speed reducer

Abstract

To improve the durability against thrust loads in a reduction gear that can be made thinner. [Solution] The reducer 100 for reducing rotational power includes a plurality of rolling elements 120, a rolling element holding plate 130 that restricts the circumferential and radial movement of the rolling elements 120 and holds the plurality of rolling elements 120 so that the axis of symmetry of the rolling elements 120 faces radially, and two gear parts 112, 140 that are stacked in the direction of the axis C and are in constant contact with at least a portion of the plurality of rolling elements 120. The two gear parts 112, 140 have tooth profiles 115, 145 formed on the surfaces facing the rolling elements 120, respectively. The tooth profiles 115, 145 are determined based on the outer circumferential trajectory of the rolling elements 120 when the center of the rolling element 120 moves along an axial sinusoidal guidance curve with the same distance from the axis C and amplitude, with wave numbers M, N (where M, N are natural numbers such that M > N).

Description

[Technical Field]

[0001] The present invention relates to a speed reducer that decelerates and transmits power, and particularly relates to a speed reducer that can be made thinner. [Background Art]

[0002] In a joint driving device that drives a joint of a robot, a motor is used as a power generator. However, the rotation speed of the motor may be unnecessarily higher than the rotation speed suitable for driving the joint. For this reason, speed reducers that decelerate and transmit rotational power are usually used in joint driving devices and the like. In addition, when the speed reducer increases in size, the joint driving device and the like also increase in size, so speed reducers used in robots and the like are required to be thinner. Accordingly, various speed reducers such as planetary gear speed reducers (see, for example, Non-Patent Document 1) have been used as speed reducers that can be made thinner. [Prior Art Literature] [Patent Literature]

[0003] [Non-Patent Literature 1] "Maxicor General Catalog 2019 Edition", Maxicor Co., Ltd., pp. C-2 to C-8 [Summary of the Invention] [Problem to be Solved by the Invention]

[0004] However, since a planetary gear speed reducer is constituted by a gear train in which a plurality of mutually meshing gears are arranged on the same plane, when a load in the rotational axis direction (called "thrust load" or "axial load") is applied, the positions of the mutually meshing gears are displaced, which may impair the function as a planetary gear speed reducer. Therefore, as generally described in Non-Patent Document 1, it is not necessarily easy to increase durability against thrust load in a speed reducer that can be made thinner such as a planetary gear speed reducer.

[0005] This invention was made to solve the above-mentioned conventional problems, and aims to provide a technology that improves the durability against thrust loads in a reduction gear that can be made thinner. [Means for solving the problem]

[0006] To achieve at least some of the above objectives, the present invention can be realized in the following forms or applications.

[0007] [Application Example 1] A reduction gear that outputs reduced rotational power in response to an input of rotational power rotating around an axis, comprising: a plurality of rolling elements; a rolling element holding plate that restricts the movement of the rolling elements in the circumferential and radial directions of rotation while allowing movement of the rolling elements in the axial direction, and holding the plurality of rolling elements such that the axis of symmetry of the rolling elements faces the radial direction; and first and second gear sections stacked in the axial direction so as to sandwich the plurality of rolling elements and the rolling element holding plate, with at least a portion of the plurality of rolling elements constantly in contact with each other, wherein the first and second gear sections are connected to the plurality of rolling elements and the rolling element holding plate A gearbox is provided in which first and second tooth profiles are formed on the surfaces facing each other, and the first and second tooth profiles are determined based on the trajectory of the outer circumference of the rolling element when the center of the rolling element moves along an axial sinusoidal guide curve in which the distance from the axis and amplitude are set to be the same at wavenumber M and wavenumber N (where M and N are natural numbers such that M > N), respectively, and the rotational power is input to the second gear section, and the reduced rotational power is output from the other of the first gear section and the rolling element holding plate, with the first gear section and the rolling element holding plate fixed to the direction of rotation.

[0008] In this application example, the thickness (axial length) of the mechanism directly involved in the reduction operation is equal to the sum of the axial length of the rolling element and twice the amplitude of the axial sinusoidal guide curve. Therefore, it is possible to make the reduction gear thinner. Furthermore, since the reduction gear consists of multiple rolling elements and the first and second gear sections stacked in the axial direction, with multiple rolling elements sandwiched between them, the positional relationship between the multiple rolling elements and the first and second gear sections is maintained even when a thrust load is applied to the reduction gear. Therefore, according to this application example, the resistance of the reduction gear to thrust loads can be increased.

[0009] [Application Example 2] A gear reducer according to Application Example 1, further comprising a cylindrical aligning portion having a side surface extending in the axial direction, provided at the center of any one of the first gear portion, the rolling element retaining plate, and the second gear portion, wherein the remaining two centers of the first gear portion, the rolling element retaining plate, and the second gear portion have central holes formed therein, the inner diameter of which is larger than the outer diameter of the aligning portion and which penetrate in the axial direction.

[0010] According to this application example, by setting the inner diameter of the central hole sufficiently close to the outer diameter of the centering portion, the relative movement between the first and second gear portions and the rolling element retaining plate in the radial direction can be restricted. Therefore, the misalignment of the rotation axes between the first and second gear portions and the rolling element retaining plate can be suppressed without using other members, thus reducing the number of components in the reduction gear.

[0011] [Application Example 3] The gearbox according to Application Example 2, wherein the self-aligning portion is provided in either the first or second gear portion.

[0012] This application example makes it easier to assemble the gearbox.

[0013] [Application Example 4] The reduction gear according to any one of Application Examples 1 to 3, wherein the number of rolling elements is either (M+N) or (MN).

[0014] According to this application example, the efficiency of transmitting rotational power from the second gear section, which receives rotational power, to the first gear section or rolling element holding plate, which outputs reduced rotational power, can be increased.

[0015] [Application Example 5] The reduction gear according to any one of Application Examples 1 to 3, wherein the rolling elements are balls, and the rolling element holding plate is a plate-shaped member having the same number of circular ball holes that penetrate in the axial direction as the number of rolling elements.

[0016] According to this application example, the shape of the rolling element retaining plate can be made simpler. Furthermore, by using balls as the rolling elements, the axis of symmetry of the rolling elements is no longer deviated from the radial direction, allowing the rolling elements (balls) to roll more efficiently.

[0017] [Application Example 6] The gearbox according to Application Example 5, wherein grooves are formed on the surfaces on which the first and second tooth profiles are formed, at positions where the distance from the axis is the same as the axial sinusoidal guide curve, and the edge or inner surface of the grooves contacts the ball.

[0018] According to this application example, the radial movement of the rolling elements (balls) is more reliably restricted, thereby suppressing the generation of vibrations associated with the radial movement of the rolling elements (balls).

[0019] [Application Example 7] The reduction gear according to any one of Application Examples 1 to 3, wherein the axial sinusoidal guide curve is an axial sinusoidal curve.

[0020] According to this application example, the shapes of the first and second tooth profiles can be made simpler.

[0021] [Application Example 8] The reduction gear according to any one of Application Examples 1 to 3, wherein the axial sinusoidal induction curve is an axial triangular wave curve.

[0022] According to this application example, the shapes of the first and second tooth profiles can be made further simpler.

[0023] Note that the present invention can be implemented in various aspects. For example, it can be implemented in aspects such as a speed reducer, a drive mechanism using the speed reducer, and a drive device combining the speed reducer with a power generator such as a motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] [Figure 1] 1 is an exploded perspective view showing the configuration of the speed reducer according to a first embodiment. [Figure 2] 2 is an explanatory diagram showing the assembled state of the speed reducer. [Figure 3] 3 is an explanatory diagram showing how the shape of a tooth profile formed on a gear portion is determined. [Figure 4] 4 is an explanatory diagram showing the operation of the speed reducer according to the first embodiment. [Figure 5] 5 is an explanatory diagram showing the operation of the speed reducer according to the first embodiment. [Figure 6] 6 is an exploded perspective view showing the configuration of a speed reducer according to a second embodiment. [Figure 7] 7 is an explanatory diagram showing the operation of the speed reducer according to the second embodiment. [Figure 8] 8 is an explanatory diagram showing the operation of the speed reducer according to the second embodiment. [Figure 9] 9 is an exploded perspective view showing the configuration of a speed reducer according to a third embodiment. [Figure 10] 10 is an explanatory diagram showing the operation of the speed reducer according to the third embodiment. [Figure 11] 11 is an exploded perspective view showing the configuration of a speed reducer according to a fourth embodiment. [Figure 12] 12 is an explanatory diagram showing the configuration and arrangement of a first gear member, balls, a ball holding plate and a second gear member in the speed reducer according to the fourth embodiment. MODE FOR CARRYING OUT THE INVENTION

[0025] Hereinafter, embodiments for carrying out the present invention will be described in the following order. A. First Embodiment: A1. Gearbox configuration: A2. Tooth profile shape: A3. Specific configurations of the central path curve and ball placement: A4. Operation of the gearbox: B. Second Embodiment: C. Third Embodiment: C1. Gearbox configuration and operation: C2. General form of the central path curve: D. Fourth Embodiment: E. Variations:

[0026] A. First Embodiment: A1. Gearbox configuration: Figure 1 is an exploded perspective view showing the configuration of a speed reducer 100 as a first embodiment of the present invention, and Figure 2 is an explanatory diagram showing the assembled state of the speed reducer 100. Figure 2(a) is a projection view of the speed reducer 100 as seen from the +Z direction, and Figure 2(b) is an external view of the speed reducer 100 as seen from the +X direction. Note that in Figure 2(a), the ball 120 (described later) is omitted from the illustration for convenience. Also, the X, Y, and Z directions shown in Figures 1 and 2 and other drawings represent three orthogonal directions.

[0027] The gearbox 100 is configured to output reduced rotational power in response to input power (rotational power) that rotates around the axis C extending in the Z direction of the gearbox 100. Hereafter, this direction of rotation will also be called the "circumferential direction of rotation" or simply the "circumferential direction," and the direction extending from the axis C in the XY plane (i.e., in the direction perpendicular to the axis C) will also be called the "radial direction of rotation" or simply the "radial direction." Furthermore, unless otherwise specified, rotation hereafter refers to rotation around the axis C.

[0028] As shown in Figure 1, the gear reducer 100 comprises a first gear member 110, 22 spherical balls 120 (hereinafter also simply referred to as "balls 120"), a ball retaining plate 130, and a second gear member 140. As shown in Figure 2(b), the gear reducer 100 is constructed by stacking the first gear member 110, the balls 120 and ball retaining plate 130, and the second gear member 140 in this order toward the +Z direction.

[0029] The first gear member 110 has a cylindrical tubular portion 111 extending in the Z direction, with a central hole 118 that penetrates in the Z direction (axis C direction), and an annular gear portion 112 extending outward (radially away from the axis C) from the -Z direction end of the tubular portion 111. A tooth profile 115 is formed on the +Z direction side of the gear portion 112, that is, the ball 120 side surface (the surface facing the ball 120). The shape of the tooth profile 115 formed on the gear portion 112 will be described later.

[0030] The second gear member 140 is an annular member with a central hole 148 that penetrates in the Z direction. A tooth profile 145 is formed on the -Z side of the second gear member 140, that is, on the ball 120 side (the surface facing the ball 120). Thus, since the second gear member 140 has a tooth profile 145 formed on it, similar to the gear portion 112 of the first gear member 110, it can also be called the "gear portion 140". The shape of the tooth profile 145 formed on the second gear member 140 will be described later.

[0031] The inner diameter of the central hole 148 formed in the second gear member 140 is set to be slightly larger than the outer diameter of the cylindrical portion 111 of the first gear member 110. Therefore, as shown in Figure 2(a), the second gear member 140 is restricted from moving radially relative to the first gear member 110, while being able to rotate freely around the axis C.

[0032] The ball retaining plate 130 is an annular plate-shaped member with a central hole 138 that penetrates in the Z direction. In addition to the central hole 138, the ball retaining plate 130 has the same number of circular ball holes 139 as the number of balls 120 (22). As shown in Figures 1 and 2(a), the ball holes 139 are arranged at equal angles around the axis C. Furthermore, the inner diameter of the ball holes 139 is set to be slightly larger than the outer diameter of the balls 120. As a result, the movement of the balls 120 in the circumferential and radial directions relative to the ball retaining plate 130 is restricted, while the balls 120 themselves can rotate freely around their individual centers. In this way, the ball retaining plate 130 allows the movement of the balls 120 in the direction of the axis C while restricting their movement in the circumferential and radial directions.

[0033] Similar to the central hole 148 formed in the second gear member 140, the inner diameter of the central hole 138 formed in the ball retaining plate 130 is set to be slightly larger than the outer diameter of the cylindrical portion 111 of the first gear member 110. Therefore, the ball retaining plate 130 is restricted from moving radially relative to the first gear member 110, while being able to rotate freely around the axis C.

[0034] In this way, as the ball retaining plate 130 rotates about its axis C, the center of the ball 120, whose movement in the circumferential and radial directions is restricted relative to the ball retaining plate 130, moves along a central path PC (the dashed line in Figure 2(a)) that forms a circle with radius R centered on axis C when viewed from the +Z direction.

[0035] As the second gear member 140 and the ball retaining plate 130 rotate relative to the first gear member 110, and the ball 120 rotates on its own axis, the ball 120, sandwiched between the second gear member 140 (gear portion 140) and the gear portion 112 of the first gear member 110, rotates (rolls).

[0036] The distance between the peaks and valleys in the Z-direction of the tooth profiles 115 and 145 formed on the gear sections 112 and 140, the thickness of the ball retaining plate 130, and the diameter of the balls 120 are set appropriately to avoid interference between the gear sections 112 and 140 and the ball retaining plate 130. In addition, the diameters of the gear sections 112 and 140 and the ball retaining plate 130 are set appropriately based on the number and diameter of the balls 120 so that the ball holes 139 can be positioned considering the mechanical strength of the ball retaining plate 130.

[0037] A2. Tooth profile shape: Figure 3 is an explanatory diagram illustrating how the shapes of the tooth profile 145 formed on the second gear member 140 (gear portion 140) and the tooth profile 115 formed on the gear portion 112 of the first gear member 110 are determined. Figures 3(a) and 3(d) show cross-sections of the gear portion 140 and gear portion 112, respectively, cut by a cylindrical surface with radius R centered on the axis C (i.e., a cylindrical surface including the central path PC shown in Figure 2). Figures 3(b) and 3(c) show how the center of the ball 120 moves along the curves CS2 and CS1 used to determine the tooth profiles 145 and 115. In Figure 3, for illustrative purposes, only the region in the +X direction from the axis C (see Figures 1 and 2), which corresponds to half a circumference, is depicted. Also, the θ direction shown in Figure 3 and other figures represents the circumferential direction.

[0038] Curve CS2 is a curve (axial sinusoid curve) where the distance from the axis C is constant (R), and as shown in Figure 3(b), the Z direction (axis C direction) traces a sine wave as the circumferential movement (θ direction), i.e., rotation, occurs. As can be seen from Figure 3(b), the wavenumber (hereinafter simply referred to as "wavenumber") N of curve CS2 is set to 2.

[0039] As the ball 120 moves along this curve CS2, the trajectory traced by the outer circumference of the ball 120 (outer circumference trajectory) traces two contour curves T21 and T22 on a cylindrical surface with radius R centered on axis C (the cross-sectional view shown in Figure 3(a)). The tooth profile 145 of the gear section 140 is determined based on the contour curve T21 on the gear section 140 side (+Z direction side) of these contour curves T21 and T22. Specifically, the shape of the tooth profile 145 is the shape obtained by extending the contour curve T21 in the radial direction.

[0040] By forming the tooth profile 145 on the gear portion 140 in this way, when the ball 120 is in contact with the gear portion 140 (second gear member 140) and the ball 120 is moved (rotated) in the θ direction relative to the gear portion 140, the center of the ball 120 moves along the curve CS2.

[0041] Similarly, the tooth profile 115 formed on the gear portion 112 of the first gear member 110 is determined by the curve CS1 shown in Figure 3(c). Curve CS1 is an axial sinusoid curve with a constant distance (R) from the axis C, a wave number M set to 20, and the same amplitude as curve CS2. When the ball 120 moves along this curve CS1, the outer trajectory of the ball 120 traces two contour curves T11 and T12 on a cylindrical surface with radius R centered on the axis C (the cross-sectional view shown in Figure 3(d)). The tooth profile 115 of the gear portion 112 is then determined based on the contour curve T12 on the gear portion 112 side (-Z direction side) of the contour curves T11 and T12.

[0042] In the example shown in Figure 3(c), curve CS1 is defined as an axial sinusoid curve with wavenumber M of 20. Therefore, when a disk of the same diameter as the ball 120 is moved so that its center follows curve CS1 while maintaining its perpendicularity to the curve CS1, an overlap occurs in the area swept by the disk. In this overlapping area (superimposed area) where the area swept by the disk of the same diameter as the ball 120 overlaps, the shapes of the contour curves T11 and T12 traced by the outer perimeter trajectory deviate from the shape of curve CS1, which is an axial sinusoid curve.

[0043] Therefore, when the ball 120 is in contact with the gear 112 and rotated relative to the gear 112, in the superimposed region, the center of the ball 120 moves to a position closer to the gear 112 than to the curve CS2. However, in most regions outside the superimposed region, the center of the ball 120 moves along the curve CS2. Therefore, overall, it is possible to treat the center of the ball 120 as moving along the curve CS2.

[0044] In the first embodiment of the gearbox 100, as shown in Figure 2(b), in most areas other than the superposition region, the ball 120 is in contact with both the gear portion 112 of the first gear member 110 and the second gear member 140 (gear portion 140). Therefore, the center of the ball 120 moves along the curves CS1 and CS2, and the curves CS1 and CS2 can also be called "center path curves CS1 and CS2" that represent the movement path of the center of the ball 120.

[0045] As can be seen from the above explanation and Figure 3, the periods of the central path curves CS1 and CS2 coincide with the periods of tooth profiles 115 and 145 determined using them, respectively. Therefore, the wavenumbers M and N of the central path curves CS1 and CS2 can also be said to be the wavenumbers M and N of tooth profiles 115 and 145.

[0046] A3. Specific configurations of the central path curve and ball placement: As described above, the central path curves CS1 and CS2 are axial sinusoid curves with the same amplitude, where the wavenumber M and wavenumber N are set to 20 and 2, respectively. The positions of these central path curves CS1 and CS2 in the Z direction are expressed by the following equations (1a) and (1b), using the amplitude A, the wavenumbers M and N (where M and N are natural numbers such that M > N; in the first embodiment, M = 20, N = 2), the rotation angle θ, and the central position Zo of the central path curves CS1 and CS2 in the Z direction.

number

[0047] Furthermore, in the reduction gear 100, the ball 120 is configured to contact both the gear portion 112 of the first gear member 110 and the second gear member 140 (gear portion 140). Therefore, the rotation angle θ at which the ball 120 can be positioned is the rotation angle θ at which the center position Z of the ball 120 in the Z direction, as expressed by equations (1a) and (1b), is the same, and is the rotation angle θ that satisfies the following equation (2).

number

[0048] Equation (2) above can be transformed into equation (3) using the sum-to-product formulas for trigonometric functions.

number

[0049] From equation (3) above, it can be seen that the rotation angle θ at which ball 120 can be positioned is the rotation angle θ that satisfies either equation (4) or (5) below.

number

number

[0050] During one rotation (0 ≤ θ < 2π), there are (M + N) rotation angles θ that satisfy equation (4) above, and there are (MN) rotation angles θ that satisfy equation (5) above. Therefore, when the rotation angle θ satisfies equation (4), it is possible to place (M + N) balls at equilateral positions, and when the rotation angle θ satisfies equation (5), it is possible to place (MN) balls at equilateral positions.

[0051] In the first embodiment of the gearbox 100, the balls 120 are arranged at equiangular positions that satisfy the above equation (4). Since the wavenumber M of the central path curve CS1 is set to 20 and the wavenumber N of the central path curve CS2 is set to 2, the number of balls 120 and the number of ball holes 139 formed in the ball holding plate 130 are both set to 22.

[0052] A4. Operation of the gearbox: Figures 4 and 5 are explanatory diagrams showing the operation of the reduction gear 100 of the first embodiment. Figures 4 and 5 show the arrangement of the gear portion 112 of the first gear member 110, the ball 120, and the second gear member 140 (gear portion 140) in each state described later.

[0053] Figure 4 shows the state in which rotational power is input to the second gear member 140 (gear section 140) with the ball retaining plate 130 (see Figures 1 and 2(b)) acting as a stator. Specifically, Figures 4(b) to 4(d) show the state in which the second gear member 140 (gear section 140) is rotated from the initial state shown in Figure 4(a) while keeping the rotation angle θ of each ball 120 constant (i.e., with the ball retaining plate 130 fixed).

[0054] As shown in Figure 4, as the gear portion 140 moves in the +θ direction, the individual balls 120 reciprocate in the Z direction. The balls 120 that move in the -Z direction as the gear portion 140 rotates in the +θ direction (shaded balls 120) come into contact with the +θ side surface of the tooth profile 115 formed on the gear portion 112.

[0055] Therefore, as shown in Figure 4, when the rotation angle θ of each ball 120 is kept constant (i.e., the ball holding plate 130 is fixed), when the gear section 140 moves in the +θ direction, the gear section 112 moves in the -θ direction.

[0056] Furthermore, while the gear section 112 and gear section 140 rotate once, each ball 120 reciprocates in the Z direction M and N times (20 times and 2 times in the first embodiment), respectively. Therefore, the number of rotations of the gear sections 112 and 140 when each ball 120 reciprocates once in the Z direction is the reciprocal of the wave numbers M and N (20 and 2) of the tooth profiles 115 and 145 formed thereon (1 / M = 1 / 20, 1 / N = 1 / 2).

[0057] Thus, when the rotation angle θ of the ball 120 is kept constant, that is, when the ball retaining plate 130 (Figures 1 and 2(b)) is used as a stator, when rotational power is input to the second gear member 140 (gear section 140), the first gear member 110 having the gear section 112 outputs rotational power that rotates in the opposite direction, reduced by a reduction ratio of 10 (M / N).

[0058] Figure 5 shows the state in which the first gear member 110 is used as a stator and rotational power is input to the second gear member 140 (gear section 140). Specifically, Figures 5(b) to 5(d) show the state in which the second gear member 140 (gear section 140) is rotated from the initial state shown in Figure 5(a), with the gear section 112 of the first gear member 110 fixed.

[0059] As shown in Figure 5, as the gear portion 140 moves in the +θ direction, the individual balls 120 reciprocate in the Z direction and also move in the +θ direction. As the balls 120 move, the ball retaining plate 130 rotates in the same direction as the second gear member 140.

[0060] Incidentally, as explained with reference to Figure 4, when the ball retaining plate 130 is fixed, the relationship between the rotational speed of the second gear member 140 and the rotational speed of the first gear member 110 is given. In this case, the relationship between the rotational speed of the second gear member 140 and the rotational speed of the ball retaining plate 130 when the first gear member 110 is fixed can be calculated using a table method or the like.

[0061] Specifically, as shown in Table 1 below, the rotational speeds of the ball retaining plate 130 and the first gear member 110 are calculated for two cases: when the second gear member 140 is rotated by +1 / N with the ball retaining plate 130 fixed, and when the second gear member 140 is rotated by +1 / M to counteract the rotation of the first gear member 110 with the entire assembly glued together. Next, the rotational speeds of the second gear member 140 and the ball retaining plate 130 are calculated by adding the rotational speeds of each part under these two conditions, with the first gear member 110 fixed. Then, the reduction ratio when the first gear member 110 is used as a stator and rotational power is input to the second gear member 140 is calculated as the absolute value of the quotient obtained by dividing the rotational speed of the second gear member 140 by the rotational speed of the ball retaining plate 130. [Table 1]

[0062] Thus, when the first gear member 110 is used as a stator, and rotational power is input to the second gear member 140 (gear section 140), the ball retaining plate 130 outputs rotational power that rotates in the same direction, reduced by a reduction ratio of 11 (M / N+1).

[0063] As shown in Figure 4, when the rotation angle θ of the ball 120 is kept constant, that is, when the ball retaining plate 130 is used as a stator, the ball retaining plate 130 can be fixed, for example, by providing fixing means on the outer circumference of the ball retaining plate 130. Also, as shown in Figure 5, when the first gear member 110 is used as a stator and the ball 120 is rotated to output rotational power from the ball retaining plate 130, the output of rotational power can be provided, for example, by providing power transmission means such as gears on the outer circumference of the ball retaining plate 130.

[0064] As can be seen from the above explanation, according to the first embodiment, the tooth profiles 115 and 145 formed on the gear sections 112 and 140 are determined based on the outer circumferential trajectory of the ball 120 when it moves along axial sinusoid curves (center path curves CS1 and CS2) with wave numbers M and N (where M and N are natural numbers such that M > N). This allows the gearbox 100 to be constructed using gear sections 112 and 140 with tooth profiles 115 and 145 formed on the ball 120 side, (M + N) balls 120, and a ball retaining plate 130 that restricts the relative movement of the balls 120 in the circumferential and radial directions. Furthermore, by appropriately setting the wave numbers M and N, the reduction ratio of the gearbox can be flexibly changed.

[0065] In the first embodiment, the first gear member 110 is provided with a cylindrical portion 111, and the ball retaining plate 130 and the second gear member 140 are formed with central holes 138 and 148, respectively, whose inner diameters are set to be slightly larger than the outer diameter of the cylindrical portion 111. This restricts the radial movement of the ball retaining plate 130 and the second gear member 140 relative to the first gear member 110, thereby suppressing misalignment of the rotation axes of the gear portion 112 of the first gear member 110, the ball retaining plate 130, and the second gear member 140 (gear portion 140).

[0066] However, generally speaking, if the two gears and the ball retaining plate can rotate coaxially, the cylindrical portion can be omitted, and furthermore, the formation of a central hole can also be omitted. For example, an annular member with an inner diameter slightly larger than the outer diameter of the two gears and the ball retaining plate may be placed on the outer circumference of the two gears and the ball retaining plate to restrict the relative radial movement of the two gears and the ball retaining plate. Alternatively, a shaft may be placed along the axis, and the two gears and the ball retaining plate may be attached to the shaft via bearings.

[0067] However, in order to further reduce the number of components of the speed reducer, it is preferable to provide a cylindrical or columnar (i.e., a cylindrical surface with its side extending in the direction of axis C) centered on the center of either of the two gear sections or the ball retaining plate, and to form a central hole in the other member with an inner diameter slightly larger than the outer diameter of the centering section. Furthermore, in order to make the assembly of the speed reducer easier, it is preferable to provide the centering section (cylindrical section 111 in the first embodiment) on either of the two gear sections, as in the first embodiment.

[0068] Furthermore, the gear reducer 100 of the first embodiment is constructed by stacking the gear portion 112, ball 120, and second gear member 140 (gear portion 140) provided on the first gear member 110 in this order in the direction of the axis C. Therefore, even when a load in the -Z direction (called a "thrust load" or "axial load") is applied to the second gear member 140, the positional relationship between the two gear portions 112, 140 and the ball 120 is maintained, so the durability of the gear reducer 100 against thrust loads can be made higher than that of various gear reducers, including planetary gear reducers.

[0069] Furthermore, even when a thrust load is applied, the ball 120 rolls between the two gear sections 112 and 140, reducing friction between the two gear sections 112 and 140 and the ball 120. This suppresses a decrease in power transmission efficiency due to the thrust load.

[0070] Furthermore, as is clear from the above explanation, in the first embodiment of the gearbox 100, the length (thickness) in the axial direction C of the mechanism directly involved in the reduction operation (tooth profiles 115, 145, ball 120, and ball retaining plate 130) is equal to the sum of the diameter of the ball 120 and twice the amplitude of the central path curves CS1 and CS2. Therefore, according to the first embodiment, it is possible to make the gearbox thinner.

[0071] B. Second Embodiment: Figure 6 is an exploded perspective view showing the configuration of a gearbox 200 as a second embodiment of the present invention. The gearbox 200 of the second embodiment differs from the gearbox 100 of the first embodiment in that the number of balls 220 is changed, and the number of ball holes 239 formed in the ball retaining plate 230 is changed in accordance with the change in the number of balls 220. Other aspects are the same as the gearbox 100 of the first embodiment, so unless particularly necessary, explanations of the contents common to the first embodiment will be omitted.

[0072] In the second embodiment of the reduction gear 200, elements that have the same configuration as the reduction gear 100 of the first embodiment are given the same reference numerals as the reduction gear 100, and elements corresponding to elements in the reduction gear 100 have the hundreds digit of their reference numeral changed from "1" to "2". Although the configuration of each ball 220 is the same as the ball 120 of the first embodiment, the number of balls is different, so the reference numerals assigned to the balls 220 are changed in the second embodiment. The same reference numerals are used in each embodiment shown later.

[0073] In the second embodiment, the balls 220 are positioned at equiangular positions satisfying equation (5) among the above equations (4) and (5) which define the arrangement of the balls 220. As described above, there are (MN) rotation angles θ that satisfy equation (5) during one revolution (0≦θ<2π). In the reduction gear 200, the wave number M of the tooth profile 115 formed on the gear portion 112 of the first gear member 110 is set to 20, and the wave number N of the tooth profile 145 formed on the second gear member 140 (gear portion 140) is set to 2, so the number of balls 220 and the number of ball holes 239 are 18 (MN).

[0074] Figures 7 and 8 are explanatory diagrams showing the operation of the reduction gear 200 of the second embodiment. Figures 7 and 8 show the arrangement of the gear portion 112 of the first gear member 110, the ball 220, and the second gear member 140 (gear portion 140) in each state described later.

[0075] Figure 7 shows the state in which the ball retaining plate 230 (Figure 6) is used as a stator and rotational power is input to the second gear member 140 (gear section 140). Specifically, Figures 7(b) to 7(d) show the state in which the second gear member 140 (gear section 140) is rotated from the initial state shown in Figure 7(a) while the rotation angle θ of each ball 220 is kept constant (i.e., the ball retaining plate 230 is fixed).

[0076] As shown in Figure 7, as the gear portion 140 moves in the +θ direction, the individual balls 220 reciprocate in the Z direction. The balls 220 that move in the -Z direction as the gear portion 140 rotates in the +θ direction (shaded balls 220) come into contact with the -θ side surface of the tooth profile 115 formed on the gear portion 112.

[0077] Therefore, as shown in Figure 7, when the rotation angle θ of each ball 220 is kept constant (i.e., the ball holding plate 230 is fixed), when the gear section 140 moves in the +θ direction, the gear section 112 also moves in the +θ direction.

[0078] Furthermore, similar to the first embodiment, the rotational speed of the gear sections 112 and 140 when each ball 220 moves back and forth once in the Z direction is the reciprocal of the wave numbers M and N (20, 2) of the tooth profiles 115 and 145 formed thereon (1 / M = 1 / 20, 1 / N = 1 / 2).

[0079] Thus, in the second embodiment, when the rotation angle θ of the ball 220 is kept constant, that is, when the ball retaining plate 230 (Figure 6) is used as a stator, when rotational power is input to the second gear member 140 (gear section 140), the first gear member 110 having the gear section 112 outputs rotational power that rotates in the same direction, reduced by a reduction ratio of 10 (M / N).

[0080] Figure 8 shows the state in which the first gear member 110 is used as a stator and rotational power is input to the second gear member 140 (gear section 140). Specifically, Figures 8(b) to 8(d) show the state in which the second gear member 140 (gear section 140) is rotated from the initial state shown in Figure 8(a), with the gear section 112 of the first gear member 110 fixed.

[0081] As shown in Figure 8, as the gear portion 140 moves in the +θ direction, the individual balls 220 reciprocate in the Z direction and also move in the -θ direction. As the balls 220 move, the ball retaining plate 230 rotates in the opposite direction to the second gear member 140.

[0082] Furthermore, as described in the first embodiment, the relationship between the rotational speed of the second gear member 140 and the rotational speed of the ball retaining plate 230 when the first gear member 110 is fixed can be calculated using a table-making method or the like.

[0083] Specifically, as shown in Table 2 below, the rotational speeds of the ball retaining plate 230 and the first gear member 110 are calculated for two cases: when the second gear member 140 is rotated by +1 / N with the ball retaining plate 230 fixed, and when the second gear member 140 is rotated by -1 / M to counteract the rotation of the first gear member 110 with the entire assembly glued together. Next, the rotational speeds of the second gear member 140 and the ball retaining plate 230 with the first gear member 110 fixed are calculated by adding the rotational speeds of each part under these two conditions. Then, the reduction ratio when the first gear member 110 is used as a stator and rotational power is input to the second gear member 140 is calculated as the absolute value of the quotient obtained by dividing the rotational speed of the second gear member 140 by the rotational speed of the ball retaining plate 230. [Table 2]

[0084] Thus, when the first gear member 110 is used as a stator, and rotational power is input to the second gear member 140 (gear section 140), the ball retaining plate 230 outputs rotational power that rotates in the opposite direction, reduced by a reduction ratio of 9 (M / N-1).

[0085] The gearbox 200 of the second embodiment differs in the number of balls 220 and the number of ball holes 239 formed in the ball retaining plate 230, but the other configurations are the same as those of the gearbox 100 of the first embodiment (Figure 1). Therefore, according to the second embodiment, as with the first embodiment, the reduction ratio of the gearbox can be flexibly changed, and the durability of the gearbox against thrust loads can be increased, while suppressing the decrease in power transmission efficiency due to thrust loads. Furthermore, the second embodiment also makes it possible to make the gearbox thinner, as with the first embodiment.

[0086] C. Third Embodiment: C1. Gearbox configuration and operation: Figure 9 is an exploded perspective view showing the configuration of a gearbox 300 as a third embodiment of the present invention, and Figure 10 is an explanatory diagram showing the operation of the gearbox 300 of the third embodiment. The gearbox 300 of the third embodiment differs from the gearbox 100 of the first embodiment in that the shape of the tooth profile 315 formed on the gear portion 312 of the first gear member 310 and the shape of the tooth profile 345 formed on the second gear member 340 (gear portion 340) are different. Other aspects are the same as the gearbox 100 of the first embodiment, so unless particularly necessary, explanations of the contents common to the first embodiment will be omitted.

[0087] As described above, in the first embodiment, axial sinusoid curves are used as the central path curves CS1 and CS2 used to determine the shape of the tooth profiles 115 and 145. However, in the third embodiment, axial triangular wave curves are used as the two central path curves CT1 and CT2 (Figure 10) used to determine the shape of the tooth profiles 315 and 345, respectively. Here, an axial triangular wave curve is a curve in which the distance from the axis C is constant (R), and as movement in the circumferential direction (θ direction), i.e., rotation, the Z direction (axis C direction) draws a triangular waveform.

[0088] Similar to the first embodiment, in the third embodiment, the shape of the tooth profile 315 formed on the gear portion 312 of the first gear member 310 is determined by the circumferential trajectory of the ball 120 when it moves along a central path curve CT1 with wavenumber M of 20 on a cylindrical surface with radius R centered on axis C. Similarly, the shape of the tooth profile 345 formed on the second gear member 340 (gear portion 340) is determined by the circumferential trajectory of the ball 120 when it moves along a central path curve CT2 with wavenumber N of 2 on a cylindrical surface with radius R centered on axis C.

[0089] As described above, in the third embodiment, the central path curves CT1 and CT2 are triangular wave curves with the same amplitude in the axial direction, with wavenumbers M and N set to 20 and 2, respectively, and are expressed by the following equations (6a) and (6b), using the amplitude A, wavenumbers M and N (where M and N are natural numbers such that M > N, in the third embodiment, M=20, N=2), rotation angle θ, the position Zo of the center of the central path curve in the Z direction, and the function Tri that represents the triangular wave curve (hereinafter referred to as the "triangular wave function Tri").

number

[0090] Here, the triangular wave function Tri(t) is a periodic function with a period of 2π and a range of -1 to +1, and is a piecewise linear function that is linear in the intervals t from -π to -π / 2, -π / 2 to π / 2, and π / 2 to π. In general, it is expressed by the following equation (7).

number

[0091] Similar to the first embodiment, the positions (rotation angle θ) in which the ball 120 can be placed are the rotation angles θ in which the center position Z of the ball 120 in the Z direction, as expressed by equations (6a) and (6b), are the same, and the rotation angles θ satisfy the following equation (8).

number

[0092] On the other hand, the triangular wave function Tri(t) can be expressed by equation (9) below, using the inverse trigonometric function (arcsin) which takes the principal value, in addition to equation (7) above.

number

[0093] Here, the inverse trigonometric function arcsin is a strictly monotonically increasing function that is continuous in its domain from -1 to +1, so the condition for satisfying equation (8) above is equivalent to the condition for satisfying equation (2). Therefore, in the third embodiment as in the first embodiment, it is possible to place the balls at a rotation angle θ that satisfies equation (2), that is, at a rotation angle θ that satisfies equation (4) or equation (5), and it is possible to place (M+N) or (MN) balls at equiangled positions.

[0094] In the third embodiment of the speed reducer 300, the balls 120 are arranged at equiangular positions that satisfy equation (4) above, similar to the speed reducer 100 of the first embodiment. Since the wavenumber M of the central path curve CT1 is set to 20 and the wavenumber N of the central path curve CT2 is set to 2, the number of balls 120 and the number of ball holes 139 formed in the ball holding plate 130 are both set to 22 (M + N).

[0095] As described above, in the third embodiment, the ball 120 is positioned at equiangled positions that satisfy equation (4) above, but as in the second embodiment, it is also possible to position the ball 220 at equiangled positions that satisfy equation (5) above. In this case, both the number of balls and the number of ball holes formed in the ball retaining plate are set to 18 (MN).

[0096] Figure 10 shows the state in which the first gear member 310 is used as a stator and rotational power is input to the second gear member 340 (gear section 340). Specifically, Figures 10(b) to 10(d) show the state in which the second gear member 340 (gear section 340) is rotated from the initial state shown in Figure 10(a), with the gear section 312 of the first gear member 310 fixed.

[0097] As shown in Figure 10, as the gear section 340 moves in the +θ direction, the individual balls 120 reciprocate in the Z direction and also move in the +θ direction. As the balls 120 move, the ball retaining plate 130 rotates in the same direction as the second gear member 340. The reduction ratio at this time is calculated in the same way as in the first embodiment, and is 11 (M / N+1) from the wave number of tooth profile 315, which is 20 (M), and the wave number of tooth profile 3, which is 2 (N).

[0098] In Figure 10, the first gear member 310 is shown as the stator and rotational power is input to the second gear member 340 (gear section 340). However, it is also possible to use the ball retaining plate 130 as the stator and input rotational power to the second gear member 340 (gear section 340).

[0099] In the third embodiment of the gearbox 300, although the tooth profile 315 formed on the gear portion 312 of the first gear member 310 and the tooth profile 345 formed on the second gear member 340 (gear portion 340) are different, the other configurations are the same as those of the gearbox 100 of the first embodiment (Figure 1). Therefore, according to the third embodiment, as with the first embodiment, the reduction ratio of the gearbox can be flexibly changed, and the durability of the gearbox against thrust loads can be increased, while suppressing the decrease in power transmission efficiency due to thrust loads. Furthermore, in the third embodiment as with the first embodiment, it is possible to make the gearbox thinner.

[0100] As can be seen from Figures 9 and 10, in the third embodiment, by adopting axial triangular wave curves as the central path curves CT1 and CT2, a portion of the tooth profiles 315 and 345 has a planar shape. Therefore, in the third embodiment, the shape of the tooth profiles 315 and 345 is simpler than in the first and second embodiments, where the entire surface of the tooth profiles 115 and 145 is curved. In this respect, the third embodiment is preferable to the first and second embodiments.

[0101] On the other hand, in the third embodiment, compared to the first and second embodiments, when a disc with the same diameter as the ball 120 is moved so that its center follows the central path curve CT1 while maintaining a state perpendicular to the central path curve CT1, the deviation of the shape of the tooth profile 315 from the central path curve CT1 becomes larger in the overlapping region where the area swept by the disc overlaps. As a result, the area that does not contribute to the transmission of rotational power by the ball 120 increases, and there is a risk that the overall rotational power transmission efficiency will decrease. In this respect, the first and second embodiments are preferable to the third embodiment.

[0102] C2. General form of the central path curve: In the third embodiment, the central path curves CT1 and CT2 that determine the shape of the tooth profiles 315 and 345 are axial triangular wave curves represented by equations (6a) and (6b), but the central path curve used for the shape of the tooth profile can be changed in various ways. Specifically, the central path curve used for the shape of the tooth profile can be any strictly monotonic function Fm(t) that is continuous in the domain (t:-1 to +1), and the position in the Z direction can be represented by the following equations (10a) and (10b).

number

[0103] In this case as well, similar to the first to third embodiments, the operation as a gearbox can be achieved by arranging the balls 120 and 220 at a rotation angle θ that satisfies equation (2). However, depending on the strictly monotonic function Fm(t) that defines the center path curve, the shape of the tooth profile may become more complex than when an axial sinusoid curve or an axial triangular wave curve is adopted. In this respect, it is preferable to adopt an axial sinusoid curve or an axial triangular wave curve as the center path curve.

[0104] Furthermore, the curves (center path curves) used to determine the shape of the tooth profile, in which the position in the Z direction is represented by the above equations (1a) and (1b), (6a) and (6b), and (10a) and (10b), are all curves in which the distance from the axis C is constant (=R), and as movement in the circumferential direction (θ direction), i.e., rotation, the Z direction (axis C direction) draws a waveform derived from a sine wave using a strictly monotonic function. For this reason, in the present invention and this specification, these curves are collectively referred to as axial sinusoid induction curves.

[0105] D. Fourth Embodiment: Figure 11 is an exploded perspective view showing the configuration of a gearbox 400 as a fourth embodiment of the present invention. The gearbox 400 of the fourth embodiment differs from the gearbox 100 of the first embodiment in that the configuration of the first gear member 410 and the second gear member 440 has been changed, and the ball retaining plate 430 has been made thinner to avoid interference between the first gear member 410 and the second gear member 440 and the ball retaining plate 430. Other aspects are the same as the gearbox 100 of the first embodiment, so unless particularly necessary, explanations of the contents common to the first embodiment will be omitted.

[0106] Figure 12 is an explanatory diagram showing the configuration and arrangement of the first gear member 410, ball 120, ball retaining plate 430, and second gear member 440 in the reduction gear 400 of the fourth embodiment. Figure 12(a) shows a cross-section of the reduction gear 400 cut in the XZ plane including the axis C, and Figure 12(b) shows a cross-section of the reduction gear 400 cut by a cylindrical plane with radius R centered on the axis C. Note that in Figure 12(b), for convenience of illustration, the ball retaining plate 430 is not shown and the hatching of the ball 120 is omitted.

[0107] As shown in Figure 12, on the surface of the gear portion 412 of the first gear member 410 where the tooth profile 415 is formed, a groove 417 with a rectangular cross-section and width W is formed at a position where the distance from the axis C is R. Similarly, on the surface of the second gear member 440 (gear portion 440) where the tooth profile 445 is formed, a groove 447 with a rectangular cross-section and width W is formed at a position where the distance from the axis C is R. Therefore, the ball 120 comes into contact with the gear portions 412 and 440 at a position where the distance from the axis C is Rn (RW / 2) and at a position where the distance from the axis C is Rx (= R + W / 2).

[0108] Therefore, in the fourth embodiment, the tooth profile 415 of the gear portion 412 is determined based on the contour curve on the gear portion 412 side of two contour curves (not shown) drawn by the outer circumferential trajectory when the ball 120 moves along the central path curve CS1 on a cylindrical surface with radius Rn centered on the axis C. Specifically, the shape of the tooth profile 415 is the shape obtained by extending the said contour curve in the radial direction.

[0109] Similarly, the tooth profile 445 of the gear portion 440 is determined based on the contour curve on the gear portion 440 side of two contour curves (not shown) drawn by the outer circumferential trajectory of the ball 120 when it moves along the central path curve CS2 on a cylindrical surface with radius Rn centered on axis C. Specifically, the shape of the tooth profile 445 is the shape obtained by extending the said contour curve in the radial direction.

[0110] Thus, in the fourth embodiment as well, the tooth profiles 415 and 445 formed on the gear portions 412 and 440 are determined based on the trajectory of the outer circumference of the ball 120 when it moves along the central path curves CS1 and CS2, which are axial sinusoid curves with wave numbers M and N (where M and N are natural numbers such that M > N). Therefore, when the ball 120 is moved (rotated) in the θ direction relative to the gear portions 412 and 440 with respect to the contact portion 421 of the ball 120, whose distances from the axis C are Rn and Rx, the center of the ball 120 moves along the central path curves CS1 and CS2.

[0111] As can be seen from the above explanation, in the fourth embodiment as well, since the center of the ball 120 moves along the center path curves CS1 and CS2, similar to the first embodiment, when the ball retaining plate 430 is used as a stator, and rotational power is input to the second gear member 440, the first gear member 410 outputs rotational power that rotates in the opposite direction, reduced by a reduction ratio of 10 (M / N). Also, when the first gear member 410 is used as a stator, and rotational power is input to the second gear member 440, the ball retaining plate 430 outputs rotational power that rotates in the same direction, reduced by a reduction ratio of 11 (M / N+1).

[0112] In the fourth embodiment of the gearbox 400, grooves 417 and 447 are formed on the surfaces where the tooth profiles 415 and 445 of the gear sections 412 and 440 are formed, respectively, and the shape of the tooth profiles 415 and 445 is changed in accordance with the formation of the grooves 417 and 447. However, the other configurations are the same as those of the gearbox 100 of the first embodiment (Figure 1). Therefore, according to the fourth embodiment, as with the first embodiment, the reduction ratio of the gearbox can be flexibly changed, and the durability of the gearbox against thrust loads can be increased, while suppressing the decrease in power transmission efficiency due to thrust loads.

[0113] Furthermore, as is clear from the above description and Figure 12(a), in the gearbox 400 of the fourth embodiment, the length (thickness) in the axial direction C of the mechanism directly involved in the reduction operation (tooth profiles 415, 445, grooves 417, 447, ball 120, and ball retaining plate 430) is shorter (thinner) than the sum of the diameter of the ball 120, twice the amplitude of the central path curves CS1, CS2, and twice the depth of the two grooves 417, 447. Therefore, even with the fourth embodiment, it is possible to make the gearbox thinner.

[0114] In the fourth embodiment, 22(M+N) balls 120 are arranged at equiangular positions satisfying equation (4) above, but as in the second embodiment, it is also possible to arrange the balls 220 at equiangular positions satisfying equation (5) above. In this case, both the number of balls and the number of ball holes formed in the ball retaining plate are set to 18(MN).

[0115] Furthermore, in the fourth embodiment, rectangular grooves 417 and 447 are formed on the surfaces where the tooth profiles 415 and 445 of the gear sections 412 and 440 are formed. However, the shape of the grooves can be changed in various ways as long as the edges of the grooves or the inner surfaces of the grooves come into contact with the ball 120. For example, it is possible to form grooves with triangular or arc-shaped cross-sections on the surfaces where the tooth profiles of the gear sections are formed. In this case as well, the shape of the tooth profile is determined based on the outer circumferential trajectory when the ball 120 moves along the central path curves CS1 and CS2.

[0116] In the fourth embodiment, grooves 417 and 447 are provided on the surfaces where the tooth profiles 415 and 445 of the gear portions 412 and 440 are formed, thereby more reliably restricting the radial movement of the ball 120. As a result, the generation of vibrations associated with the radial movement of the ball 120 can be suppressed. In this respect, the fourth embodiment is preferable to the first to third embodiments. On the other hand, the first to third embodiments are preferable to the fourth embodiment in that the shape of the surfaces where the tooth profiles 115, 315, 145, and 345 are formed can be made simpler.

[0117] E. Variations: The present invention is not limited to the embodiments described above, and can be implemented in various forms without departing from its spirit, for example, the following modifications are also possible.

[0118] E1. Variation 1: In each of the above embodiments, balls 120 and 220 are used as rolling elements that are sandwiched and rolled between the gear portions 112, 312, and 412 of the first gear members 110, 310, and 410 and the second gear members 140, 340, and 440 (gear portions 140, 340, and 440). However, various shapes of members having axial symmetry can be used as rolling elements. For example, instead of balls 120 and 220, members in the shape of a spheroid, cylinder, or frustocone can be used as rolling elements.

[0119] In this case, the rolling element retaining plates corresponding to the ball retaining plates 130, 230, and 430 have rolling element retaining holes formed in them to restrict the movement of the rolling elements in the circumferential and radial directions relative to the rolling element retaining plate, thereby retaining the rolling elements. These holes are sized to match the outer shape of the rolling elements when the axis of symmetry of the rolling elements is arranged parallel to the radial direction.

[0120] Furthermore, by determining the shape of the tooth profile formed on each of the two gear sections based on the outer circumferential trajectory of the rolling element when the center of the rolling element moves along each of the two central path curves, with the axis of symmetry of the rolling element oriented radially, it is possible to flexibly change the reduction ratio, and a reduction gear can be realized that has higher durability against thrust loads and suppresses the reduction in power transmission efficiency due to thrust loads. In this case as well, similar to the first to fourth embodiments, the reduction gear can be made thinner.

[0121] However, by using balls as the rolling elements, the axis of symmetry of the rolling elements does not deviate from the radial direction, and the rolling elements (balls) can be rolled more appropriately. Therefore, it is preferable to use balls as the rolling elements.

[0122] E2. Modification example 2: In each of the above embodiments, the number of balls 120, 220 and the number of ball holes 139, 239, 439 formed in the ball retaining plates 130, 230, 430 are defined as the sum (M+N) or difference (MN) of the wavenumbers M of the central path curves CS1, CT1 (tooth profiles 115, 315, 415) and the wavenumbers N of the central path curves CS2, CT2 (gear sections 145, 345, 445). However, the number of balls and the number of ball holes can be less than the sum (M+N) or difference (MN) of the wavenumbers depending on the equiangular positions where the balls are arranged. However, it is preferable that the number of balls and ball holes be 3 or more, in order to suppress the tilt of the axial direction of the two gear parts, and it is even more preferable that the number of balls and ball holes be (M+N) or (MN), in order to increase the number of balls that contribute to the transmission of rotational power and to increase the efficiency of rotational power transmission. [Explanation of Symbols]

[0123] 100,200,300,400...Reducer 110, 310, 410… First gear member 111,311,411…Cylindrical part 112,312,412… Gear section 115,315,415… tooth marks 118,318,418…center hole 120,220... balls 130, 230, 430... Ball holding plate 138,238,438…center hole 139,239,439...ball holes 140, 340, 440… Second gear component 145,345,445…tooth marks 148,348,448…center hole 417,447…Groove 421... Contact area C…Axis center CS1, CS2, CT1, CT2... Central path curves PC...Central Route T11, T12, T21, T22... Contour curves

Claims

1. A reduction gear that outputs reduced rotational power in response to an input of rotational power rotating around an axis, Multiple rolling elements, A rolling element holding plate that allows the rolling element to move in the axial direction, restricts the circumferential and radial movement of the rolling element's rotation, and holds the plurality of rolling elements such that the axis of symmetry of the rolling element faces the radial direction, The plurality of rolling elements and the rolling element retaining plate are stacked in the axial direction, and the first and second gear sections are in constant contact with at least a portion of the plurality of rolling elements, Equipped with, The first and second gear sections have first and second tooth profiles formed on the surfaces facing the plurality of rolling elements and the rolling element retaining plates, respectively. The first and second tooth profiles are determined based on the trajectory of the outer circumference of the rolling element when the center of the rolling element moves along an axial sinusoidal guide curve, where the distance from the axis and amplitude are set to be the same at wavenumbers M and N (where M and N are natural numbers such that M > N), respectively. The rotational power is input to the second gear section, and the reduced rotational power is output from the other of the first gear section and the rolling element retaining plate, with the other of the first gear section and the rolling element retaining plate fixed in the direction of rotation. reducer.

2. The gearbox according to claim 1, further, The first gear section, the rolling element retaining plate, and the second gear section are provided with a cylindrical aligning section whose side surface extends in the axial direction, located at the center of any one of them. A gearbox in which the first gear section, the rolling element retaining plate, and the remaining two centers of the second gear section each have a central hole formed therein that has an inner diameter larger than the outer diameter of the self-aligning section and penetrates in the axial direction.

3. The gearbox according to claim 2, wherein the self-aligning portion is provided in either the first or second gear portion.

4. The gearbox according to any one of claims 1 to 3, wherein the number of rolling elements is either (M + N) or (M - N).

5. The speed reducer according to any one of claims 1 to 3, wherein the rolling element is a ball, and the rolling element holding plate is a plate-shaped member having the same number of circular ball holes that penetrate in the axial direction as the number of rolling elements.

6. The gearbox according to claim 5, wherein grooves are formed on the surfaces on which the first and second tooth profiles are formed, at positions where the distance from the axis is the same as the axial sinusoidal guide curve, and the edge or inner surface of the grooves contacts the ball.

7. The gearbox according to any one of claims 1 to 3, wherein the axial sinusoidal guide curve is an axial sinusoidal curve.

8. The gearbox according to any one of claims 1 to 3, wherein the axial sinusoidal induction curve is an axial triangular wave curve.

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