. 6. However, even in the conventional intersecting type spherical gear 51, the movable range is practically limited by the support 12, etc., so that the movable range of the spherical gear 11 can be set to a practically problem-free range while ensuring drive with three rotational degrees of freedom by appropriately setting the arrangement of the first tooth structure 21, the second tooth structure 22, the first gear 13, and the second gear 14. The spherical gear rotation system 10 can be used in things that are driven with three rotational degrees of freedom, such as the joints of a robot arm and omnidirectional mobile wheels.

[0033] 3, even if the spherical gear rotation system 10 has a portion 25 on the surface of the sphere of the spherical gear 11 where the first tooth structure 21 and the second tooth structure 22 are provided overlapping each other, the other portions are configured to be supported by the support body 12, thereby making it possible to suppress damage and wear due to the load between the support body 12 and the spherical gear 11. Furthermore, if the spherical gear rotation system 10 has a portion 26 where the first tooth structure 21 and the second tooth structure 22 are not provided, friction can be further reduced by supporting that portion by the support body 12 in rolling contact. EXAMPLES

[0034] A driving test of the spherical gear 11 was conducted using the spherical gear rotation system 10 shown in FIG. 1. In the driving test, a reflective marker was attached to the output shaft 18, and the reflective marker was photographed by a motion capture camera ("Optitrack V120 Trio" manufactured by NaturalPoint Inc.) by optical tracking to obtain spatial position data. In the driving test, in order to avoid interference between the reflective marker and the first gear 13 and the second gear 14, the first gear 13 and the second gear 14 were not placed directly opposite the spherical gear 11, but were placed so that the angle between the third axis and the fourth axis was 160 degrees. In addition, the spherical gear 11 and the support 12 were manufactured using an acrylic photocurable resin by a 3D printer.

[0035] In the drive test, the attitude of the spherical gear 11 was expressed by XYZ Euler angles (roll, pitch, yaw), and the output shaft 18 (reflective marker) of the spherical gear 11 was rotated to pass through the way points P0 to P8 shown in Table 1, at which point the attitude of the spherical gear 11 was measured. Note that in Table 1, r is roll, p is pitch, and y is yaw.

[0036] [Table 1]

[0037] The results of the drive test are shown in Figure 5. As shown in Figure 5, it was confirmed that the spherical gear 11 was driven to linearly connect each of the via points. From this result, it can be said that the spherical gear rotation system 10 shown in Figure 1 is able to achieve three degrees of freedom of rotation drive of the spherical gear 11 using three drive means, the first drive means 15, the second drive means 16, and the third drive means 17. [Explanation of symbols]

[0038] 10 Spherical Gear Rotating System 11 Spherical gear 21 First Tooth Structure 22 Secondary Tooth Structure 23 First axis 24 Second Axis 12 Support 13 First Gear 14 2nd Gear 15 First driving means 16 Second driving means 17 Third driving means 18 Output shaft 51 Intersecting spherical gear 52 Saddle Gear 53 First Motor 54 Second Motor 55 Support 56 Output shaft

Claims

1. a spherical gear having a first tooth structure having a plurality of teeth arranged in a first direction along a surface of a sphere, and a second tooth structure having a plurality of teeth arranged in a second direction intersecting the first direction, the spherical gear having a portion on the surface of the sphere where only the first tooth structure is provided and a portion on the surface of the sphere where only the second tooth structure is provided; a support that supports the spherical gear rotatably along a surface of the sphere; a first gear that is engaged with each tooth of the first tooth structure and rotates about a first rotation axis to rotate the spherical gear in the first direction; a second gear that meshes with each tooth of the second tooth structure and rotates about a second rotation axis to rotate the spherical gear in the second direction; a first driving means for rotating the first gear about the first rotation axis; a second driving means for rotating the second gear about the second rotation axis; a third driving means for rotating the first gear about a third axis that passes through the center of the sphere and is perpendicular to the first rotation axis, By rotating the first gear by the third driving means, the spherical gear is also rotated together with the first gear, and the central axes of rotation of the spherical gear by the first driving means, the second driving means and the third driving means are configured not to overlap with each other. A spherical gear rotation system.

2. The first tooth structure is formed by forming a plurality of grooves along a line where a plurality of planes perpendicular to a first axis passing through the center of the sphere and a surface of the sphere intersect, The second tooth structure is formed by forming a plurality of grooves along a line where a plurality of planes perpendicular to a second axis that passes through the center of the sphere and intersects with the first axis and the surface of the sphere intersect.

2. The spherical gear rotating system according to claim 1 .

3. 3. The spherical gear rotating system according to claim 2, wherein said first axis and said second axis are perpendicular to each other.

4. the first tooth structure is provided on a surface of the sphere on one side of a plane including the first axis; the second tooth structure is provided on a surface of the sphere on one side of a plane including the second axis, 4. A spherical gear rotating system according to claim 2 or 3.

5. 5. The spherical gear rotation system according to claim 1, wherein the spherical gear has a portion on a surface of the sphere where the first tooth structure and the second tooth structure are provided overlapping each other.

6. 6. The spherical gear rotation system according to claim 1, wherein the spherical gear has a portion on a surface of the sphere where the first tooth structure and the second tooth structure are not provided.

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