Gear pairs, transmissions, and drive systems

Abstract

To provide gear pairs, transmissions, and drive systems with optimal tooth profile curves tailored to specific applications while suppressing angular transmission errors. [Solution] A gear pair comprising an internal gear having N+1 internal teeth, at least a portion of which are drawn by a first tooth profile curve, and an external gear having N external teeth, at least a portion of which are drawn by a second tooth profile curve, which meshes internally with the internal gear, wherein the first tooth profile curve and the second tooth profile curve are formed based on a cycloid curve drawn as the trajectory of a first drawing point located on, inside, or outside the circumference of a first rotation circle rolling around a first base circle, and the cycloid curve formed based on first and second parameters defined as a ratio of rotation circle radii and a combination of drawing point distances is offset by a third parameter P3 to form the first tooth profile curve and the second tooth profile curve.

Description

Technical Field

[0001] The present invention relates to a gear pair, a transmission, and a drive device.

Background Art

[0002] Conventionally, a cycloid gear pair composed of an internal gear and an external gear formed by a tooth profile curve formed by combining a hypocycloid curve and an epicycloid curve is known (see, for example, Patent Document 1).

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] When attempting to adjust the tooth profile of a cycloid gear for purposes such as reducing surface pressure, there is a problem that the angular transmission error increases.

[0005] One object of the present invention is to provide a gear pair, a transmission, and a drive device having an optimal tooth profile curve according to the application while suppressing the angular transmission error in consideration of the above problems.

Means for Solving the Problems

[0006] [1] An internal gear having internal teeth with a tooth number N + 1, at least a part of which is drawn by a first tooth profile curve, and an external gear having external teeth with a tooth number N, at least a part of which is drawn by a second tooth profile curve and internally meshing with the internal gear, where the first tooth profile curve is formed based on a first cycloid curve drawn as a locus of a first drawing point located on, inside, or outside the circumference of a first rolling circle that rolls on a first base circle, The second tooth profile curve is formed based on a second cycloid curve, which is drawn as the trajectory of a second drawing point located on, inside, or outside the circumference of a second rotation circle rolling around a second base circle. Let the radius of the first base circle be the first base circle radius a1. Let the radius of the first inversion be the first inversion radius b1. Let the distance from the center of the first rotation circle to the first drawing point be the first drawing point distance c1. Let the radius of the second base circle be the second base circle radius a2. Let the radius of the second inversion be the second inversion radius b2. Let the distance from the center of the second rotation circle to the second drawing point be the second drawing point distance c2. Let the distance between the center of the first base circle and the center of the second base circle be the eccentricity Ec. The first rotation radius b1, the second rotation radius b2, the first drawing point distance c1, and the second drawing point distance c2 each take positive or negative values. The sign of the first drawing point distance c1 is assumed to be the same as the sign of the first rotation radius b1. The sign of the second drawing point distance c2 is assumed to be the same as the sign of the second rotation radius b2. The first cycloid curve is a hypocycloid curve with a radius of |b1| when the first radius of inversion b1 is a positive value, and an epicycloid curve with a radius of |b1| when the first radius of inversion b1 is a negative value. The second cycloid curve is an epicycloid curve with a radius of |b2| when the second radius of inversion b2 is a positive value, and a hypocycloid curve with a radius of |b2| when the second radius of inversion is a negative value. The first cycloid curve and the second cycloid curve satisfy the following conditions 1, 2, 3, and 4. a1=(N+1)×(b1+b2) …(conditional expression 1) a2=N×(b1+b2) …(conditional expression 2) b1:c1=b2:c2 …(conditional expression 3) Ec=c1+c2 …(conditional expression 4) Let the ratio of the second rotation radius b2 to the first rotation radius b1 (b2 / b1) be the first parameter P1. The second parameter P2 is the eccentricity adjustment amount ((b1+b2)-(c1+c2)), which is the value obtained by subtracting the sum of the first drawing point distance c1 and the second drawing point distance c2 from the sum of the first rotation radius b1 and the second rotation radius b2. The third parameter P3 is defined as the offset amount that offsets the first cycloid curve and the second cycloid curve by the same distance in the normal direction. The first tooth profile curve and the second tooth profile curve are drawn satisfying at least one of the following settings: first setting, second setting, or third setting. The first setting draws the first cycloid curve and the second cycloid curve using the first parameter P1 that satisfies P1 > 1 or P1 < 1. The second setting draws the first cycloid curve and the second cycloid curve using the second parameter P2 satisfying P2≠0. The third setting involves using the third parameter P3 that satisfies P3 ≠ 0 to offset the first cycloid curve and the second cycloid curve in the normal direction by the third parameter P3, thereby obtaining the first tooth profile curve and the second tooth profile curve. Gears.

[0007] According to the above configuration, the first and second tooth profile curves are drawn satisfying at least one of the following first, second, or third settings, allowing for the adoption of a tooth profile different from that of conventional standard cycloidal gears. This makes it possible to provide gear pairs with optimal tooth profile curves tailored to specific applications, such as reducing surface pressure, improving ease of assembly, and increasing transmission efficiency. Furthermore, according to the above configuration, Camus' theorem holds for the gear pair when the first and second tooth profile curves satisfy conditions 1 to 4. In other words, this configuration makes it possible to provide gear pairs that enable smooth meshing while increasing the degree of freedom of the tooth profile and suppressing angular transmission errors.

[0008] [2] The gear pair described in [1], wherein the first tooth profile curve and the second tooth profile curve are drawn satisfying all of the settings of the first setting, the second setting, and the third setting.

[0009] According to the above configuration, by combining the first setting, second setting, and third setting to form the first tooth profile curve and the second tooth profile curve, it is possible to provide a gear pair with an even greater degree of freedom in tooth surface shape.

[0010] [3] The first cycloid curve and the second cycloid curve are drawn using the first parameter P1 which satisfies the first setting and P1 < 1, where both the first eclipse radius b1 and the second eclipse radius b2 are positive values ​​(b1 > 0, b2 > 0), and satisfies the first setting. A gear pair according to [1] or [2], satisfying the third setting, wherein the first cycloid curve and the second cycloid curve are offset radially outward from the first base circle and the second base circle to form the first tooth profile curve and the second tooth profile curve.

[0011] According to the above configuration, it is possible to suppress the increase in surface pressure on the tooth surfaces at the contact point between the external gear and the internal gear. This makes it possible to extend the lifespan of the gear pair.

[0012] [4] The first setting is satisfied, the first radius of rotation is positive, and the second radius of rotation is negative (b1>0, b2<0), The gear pair according to [1], wherein the third setting is satisfied and the second tooth profile curve is formed by offsetting the second cycloid curve radially outward from the second base circle.

[0013] According to the above configuration, it is possible to suppress the increase in surface pressure on the tooth surfaces at the contact point between the external gear and the internal gear. This makes it possible to extend the lifespan of the gear pair.

[0014] [5] Satisfying the first setting, the first rolling circle radius takes a negative value, and the second rolling circle radius takes a positive value (b1 < 0, b2 > 0), The gear pair according to [1], satisfying the third setting, and forming the first tooth profile curve by offsetting the first cycloid curve radially inward from the first basic circle.

[0015] According to the above configuration, it is possible to suppress an increase in the surface pressure of the tooth surface at the contact point between the external gear and the internal gear. Thereby, the long life of the gear pair can be achieved.

[0016] [6] The gear pair according to any one of [1] to [5], satisfying the second setting and using the second parameter P2 satisfying P2 > 0, on which the first cycloid curve and the second cycloid curve are drawn.

[0017] According to the above configuration, since a gap in the eccentric direction can be created between the internal gear and the external gear, the assembly of the gear pair becomes easy.

[0018] [7] The outer shape of the internal teeth is drawn at the portion of the first tooth profile curve that is convex radially inward, The outer shape of the external teeth is drawn at the portion of the second tooth profile curve that is convex radially outward. The gear pair according to any one of [1] to [6].

[0019] According to the above configuration, the tooth tip portion of the internal gear can be formed by the first tooth profile curve, and the tooth tip portion of the external gear can be formed by the second tooth profile curve. Therefore, a gear pair with smooth meshing between the tooth tip portions can be provided.

[0020] [8] At least a part of the bottom of the internal gear is drawn by a third tooth profile curve, At least a part of the bottom of the external gear is drawn by a fourth tooth profile curve, The third tooth profile curve is formed based on a third cycloid curve drawn as the locus of a third drawing point located on, inside, or outside the circumference of a third rolling circle that rolls on the first basic circle. The fourth tooth profile curve is formed based on the fourth cycloid curve, which is drawn as the trajectory of a fourth drawing point located on, inside, or outside the circumference of the fourth inversion circle rolling around the second base circle. The radius of the third inversion, b3, is equal to the radius of the second inversion, b2 (b3=b2). The absolute value of the third drawing point distance c3, which is the distance from the center of the third rotation circle to the third drawing point, is greater than or equal to the absolute value of the second drawing point distance c2 (|c3|≧|c2|), The radius of the fourth inversion, b4, is equal to the radius of the first inversion, b1 (b4=b1). The absolute value of the fourth drawing point distance c4, which is the distance from the center of the fourth rotation circle to the fourth drawing point, is greater than or equal to the absolute value of the first drawing point distance c1 (|c4|≧|c1|), When the third cycloid curve is offset by a third offset amount in the normal direction to form the third tooth profile curve, the third offset amount is set to be in the same direction as the offset direction of the second tooth profile curve and to not interfere with the second tooth profile curve during meshing. The gear pair according to any one of [1] to [7], wherein the fourth tooth profile curve is formed by offsetting the fourth cycloid curve in the normal direction by a fourth offset amount, the fourth offset amount is set so as not to interfere with the first tooth profile curve during meshing.

[0021] According to the above configuration, interference between the third tooth profile curve, which constitutes the tooth root of the internal gear, and the second tooth profile curve of the external gear can be suppressed when the internal gear and external gear mesh together. Similarly, interference between the fourth tooth profile curve, which constitutes the tooth root of the external gear, and the first tooth profile curve of the internal gear can be suppressed when the internal gear and external gear mesh together.

[0022] [9] The third drawing point distance c3 is equal to the second drawing point distance c2 (c3=c2), The distance c4 of the fourth drawing point is equal to the distance c1 of the first drawing point (c4=c1), The third offset amount is equal to the third parameter P3 (d3=P3), The fourth offset amount is equal to the third parameter P3 (d4=P3), as described in [8] for the gear pair.

[0023] With the above configuration, smooth meshing can be achieved by avoiding interference between the third tooth profile curve that constitutes the tooth root of the internal gear and the second tooth profile curve of the external gear. Similarly, smooth meshing can be achieved by avoiding interference between the fourth tooth profile curve that constitutes the tooth root of the external gear and the first tooth profile curve of the internal gear.

[0024]

[10] The outer shape of the tooth root of the internal gear is drawn in the portion of the third tooth profile curve that is concave toward the radially outward direction, The gear pair according to [8] or [9], wherein the outer shape of the tooth root of the external gear is drawn in the portion of the fourth tooth profile curve that is concave radially inward.

[0025] According to the above configuration, the concave shape of the tooth root of the internal gear and the concave shape of the tooth root of the external gear can be formed by a tooth profile curve based on a cycloid curve. Therefore, by avoiding interference between the tooth tip and tooth root, a gear pair with smooth meshing can be provided.

[0026]

[11] In the internal gear, the first tooth profile curve and the third tooth profile curve are smoothly connected by a Bézier curve. The gear pair according to any one of [8] to

[10] , wherein the second tooth profile curve and the fourth tooth profile curve are smoothly connected by a Bézier curve in the external gear.

[0027] According to the above configuration, the connection between the first tooth profile curve and the third tooth profile curve in the internal gear can be smoothly connected by a Bézier curve. Similarly, the connection between the second tooth profile curve and the fourth tooth profile curve in the external gear can be smoothly connected by a Bézier curve.

[0028]

[12] The gear pair described in

[11] , wherein the Bézier curve is a cubic Bézier curve defined by four control points.

[0029] According to the above configuration, by connecting the first tooth profile curve and the third tooth profile curve, or the second tooth profile curve and the fourth tooth profile curve, with a cubic Bézier curve, a tooth profile with a smoothly changing curvature direction can be formed.

[0030]

[13] A transmission having a gear pair as described in any one of items [1] to

[12] .

[0031] According to the above configuration, a transmission with suppressed angular transmission errors can be provided.

[0032] A drive system for a human-powered vehicle, including the transmission described in

[14]

[13] .

[0033] According to the above configuration, a drive device that suppresses angular transmission errors can be provided. [Effects of the Invention]

[0034] According to the present invention, it is possible to provide a gear pair, a transmission, and a drive device having an optimal tooth profile curve according to the application while suppressing angular transmission errors. [Brief explanation of the drawing]

[0035] [Figure 1] A side view showing a human-powered vehicle equipped with a drive device according to one embodiment. [Figure 2] A schematic diagram of a drive device according to one embodiment. [Figure 3] A schematic diagram illustrating the different types of cycloid curves. [Figure 4] A schematic diagram illustrating the different types of cycloid curves. [Figure 5] Schematic diagram of a standard gear pair. [Figure 6] A partially enlarged view of the standard gear pair shown in Figure 5. [Figure 7] Figure 5 is a partially enlarged view of a standard gear pair, showing the trajectory of the center of rotation. [Figure 8] A front view of a gear pair according to one embodiment. [Figure 9] A partially enlarged view of a gear pair in one embodiment shown in Figure 8. [Figure 10] This diagram illustrates the cycloid curves drawn when the first or fourth transposition radius takes on a positive or negative value, respectively. [Figure 11] This diagram illustrates the cycloid curves drawn when the second or third radius of rotation takes on a positive or negative value, respectively. [Figure 12] A schematic diagram illustrating the progression of meshing between the tooth tips of the internal gear and the tooth tips of the external gear in a cycloidal gear system. [Figure 13] Schematic diagrams of the first and second rotations illustrating the contact points between the internal and external gears of a cycloidal gear. [Figure 14] A diagram showing the relationship between the first inversion circle, the second inversion circle, and the contact point when the first parameter exceeds 1. [Figure 15] A diagram showing the relationship between the first inversion circle, the second inversion circle, and the contact point when the first parameter is between -1 and 0 (exclusive). [Figure 16] A diagram showing the relationship between the first inversion circle, the second inversion circle, and the contact point when the second parameter is positive. [Figure 17] A diagram showing the relationship between the first inversion circle, the second inversion circle, and the contact point when the second parameter is negative. [Figure 18] A diagram showing the relationship between the first inversion circle, the second inversion circle, and the contact point when the third parameter is positive. [Figure 19] A diagram showing the relationship between the first inversion circle, the second inversion circle, and the contact point when the third parameter is negative. [Figure 20] A diagram showing the procedure for forming the first tooth profile curve at the tooth tip of an internal gear according to one embodiment. [Figure 21] This figure shows the procedure for forming the second tooth profile curve at the tooth tip of an external gear according to one embodiment. [Figure 22] This is a schematic diagram showing the connection portion of an internal gear in one embodiment. [Figure 23] This is a schematic diagram of the tooth tips of a standard internal gear and a standard external gear that mesh with each other in a standard gear pair. [Figure 24] This is a schematic diagram of the tooth tips of an internal gear and an external gear that mesh with each other in a gear pair according to one embodiment. [Figure 25]This is a schematic diagram of the tooth tips of the internal and external gears that mesh with each other in the gear pair of Modification Example 1. [Figure 26] This figure shows the procedure for forming the second tooth profile curve at the tooth tip of the external gear in modified example 1. [Figure 27] This is a schematic diagram of the tooth tips of the internal and external gears that mesh with each other in the gear pair of modified example 2. [Modes for carrying out the invention]

[0036] A gear pair, a transmission, and a drive unit according to an embodiment of the present invention will be described with reference to the drawings. In the description of the embodiment, components having the same or similar function are denoted by the same reference numeral. Duplication of these components may be omitted. The drawings are schematic or conceptual, and the relationship between the thickness and width of each part, the ratio of sizes between parts, etc., are not necessarily identical to those of actual objects.

[0037] (Drive system) Figure 1 is a side view showing a human-powered vehicle 1 equipped with a drive unit 6 according to this embodiment. The human-powered vehicle 1 includes a vehicle frame 2, rear wheels 3, front wheels 4, a drivetrain 5, and a drive unit 6. The vehicle frame 2 is supported by the rear wheels 3 and the front wheels 4.

[0038] Drivetrain 5 is, for example, a chain drive type drivetrain. Drivetrain 5 includes a crank 5a, a front sprocket 5b, a rear sprocket 5c, and a chain 5d.

[0039] The crank 5a includes a crankshaft 5e extending around the crank axis J1, and crank arms 5f provided at both ends of the crankshaft 5e. The crankshaft 5e is rotatably supported by the vehicle frame 2 around the crank axis J1.

[0040] The front sprocket 5b is connected to the crank 5a. The front sprocket 5b rotates together with the crank 5a around the crank axis J1. The rear sprocket 5c is connected to the rear wheel 3. The rear sprocket 5c is rotatable together with the rear wheel 3 around its central axis. The chain 5d is wrapped around the front sprocket 5b and the rear sprocket 5c. The chain 5d transmits the rotation of the front sprocket 5b to the rear sprocket 5c.

[0041] Figure 2 is a schematic diagram of the drive unit 6. The drive unit 6 is connected to the crankshaft 5e. The drive unit 6 includes a motor 8, a transmission 7 connected to the motor 8, a power transmission unit 9 connected to the transmission 7, and a housing 6a that houses the motor 8, the transmission 7, and the power transmission unit 9. The power from the motor 8 is transmitted to the crankshaft 5e via the transmission 7 and the power transmission unit 9. In this way, the drive unit 6 provides propulsion to the human-powered vehicle 1.

[0042] Motor 8 is, for example, an electric motor connected to a battery (not shown). The rotation axis J2 of motor 8 is, for example, arranged parallel to the crank axis J1. Power from motor 8 is transmitted to the transmission 7.

[0043] The transmission 7 reduces the power input from the motor 8 and transmits it to the power transmission unit 9. The transmission 7 has a gear pair 40, which includes an internal gear 10 and an external gear 20. The internal gear 10 is fixed to the housing 6a, for example. The external gear 20 rotates oscillatingly by the power of the motor 8 while meshing with the internal gear 10. The transmission 7 extracts the oscillating rotation of the external gear 20 as rotation around a center O1 and transmits it to the power transmission unit 9, for example.

[0044] The power transmission unit 9 has at least one gear (not shown). One gear of the power transmission unit 9 (not shown) meshes with a gear (not shown) provided on the outer circumference of the crankshaft 5e. The power transmission unit 9 transmits power from the transmission 7 to the drivetrain 5.

[0045] (Cycloid curve) Figures 3 and 4 are schematic diagrams illustrating the cycloid curve. The internal gear 10 and external gear 20 that make up the gear pair 40 are both cycloid gears. First, we will explain the cycloid curve that constitutes a cycloid gear using Figures 3 and 4.

[0046] The cycloid curve is defined by the trajectories traced by drawing points DP1, DP2, DP3, DP4, DP5, and DP6 as the rotating circles RC1 and RC2 roll along the circumference of the base circle BC1. The base circle BC1 is set for the internal gear 10 and the external gear 20, respectively. The base circle BC1 is a hypothetical circle that serves as the basis for the tooth profile curve. The diameter of the base circle BC1 is set to different sizes when defining the tooth profile of the internal gear 10 and when defining the tooth profile of the external gear 20. When defining the tooth profile of the internal gear 10, the diameter of the base circle BC1 is φ / N × (N+1), where φ is the diameter of the base circle BC1 and N is the number of teeth when defining the tooth profile of the external gear 20.

[0047] As shown in Figure 3, the rolling circle RC1 is a circle that rolls inside the base circle BC1, along the outer edge of the base circle BC1. The drawing points DP1, DP2, and DP3 are points set relative to the rolling circle RC1. Drawing point DP1 is set on the circumference of the rolling circle RC1. Drawing point DP2 is set inside the rolling circle RC1 (inside the circle). Drawing point DP3 is set outside the rolling circle RC1 (outside the circle).

[0048] As shown in Figure 4, the rolling circle RC2 is a circle that rolls outside the base circle BC1, along the outer edge of the base circle BC1. Drawing points DP4, DP5, and DP6 are points set relative to the rolling circle RC2. Drawing point DP4 is set on the circumference of the rolling circle RC2. Drawing point DP5 is set inside the rolling circle RC2 (inside the circle). Drawing point DP6 is set outside the rolling circle RC2 (outside the circle).

[0049] Generally, a cycloid curve drawn as the trajectory of a drawing point of a rolled circle outside a base circle is called an epicycloid curve, and a cycloid curve drawn as the trajectory of a drawing point of a rolled circle inside a base circle is called a hypocycloid curve. On the other hand, a cycloid curve drawn as the trajectory of a drawing point inside a rolled circle is called a curate cycloid curve, and a cycloid curve drawn as the trajectory of a drawing point outside a rolled circle is called a prolate cycloid curve.

[0050] As shown in Figures 3 and 4, the cycloid curve has different shapes depending on the combination of the inversion circles RC1, RC2 and the plotting points DP1, DP2, DP3, DP4, DP5, DP6. Multiple cycloid curves with different shapes include the hypocycloid curve La1, the curate hypocycloid curve La2, the prolate hypocycloid curve La3, the epicycloid curve La4, and the curate epicycloid curve La5 and the prolate epicycloid curve La6.

[0051] As shown in Figure 3, the hypocycloid curve La1 is drawn by the trajectory of the plotting point DP1 as the rotating circle RC1 rolls around the base circle BC1. The plotting point DP1 is in contact with the base circle BC1. As the rotating circle RC1 rolls circumferentially in one direction inside the base circle BC1, the plotting point DP1 passes radially inside the base circle BC1 and is in contact with the base circle BC1 again. As a result, the hypocycloid curve La1 is drawn as a concave shape that is indented radially inward. As the rotating circle RC1 completes one revolution around the base circle BC1, the hypocycloid curve La1 is drawn so that multiple concave shapes are continuously arranged in the circumferential direction of the base circle BC1.

[0052] The Curtate hypocycloid curve La2 is drawn by the trajectory of the plotting point DP2 as the devolving circle RC1 rolls around the base circle BC1. Since the plotting point DP2 is set inside the devolving circle RC1, the Curtate hypocycloid curve La2 does not contact the base circle BC1. As the devolving circle RC1 completes one revolution around the base circle BC1, the Curtate hypocycloid curve La2 is drawn inside the base circle BC1 such that convex portions projecting radially outward and concave portions recessing radially inward are alternately arranged in the circumferential direction of the base circle BC1.

[0053] The prolate hypocycloid curve La3 is drawn by the trajectory of the plotting point DP3 as the devolving circle RC1 rolls around the base circle BC1. Since the plotting point DP3 is set outside the devolving circle RC1, the prolate hypocycloid curve La3 intersects the base circle BC1. The prolate hypocycloid curve La3 itself also intersects the base circle BC1 radially inward. As the devolving circle RC1 completes one revolution around the base circle BC1, the curate hypocycloid curve La2 is drawn such that the portion that intersects itself and the concave portion that indents radially inward around the base circle BC1 are arranged alternately along the circumferential direction of the base circle BC1.

[0054] As shown in Figure 4, the epicycloid curve La4 is drawn by the trajectory of the drawing point DP4 as the derotation circle RC2 rolls around the base circle BC1. Since the derotation circle RC2 is located outside the base circle BC1, the epicycloid curve La4 is drawn such that, in the circumferential direction of the base circle BC1, a series of convex portions projecting radially outward from the base circle BC1 are arranged.

[0055] The Carteight epicycloid curve La5 is drawn by the trajectory of the drawing point DP5 as the devolving circle RC2 rolls around the base circle BC1. Since the devolving circle RC2 is located outside the base circle BC1, the Carteight epicycloid curve La5 is drawn outside the base circle BC1 such that concave portions that are recessed radially inward and convex portions that are projected radially outward are alternately arranged in the circumferential direction of the base circle BC1.

[0056] The prolate epicycloid curve La6 is drawn by the trajectory of the drawing point DP6 as the devolving circle RC2 rolls around the base circle BC1. Since the devolving circle RC2 is located outside the base circle BC1, the prolate epicycloid curve La6 is drawn such that the portion that intersects itself and the convex portion that projects radially outward from the base circle BC1 are continuous in the circumferential direction of the base circle BC1.

[0057] Due to the property that the transposition circles RC1 and RC2 roll smoothly on the base circle BC1, the normal to any point on these cycloid curves La1, La2, La3, La4, La5, La6 is a straight line that passes through the point of contact between the transposition circles RC1 and RC2 and the base circle BC1, starting from any point on the cycloid curves La1, La2, La3, La4, La5, La6.

[0058] (Standard cycloidal gear pair) Figure 5 is a schematic diagram of a standard cycloidal gear pair 940. The gear pair 40 of this embodiment has a configuration that is an evolution of the standard cycloidal gear pair 940 described below. For this reason, the standard cycloidal gear pair 940 will be described first.

[0059] In the following description, a standard cycloidal gear pair is referred to as the standard gear pair 940, and the internal and external gears that make up the standard gear pair 940 are referred to as the standard internal gear 910 and the standard external gear 920, respectively. The number of teeth of the standard external gear 920, N+1, is 1 less than the number of teeth of the standard internal gear 910, N (where N is a natural number). The standard external gear 920 meshes internally with the standard internal gear 910. The first base circle 912 and the second base circle 922 are set so that their radii are in the ratio N+1:N, and are arranged so that a portion of them is inscribed within the base circle. The center O1 of the first base circle 912 and the center O2 of the second base circle 922 are located at a distance of eccentricity Ec9.

[0060] The tooth profile of the standard internal gear 910 is drawn with respect to the first base circle 912. The standard internal gear 910 has a tooth tip portion 911A located radially inward with respect to the first base circle 912, and a tooth root portion 911B located radially outward with respect to the first base circle 912.

[0061] Similarly, the tooth profile of the external gear 920 is drawn with respect to the second base circle 922. The external gear 920 has a tooth tip portion 921A located radially outward with respect to the second base circle 922, and a tooth root portion 921B located radially inward with respect to the second base circle 922.

[0062] Figures 6 and 7 are partially enlarged views showing the tooth profile configuration of the standard gear pair 940 in Figure 5. As shown in Figure 6, the tooth tip portion 911A of the standard internal gear 910 consists of a first cycloid curve L915A. The first cycloid curve L915A is drawn as the trajectory of a first drawing point 914A located on the circumference of a first rotation circle 913A that rolls on the first base circle 912 while being inscribed in the first base circle 912. In other words, the first cycloid curve L915A is a hypocycloid curve.

[0063] The tooth root 911B of the standard internal gear 910 consists of a third cycloid curve L915B. The third cycloid curve L915B is drawn as the trajectory of a third drawing point 914B located on the circumference of a third rotation circle 913B that rolls on the first base circle 912 while being tangent to the first base circle 912. In other words, the third cycloid curve L915B is an epicycloid curve.

[0064] The tooth tip 921A of the standard external gear 920 consists of a second cycloid curve L925A. The second cycloid curve L925A is drawn as the trajectory of a second drawing point 924A located on the circumference of a second rotation circle 923A that rolls on the second base circle 922 while being tangent to the second base circle 922. In other words, the second cycloid curve L925A is an epicycloid curve.

[0065] The tooth root 921B of the standard external gear 920 consists of a fourth cycloid curve L925B. The fourth cycloid curve L925B is drawn as the trajectory of a fourth drawing point 924B located on the circumference of a fourth inclination 923B that rolls on the second base circle 922 while being inscribed in the second base circle 922. In other words, the fourth cycloid curve L925B is a hypocycloid curve.

[0066] Here, the parameters for the standard gear pair 940 are defined as follows. Let the radius of the first base circle 912 be the radius a91 of the first base circle. Let the radius of the second base circle 922 be the second base circle radius a92. Let the radius of the first rotation circle 913A be the first rotation radius b91. Let the radius of the second inversion circle 923A be the second inversion radius b92. Let the radius of the third inversion circle 913B be the third inversion radius b93. Let the radius of the fourth inversion circle 923B be the fourth inversion radius b94.

[0067] In the standard gear pair 940, the first rotation radius b91, the second rotation radius b92, the third rotation radius b93, and the fourth rotation radius b94 are equal to each other (b91=b92=b93=b94).

[0068] Next, we will examine the angular transmission error in the standard gear pair 940. Figure 6 illustrates the point of contact A between the first cycloid curve L915A and the second cycloid curve L925A. Figure 6 also illustrates the point of tangency B between the first inversion circle 913A and the first base circle 912, where point of contact A coincides with the first drawing point 914A. Furthermore, Figure 6 illustrates the point of tangency C between the second inversion circle 923A and the second base circle 922, where point of contact A coincides with the second drawing point 924A.

[0069] The first cycloid curve L915A and the second cycloid curve L925A are tangent at point A. Furthermore, due to the properties of cycloid curves as described above, the normal of L915A at point A is a straight line passing through points A and B, and the normal of L925A at point A is a straight line passing through points A and C. Therefore, line segments AB and AC coincide with the common normal of the first cycloid curve L915A and the second cycloid curve L925A at point A. In the following explanation, the straight line passing through points B, A, and C will be referred to as the normal BC.

[0070] On the circumference of the first base circle 912, there are the same number of tooth tips 911A and tooth roots 911B as the number of teeth N+1 of the standard internal gear 910. Therefore, the radius a91 of the first base circle is N+1 times the sum of the first rotation radius b91 and the third rotation radius b93. a91 = (N+1) × (b91 + b93)

[0071] Similarly, since the same number of tooth tips 921A and tooth roots 921B as the number of teeth N of the external gear are arranged on the circumference of the second base circle, the radius a92 of the second base circle is N times the sum of the second rotation radius b92 and the fourth rotation radius b94. a92 = N × (b92 + b94)

[0072] Figure 7 illustrates the orbit of the center D of the first rotation 913A (central orbit DO) and the orbit of the center E of the second rotation 923A (central orbit EO). As mentioned above, the length of line segment BO1 (i.e., the radius a91 of the first base circle) and the length of line segment CO2 (i.e., the radius a92 of the second base circle) are in an N+1:N ratio. From the formula for calculating the lengths of the first base circle radius a91 and the second base circle radius a92, the sum of the first inversion radius b91 and the third inversion radius b93 is equal to the sum of the second inversion radius b92 and the fourth inversion radius b94. Also, as previously stated, the 1st to 4th inversion radii b1, b2, b3, and b4 are all equal, so the difference between the length of line segment BO1 (i.e., the radius a91 of the first base circle) and the length of line segment CO2 (i.e., the radius a92 of the second base circle) is equal to two inversion radii (b91 + b92). The distance (Ec9) between the center O1 of the first base circle 912 and the center O2 of the second base circle 922 is equal to this difference because the base circles are tangent to each other. Therefore, the distance between the center D of the first transposition circle 913A and the center O1 of the first base circle 912 (length of line segment DO1) is equal to the distance between the center E of the second transposition circle 923A and the center O2 of the second base circle 922 (length of line segment EO2). Furthermore, since the first cycloid curve L915A and the second cycloid curve L925A are tangent at the point of contact A, the center D, the point of contact A, and the center E are collinear, and the distance between the center D and the center E (length of line segment DE) is equal to Ec9 (Ec9 = b91 + b92).

[0073] In other words, in the standard gear pair 940, the lengths of line segment DO1 and line segment EO2 are equal, and the length of line segment DE is equal to the length of the eccentricity Ec9. From this, the quadrilateral formed by connecting centers D, E, O1, and O2 is always a parallelogram, regardless of the phase of contact point A. Line segments DE and O1O2 always remain parallel, regardless of the position in which the standard internal gear 910 and the standard external gear 920 mesh.

[0074] Assume that on the normal vector BC, there is a pitch point P such that triangle BO1P is similar to triangles BDA and CEA. As described above, even if the contact point A moves (i.e., even if the non-standard gear 920 oscillates and rotates), line segments DE and O1O2 are always parallel. Therefore, regardless of the phase of the contact point A, the similarity relationship between triangle BO1P, triangle BDA, and triangle CEA is always maintained. Consequently, the normal vector BC always passes through one pitch point P, regardless of the phase of the contact point A. From this, the standard gear pair 940 satisfies Camus' theorem. Furthermore, if elastic deformation is not considered, the angular transmission error in the standard gear pair 940 becomes zero, enabling smooth power transmission.

[0075] Conventionally, attempts have been made to design cycloidal gears by changing the parameters of the standard gear pair 940 mentioned above, with the aim of reducing surface pressure and other factors. For example, designs have been attempted in gear pairs where the first rotation radius b91 and the second rotation radius b92 are different from each other, gear pairs where the distance between the first rotation radius b91 and the drawing point are different from each other, and gear pairs where the distance between the second rotation radius b92 and the drawing point are different from each other.

[0076] However, conventional cycloidal gears with varying parameters were not designed based on Camus' theorem, making it impossible to eliminate angular transmission errors and thus preventing smooth power transmission. The inventors devised a design method that allows for zero angular transmission errors even in cycloidal gear pairs that deviate from the standard cycloidal gears, by varying the parameters of the standard gear pair 940 within the range that satisfies Camus' theorem.

[0077] (Gear pair of the embodiment) Figure 8 is a front view of the gear pair 40 of this embodiment. Figure 9 is a partially enlarged view of Figure 8. As shown in Figure 8, the gear pair 40 includes an internal gear 10 and an external gear 20 that meshes internally with the internal gear 10.

[0078] The internal gear 10 is a cycloidal gear centered on the center O1. The internal gear 10 has nine internal teeth 11 that protrude radially inward from the center O1. At least a portion of the internal teeth 11 are drawn by the first tooth profile curve L19A, which will be described later, and at least a portion of them are drawn by the third tooth profile curve L19B, which will be described later.

[0079] The external gear 20 is a cycloidal gear centered on the center O2. The external gear 20 has eight external teeth 21 that project radially outward from the center O2. At least a portion of the external teeth 21 are drawn by the second tooth profile curve L29A described later, and at least a portion of them are drawn by the fourth tooth profile curve L29B described later.

[0080] In the gear pair 40 of this embodiment, the number of teeth of the external gear 20 should be one less than the number of teeth of the internal gear 10. That is, using a natural number N, if the number of teeth of the external gear 20 is N, the number of teeth of the internal gear 10 can be expressed as N+1. The first base circle 12 of the internal gear 10 and the second base circle 22 of the external gear 20 are set so that their radii are in the ratio N+1:N. The center O1 of the first base circle 12 and the center O2 of the second base circle 22 are positioned at a distance of eccentricity Ec, which will be described later.

[0081] The gear pair 40 in this embodiment constitutes the transmission 7 shown in Figure 2. In the transmission 7, the internal gear 10 is fixed to the housing 6a, and the external gear 20 is connected to the output shaft of the motor 8. The external gear 20 can rotate around its center O2 while oscillating around the center O1 of the internal gear 10 as the output shaft of the motor 8 rotates. By oscillating and rotating, the meshing position of the external gear 20 with respect to the internal gear 10 changes. As the meshing position changes, the external gear 20 rotates by the difference in the number of teeth between it and the internal gear 10 each time the output shaft of the motor 8 rotates once. In this embodiment, since the difference in the number of teeth is 1, the external gear 20 rotates by 1 tooth each time the output shaft of the motor 8 rotates once.

[0082] The configuration of the transmission 7 is not limited to this embodiment. For example, the transmission 7 may be connected to the motor 8 and the housing 6a such that the rotational speed of the output shaft increases relative to the rotational speed of the motor 8's output shaft. The transmission 7 may also have multiple gear pairs 40.

[0083] As shown in Figure 9, the tooth profile of the internal gear 10 is drawn with respect to the first base circle 12. The internal gear 10 has a tooth tip 11A, a tooth root 11B, and a connecting portion 11C. The tooth tip 11A is the portion of the tooth profile of the internal gear 10 that is convex radially inward. The tooth root 11B is the portion of the tooth profile of the internal gear 10 that is concave radially outward. The connecting portion 11C is the portion that connects the tooth tip 11A and the tooth root 11B.

[0084] The first tooth profile curve L19A of the tooth tip portion 11A is formed based on the first cycloid curve L15A. The first cycloid curve L15A is drawn as the trajectory of the first drawing point 14A located on, inside, or outside the circumference of the first rotation circle 13A, which rolls on the first base circle 12 while being inscribed in the first base circle 12.

[0085] Similarly, the tooth root 11B is represented by the third tooth profile curve L19B. In the internal gear 10, the third tooth profile curve L19B is formed based on the third cycloid curve L15B. The third cycloid curve L15B is represented as the trajectory of a third drawing point 14B located on, inside, or outside the circumference of a third rotation circle 13B that rolls on the first base circle 12 while being tangent to the first base circle 12.

[0086] The tooth profile of the external gear 20 is drawn with reference to the second base circle 22. The external gear 20 has a tooth tip portion 21A, a tooth root portion 21B, and a connecting portion 21C. The tooth tip portion 21A is the portion of the tooth profile of the external gear 20 that is convex radially outward. The tooth root portion 21B is the portion of the tooth profile of the external gear 20 that is concave radially inward. The connecting portion 21C is the portion that connects the tooth tip portion 21A and the tooth root portion 21B.

[0087] The tooth tip portion 21A is drawn by the second tooth profile curve L29A. In the external gear 20, the second tooth profile curve L29A is formed based on the second cycloid curve L25A. The second cycloid curve L25A is drawn as the trajectory of the second drawing point 24A located on, inside, or outside the circumference of the second rotation circle 23A, which rolls on the second base circle 22 while being tangent to the second base circle 22.

[0088] Similarly, the tooth root 21B is drawn by the fourth tooth profile curve L29B. In the external gear 20, the fourth tooth profile curve L29B is formed based on the fourth cycloid curve L25B. The fourth cycloid curve L25B is drawn as the trajectory of the fourth drawing point 24B located on, inside, or outside the circumference of the fourth inversion circle 23B, which rolls on the second base circle 22 while being inscribed in the second base circle 22.

[0089] Here, the parameters of the gear pair 40 in this embodiment are defined as follows. Let the radius of the first base circle 12 be the radius of the first base circle a1. Let the radius of the first inversion circle 13A be the first inversion radius b1. The distance from the center of the first rotation circle 13A to the first drawing point 14A is defined as the absolute value of the first drawing point distance c1. Let the radius of the second base circle 22 be the second base circle radius a2. Let the radius of the second inversion circle 23A be the second inversion radius b2. The distance from the center of the second rotation circle 23A to the second drawing point 24A is defined as the absolute value of the second drawing point distance c2. Let the radius of the third inversion circle 13B be the third inversion radius b3. The distance from the center of the third rotation circle 13B to the third drawing point 14B is defined as the absolute value of the third drawing point distance c3. Let the radius of the fourth inversion circle 23B be the fourth inversion radius b4. The distance from the center of the fourth transposition circle 23B to the fourth drawing point 24B is defined as the absolute value of the fourth drawing point distance c4. Let Ec be the eccentricity, which is the distance between the center O1 of the first base circle 12 and the center O2 of the second base circle 22.

[0090] Here, the first, second, third, and fourth radii of the rotation circle b1, b2, b3, and b4 can each take on either positive or negative values ​​(b1>0 or b1<0, b2>0 or b2<0, b3>0 or b3<0, b4>0 or b4<0). Similarly, the first, second, third, and fourth drawing point distances c1, c2, c3, and c4 can each take on either positive or negative values ​​(c1>0 or c1<0, c2>0 or c2<0, c3>0 or c3<0, c4>0 or c4<0). The sign of the first drawing point distance c1 coincides with the sign of the first rotation radius b1, the sign of the second drawing point distance c2 coincides with the sign of the second rotation radius b2, the sign of the third drawing point distance c3 coincides with the sign of the third rotation radius b3, and the sign of the fourth drawing point distance c4 coincides with the sign of the fourth rotation radius b4. Note that the first base circle radius a1, the second base circle radius a2, and the eccentricity Ec, which is the distance between the center O1 of the first base circle 12 and the center O2 of the second base circle 22, can only take positive values. Also, since the internal gear 10 meshes with the external gear 20 from the radially outside, it is natural that the first base circle radius a1 is larger than the second base circle radius a2 (a1 > a2).

[0091] Figure 10 illustrates the cycloid curves drawn when the first inversion radius b1 or the fourth inversion radius b4 takes on a positive and negative value, respectively. In Figure 10, the base circle BC1 is either the first base circle 12 or the second base circle 22.

[0092] If the radius b1 of the first inversion is positive, the first inversion 13A is moved by rolling it inscribed in the base circle BC toward one side in the circumferential direction (counterclockwise in Figure 10), thereby drawing one of the hypocycloid curves La1, La2, or La3 as the trajectory of the first drawing point 14A. Similarly, if the radius b4 of the fourth inversion is positive, the fourth inversion 23B is moved by rolling it inscribed in the base circle BC toward one side in the circumferential direction (counterclockwise in Figure 10), thereby drawing one of the hypocycloid curves La1, La2, or La3 as the trajectory of the fourth drawing point 24B.

[0093] If the radius b1 of the first inversion is negative, the first inversion 13A is moved by rolling it circumferentially around the base circle BC towards the other side in the circumferential direction (clockwise in Figure 10), thereby drawing one of the epicycloid curves Lb1, Lb2, or Lb3 as the trajectory of the first drawing point 14A. Similarly, if the radius b4 of the fourth inversion is negative, the fourth inversion 23B is moved by rolling it circumferentially around the base circle BC towards the other side in the circumferential direction (clockwise in Figure 10), thereby drawing one of the epicycloid curves Lb1, Lb2, or Lb3 as the trajectory of the fourth drawing point 24B.

[0094] Figure 11 illustrates the cycloid curves drawn when the second or third inversion radius b2 or b3 takes on a positive or negative value. In Figure 11, the base circle BC1 is either the first base circle 12 or the second base circle 22.

[0095] If the radius b2 of the second inversion is positive, the second inversion 23A is moved by rolling it circumferentially around the base circle BC towards the other side in the circumferential direction (clockwise in Figure 11), thereby drawing one of the epicycloid curves La4, La5, or La6 as the trajectory of the second drawing point 24A. Similarly, if the radius b3 of the third inversion is positive, the third inversion 13B is moved by rolling it circumferentially around the base circle BC towards the other side in the circumferential direction (clockwise in Figure 11), thereby drawing one of the epicycloid curves La4, La5, or La6 as the trajectory of the third drawing point 14B.

[0096] If the radius b2 of the second inversion is negative, the second inversion 23A is moved by rolling it inscribed in the base circle BC toward one side in the circumferential direction (counterclockwise in Figure 11), thereby drawing one of the hypocycloid curves Lb4, Lb5, or Lb6 as the trajectory of the second drawing point 24A. Similarly, if the radius b3 of the third inversion is negative, the third inversion 13B is moved by rolling it inscribed in the base circle BC toward one side in the circumferential direction (counterclockwise in Figure 11), thereby drawing one of the hypocycloid curves Lb4, Lb5, or Lb6 as the trajectory of the third drawing point 14B.

[0097] This section explains the relationship between the values ​​of the first inversion radius b1 and the first drawing point distance c1, and the first cycloid curve L15A. First, let's explain the case where both the first inversion radius b1 and the first drawing point distance c1 are positive values. In this case, the first cycloid curve L15A is a hypocycloid curve with an inversion radius of |b1| if the absolute value of the first drawing point distance c1 is equal to the absolute value of the first inversion radius b1. The first cycloid curve L15A is a curate hypocycloid curve if the absolute value of the first drawing point distance c1 is less than the absolute value of the first inversion radius b1. The first cycloid curve L15A is a prolate hypocycloid curve if the absolute value of the first drawing point distance c1 is greater than the absolute value of the first inversion radius b1.

[0098] Next, we will explain the case where both the first inversion radius b1 and the first drawing point distance c1 are negative values. In this case, the first cycloid curve L15A is an epicycloid curve with an inversion radius of |b1| if the absolute value of the first drawing point distance c1 is equal to the absolute value of the first inversion radius b1. The first cycloid curve L15A is a curate epicycloid curve if the absolute value of the first drawing point distance c1 is less than the absolute value of the first inversion radius b1. The first cycloid curve L15A is a prolate epicycloid curve if the absolute value of the first drawing point distance c1 is greater than the absolute value of the first inversion radius b1.

[0099] In the example shown in Figure 9, the first inversion radius b1 and the first drawing point distance c1 are positive values, and the first cycloid curve L15A is a Carteite hypocycloid curve.

[0100] This section explains the relationship between the values ​​of the second inversion radius b2 and the second drawing point distance c2, and the second cycloid curve L25A. First, let's explain the case where both the second inclination radius b2 and the second drawing point distance c2 are positive values. In this case, the second cycloid curve L25A is an epicycloid curve with an inclination radius of |b2| if the absolute value of the second drawing point distance c2 is equal to the absolute value of the second inclination radius b2. The second cycloid curve L25A is a curate epicycloid curve if the absolute value of the second drawing point distance c2 is less than the absolute value of the second inclination radius b2. The second cycloid curve L25A is a prolate epicycloid curve if the absolute value of the second drawing point distance c2 is greater than the absolute value of the second inclination radius b2.

[0101] Next, we will explain the case where both the second inclination radius b2 and the second drawing point distance c2 are negative values. In this case, the second cycloid curve L25A is a hypocycloid curve with an inclination radius of |b2| if the absolute value of the second drawing point distance c2 is equal to the absolute value of the second inclination radius b2. The second cycloid curve L25A is a curate hypocycloid curve if the absolute value of the second drawing point distance c2 is less than the absolute value of the second inclination radius b2. The second cycloid curve L25A is a prolate hypocycloid curve if the absolute value of the second drawing point distance c2 is greater than the absolute value of the second inclination radius b2.

[0102] In the example shown in Figure 9, the second inversion radius b2 and the second drawing point distance c2 are positive values, and the second cycloid curve L25A is a cartate epicycloid curve.

[0103] This section explains the relationship between the values ​​of the third inversion radius b3 and the third drawing point distance c3, and the third cycloid curve L15B. First, let's explain the case where both the third incline radius b3 and the third drawing point distance c3 are positive values. In this case, the third cycloid curve L15B is an epicycloid curve with an incline radius of |b3| if the absolute value of the third drawing point distance c3 is equal to the absolute value of the third incline radius b3. The third cycloid curve L15B is a curate epicycloid curve if the absolute value of the third drawing point distance c3 is less than the absolute value of the third incline radius b3. The third cycloid curve L15B is a prolate epicycloid curve if the absolute value of the third drawing point distance c3 is greater than the absolute value of the third incline radius b3.

[0104] Next, we will explain the case where both the third incline radius b3 and the third drawing point distance c3 are negative values. In this case, the third cycloid curve L15B is a hypocycloid curve with an incline radius of |b3| if the absolute value of the third drawing point distance c3 is equal to the absolute value of the third incline radius b3. The third cycloid curve L15B is a curate hypocycloid curve if the absolute value of the third drawing point distance c3 is less than the absolute value of the third incline radius b3. The third cycloid curve L15B is a prolate hypocycloid curve if the absolute value of the third drawing point distance c3 is greater than the absolute value of the third incline radius b3.

[0105] In the example shown in Figure 9, the third inversion radius b3 and the third drawing point distance c3 are positive values, and the third cycloid curve L15B is a cartate epicycloid curve.

[0106] This section explains the relationship between the values ​​of the fourth inversion radius b4 and the fourth drawing point distance c4, and the fourth cycloid curve L25B. First, let's explain the case where both the fourth incline radius b4 and the fourth drawing point distance c4 are positive values. In this case, the fourth cycloid curve L25B is a hypocycloid curve with an incline radius of |b4| if the absolute value of the fourth drawing point distance c4 is equal to the absolute value of the fourth incline radius b4. The fourth cycloid curve L25B is a curate hypocycloid curve if the absolute value of the fourth drawing point distance c4 is less than the absolute value of the fourth incline radius b4. The fourth cycloid curve L25B is a prolate hypocycloid curve if the absolute value of the fourth drawing point distance c4 is greater than the absolute value of the fourth incline radius b4.

[0107] Next, we will explain the case where both the fourth transposition radius b4 and the fourth drawing point distance c4 are negative values. In this case, the fourth cycloid curve L25B is an epicycloid curve with a transposition radius of |b4| if the absolute value of the fourth drawing point distance c4 is equal to the absolute value of the fourth transposition radius b4. The fourth cycloid curve L25B is a curate epicycloid curve if the absolute value of the fourth drawing point distance c4 is less than the absolute value of the fourth transposition radius b4. The fourth cycloid curve L25B is a prolate epicycloid curve if the absolute value of the fourth drawing point distance c4 is greater than the absolute value of the fourth transposition radius b4.

[0108] In the example shown in Figure 9, the fourth inversion radius b4 and the fourth drawing point distance c4 are positive values, and the fourth cycloid curve L25B is a Carteite hypocycloid curve.

[0109] (Regarding the tooth tip) Figure 12 schematically illustrates the progression of meshing between the tooth tip 11A of the internal gear 10 and the tooth tip 21A of the external gear 20. As shown in Figure 12, the contact point A between 11A of the internal gear 10 and the tooth tip 21A of the external gear 20 progresses along their respective tooth profiles. The rolling angle α of the first rotation circle 13A forming the tooth tip 11A of the internal gear 10 and the rolling angle β of the second rotation circle 23A forming the tooth tip 21A of the external gear 20 are synchronized with each other.

[0110] For meshing to occur, the circumferential dimensions of the tooth tips 11A of the internal gear 10 and the tooth roots 21B of the external gear 20 must be the same. Therefore, the first rotation radius b1 and the fourth rotation radius b4 are equal (b1=b4). Similarly, the circumferential dimensions of the tooth roots 11B of the internal gear 10 and the tooth tips 21A of the external gear 20 are the same. Therefore, the second rotation radius b2 and the third rotation radius b3 are equal (b2=b3).

[0111] As mentioned above, using the natural number N, the number of teeth on the internal gear 10 is expressed as N+1. As shown in Figure 9, the first oval 13A and the third oval 13B roll alternately on the circumference of the first base circle 12 N+1 times, drawing the first cycloid curve L15A and the third cycloid curve L15B. Therefore, the circumference of the first base circle 12 (2π × a1) is N+1 times the sum of the circumference of the first oval 13A (2π × b1) and the circumference of the third oval 13B (2π × b3). 2π×a1=(N+1)×(2π×b1+2π×b3)

[0112] By utilizing the fact that the third inversion radius b3 is equal to the second inversion radius b2, and by rearranging this equation, the following conditional equation 1 can be derived as the relationship that the first base circle radius a1, the first inversion radius b1, and the second inversion radius b2 must satisfy. a1=(N+1)×(b1+b2) …(conditional expression 1)

[0113] As described above, the number of teeth of the external gear 20 is represented as N. On the circumference of the second base circle 22, the second eclipse 23A and the fourth eclipse 23B roll alternately N times, drawing the second cycloid curve L25A and the fourth cycloid curve L25B. Therefore, the circumference of the second base circle 22 (2π × a²) is N times the sum of the circumference of the second eclipse 23A (2π × b²) and the circumference of the fourth eclipse 23B (2π × b⁴). 2π × a² = N × (2π × b² + 2π × b⁴)

[0114] By utilizing the fact that the fourth inclinometer radius b4 is equal to the first inclinometer radius b1, and by rearranging this equation, the following conditional equation 2 can be derived as the relationship that the second base circle radius a2, the first inclinometer radius b1, and the second inclinometer radius b2 must satisfy. a2=N×(b1+b2) …(conditional expression 2)

[0115] Furthermore, conditions 1 and 2 described above can also be satisfied when either the first inversion radius b1 or the second inversion radius b2 is a negative value. For example, when the second inversion radius b2 is a negative value, the first inversion radius b1 becomes a value sufficiently large compared to the absolute value |b2| of the second inversion radius b2, in order to satisfy conditions 1 and 2 described above.

[0116] Figure 13 is a schematic diagram illustrating the first rotation circle 13A and the second rotation circle 23A at the contact point A between the tooth tip 11A of the internal gear 10 and the tooth tip 21A of the external gear 20. Figure 13 shows the contact point A between the tooth tip 11A of the internal gear 10 and the tooth tip 21A of the external gear 20. Figure 13 also shows the contact point B between the first rotation circle 13A and the first base circle 12, where contact point A coincides with the first drawing point 14A. Furthermore, Figure 13 shows the contact point C between the second rotation circle 23A and the second base circle 22, where contact point A coincides with the second drawing point 24A. In Figure 13, the center of the first rotation circle 13A is denoted as center D, and the center of the second rotation circle 23A is denoted as center E.

[0117] Similar to the standard gear pair 940 (see Figures 6 and 7), the contact point A is located at the intersection of the normal BC and line segment DE. In the example shown in Figure 13, the first drawing point 14A is located within the circle of the first rotation 13A, and the second drawing point 24A is located within the circle of the second rotation 23A. Therefore, the first rotation 13A and the second rotation 23A partially overlap. The first drawing point 14A and the second drawing point 24A overlap at the contact point A.

[0118] Similar to the case of the standard gear pair 940, if gear pair 40 satisfies Camus' theorem, the pitch point P lies on the extension of the normal BC, regardless of the phase of contact point A. Furthermore, in order to obtain such a configuration, triangles BDA and CEA are always similar, regardless of the phase of contact point A. Therefore, for gear pair 40 to satisfy Camus' theorem, the ratio of line segment BD to line segment DA must be equal to the ratio of line segment CE to line segment EA. Here, the dimension of line segment BD is the first inversion radius b1, the dimension of line segment DA is the first drawing point distance c1, the dimension of line segment CE is the second inversion radius b2, and the dimension of line segment EA is the second drawing point distance c2. Thus, the following condition 3 is derived as a necessary condition for gear pair 40 to satisfy Camus' theorem. b1:c1=b2:c2 …(conditional expression 3)

[0119] Furthermore, if gear pair 40 satisfies Camus' theorem, triangles BDA and CEA are always similar to triangle PO2C. In this case, since the angles of each corner are equal, line segments DA and EA are parallel to line segment O1O2. That is, quadrilateral DEO1O2 is always a parallelogram regardless of the phase of contact point A, and the dimension of line segment O1O2 is equal to the sum of the dimensions of line segment DA and line segment EA. In other words, one of the necessary conditions for gear pair 40 to satisfy Camus' theorem is that the dimension of line segment O1O2 is equal to the sum of the dimensions of line segment DA and line segment EA. The dimension of line segment O1O2 is the eccentricity Ec between the first base circle 12 and the second base circle 22. Also, the dimension of line segment DA is the distance c1 of the first drawing point, and the dimension of line segment EA is the distance c2 of the second drawing point. Therefore, the following condition 4 can be derived as a necessary condition for gear pair 40 to satisfy Camus' theorem. Ec=c1+c2 …(conditional expression 4)

[0120] When conditions 1 to 4 are met, the gear pair 40 can satisfy Camus' theorem and reduce angular transmission error. In other words, as long as conditions 1 to 4 are met, freely setting the parameters of the gear pair 40 will not lead to a deterioration of angular transmission error.

[0121] Here, for the tooth tip portions 11A and 21A, a first parameter P1, a second parameter P2, and a third parameter P3 are defined. The first parameter P1, the second parameter P2, and the third parameter P3 will be described in detail below.

[0122] (First parameter P1) In the gear pair 40 of the present embodiment shown in FIG. 9, the first parameter P1 is the ratio of the second rolling circle radius b2 to the first rolling circle radius b1. P1 = b2 / b1

[0123] In the above-described standard gear pair 940 (see FIG. 6), since the first rolling circle radius b1 and the second rolling circle radius b2 are equal to each other, the first parameter P1 is 1. By setting the first parameter P1 to a value other than 1 (that is, P1 > 1 or P1 < 1), a gear pair 40 having characteristics different from those of the standard gear pair 940 can be formed.

[0124] Here, setting P1 > 1 or P1 < 1 for the first parameter P1 is referred to as the first setting. That is, the first setting means drawing the first cycloid curve L15A and the second cycloid curve L25A using the first parameter P1 that satisfies P1 > 1 or P1 < 1.

[0125] FIG. 14 is a diagram showing the relationship among the first rolling circle 13A, the second rolling circle 23A, and the contact point A when P1 > 1. That is, in the example shown in FIG. 14, the first rolling circle radius b1 is smaller than the second rolling circle radius b2 (b1 < b2). When 0 < P1 < 1, the magnitude relationship between the first rolling circle radius b1 and the second rolling circle radius b2 is reversed (b1 > b2).

[0126] FIG. 15 is a diagram showing the relationship among the first rolling circle 13A, the second rolling circle 23A, and the contact point A when -1 < P1 < 0. That is, in the example shown in FIG. 15, the first parameter P1 is less than 1 (P1 < 1). In the example shown in FIG. 15, the first rolling circle radius b1 is a positive value and is larger than the second rolling circle radius b2. Also, the second rolling circle radius b2 is a negative value (b1 > 0 > b2). In this case, the second cycloid curve L25A becomes a hypocycloid curve, a curtate hypocycloid curve, or a prolate hypocycloid curve with a rolling circle radius of |b2| and is concave toward the radially inner side. Therefore, if the second cycloid curve L25A is directly used as the tooth profile curve, the tooth tip portion 21A of the external gear 20 cannot be formed. This is the same even when the first rolling circle radius b1 is negative and the second rolling circle radius b2 is positive (P1 < -1). Therefore, when either the first rolling circle radius b1 or the second rolling circle radius b2 is negative (that is, when P1 < 0), it is necessary to deform the cycloid curve using a third parameter P3 described later (see FIG. 25).

[0127] (Second parameter P2) In the gear pair 40 of the present embodiment shown in FIG. 9, the second parameter P2 is a value obtained by subtracting the sum of the first drawing point distance c1 and the second drawing point distance c2 from the sum of the first rolling circle radius b1 and the second rolling circle radius b2. P2 = (b1 + b2) - (c1 + c2)

[0128] Note that the sum (b1 + b2) of the first rolling circle radius b1 and the second rolling circle radius b2 is the eccentricity between the base circles of the standard gear pair 940 (see FIG. 6). Also, the sum (c1 + c2) of the first drawing point distance c1 and the second drawing point distance c2 is the eccentricity between the base circles when the drawing points are shifted from the circumferences of the rolling circles (conditional expression 4). Therefore, the second parameter P2 can also be defined as the eccentricity adjustment amount when the drawing points are shifted from the circumferences of the rolling circles.

[0129] In the standard gear pair 940 (see Figure 6), the second parameter P2 is 0. By setting the second parameter P2 to a value other than 0 (i.e., P2 ≠ 0), a gear pair 40 with different characteristics from the standard gear pair 940 can be constructed.

[0130] Considering the conditions 1-4 required to satisfy Camus' theorem, in the right-hand side of the above equation representing P2, the term representing the sum of the first transposition radius b1 and the second transposition radius b2 (b1+b2), and the term representing the sum of the first drawing point distance c1 and the second drawing point distance c2 (c1+c2), are always positive. Also, when the second parameter P2 is positive, the first drawing point 14A is located within the circle of the first transposition 13A, and the second drawing point 24A is located within the circle of the second transposition 23A. Also, when the second parameter P2 is negative, the first drawing point 14A is located outside the circle of the first transposition 13A, and the second drawing point 24A is located outside the circle of the second transposition 23A.

[0131] Here, we will refer to setting the second parameter P2 to P2≠0 as the second setting. In other words, the second setting means drawing the first cycloid curve L15A and the second cycloid curve L25A using the second parameter P2 that satisfies P2≠0.

[0132] Figure 16 shows the relationship between the first inversion circle 13A, the second inversion circle 23A, and the contact point A when P2 > 0. In the example shown in Figure 16, the absolute value of the distance c1 to the first drawing point is smaller than the absolute value of the radius b1 of the first inversion circle (|c1| < |b1|), and the first drawing point 14A is located within the circle of the first inversion circle 13A. Furthermore, the absolute value of the distance c2 to the second drawing point is smaller than the absolute value of the radius b2 of the second inversion circle (|c2| < |b2|), and the second drawing point 24A is located within the circle of the second inversion circle 23A. Therefore, the cycloid curves drawn as the trajectories of the first drawing point 14A and the second drawing point 24A, respectively, are Carteight cycloid curves La2 and La5 (see Figures 3 and 4).

[0133] Figure 17 shows the relationship between the first inversion circle 13A, the second inversion circle 23A, and the contact point A when P2 < 0. In the example shown in Figure 17, the absolute value of the distance c1 to the first drawing point is greater than the absolute value of the radius b1 of the first inversion circle (|c1|>|b1|), and the first drawing point 14A is located outside the circle of the first inversion circle 13A. Furthermore, the absolute value of the distance c2 to the second drawing point is greater than the absolute value of the radius b2 of the second inversion circle (|c2|>|b2|), and the second drawing point 24A is located outside the circle of the second inversion circle 23A. Therefore, the cycloid curves drawn as the trajectories of the first drawing point 14A and the second drawing point 24A, respectively, are prolate cycloid curves La3 and La6 (see Figures 3 and 4).

[0134] (Third parameter P3) In the gear pair 40 of this embodiment shown in Figure 9, the third parameter P3 is the offset amount that offsets the first cycloid curve L15A and the second cycloid curve L25A by the same distance in the direction of the normal BC. In the tooth profile curve of this embodiment, the first cycloid curve L15A and the second cycloid curve L25A can be formed by deforming them using the third parameter P3 to create an offset.

[0135] In the standard gear pair 940 (see Figure 6), the third parameter P3 is 0. By setting the third parameter P3 to a value other than 0 (i.e., P3 ≠ 0), a gear pair 40 with different characteristics from the standard gear pair 940 can be constructed.

[0136] Here, setting the third parameter P3 to P3≠0 will be referred to as the third setting. That is, the third setting means using the third parameter P3 that satisfies P3≠0 to offset the first cycloid curve L15A and the second cycloid curve L25A in the normal direction by the third parameter P3, respectively, to obtain the first tooth profile curve L19A and the second tooth profile curve L29A.

[0137] Figure 18 shows the relationship between the first inversion circle 13A, the second inversion circle 23A, and the contact point A when P3 > 0. As shown in Figure 18, the offset amount as the third parameter P3 is defined as positive in the direction away from the centers O1 and O2 of the first base circle 12 and the second base circle 22, on the normal BC at the contact point A. When P3 > 0, the contact point A is offset by the third parameter P3 in the direction away from the centers O1 and O2 on the normal BC defined for all contact points A of the first cycloid curve L15A and the second cycloid curve L25A. Here, the point where the contact point A is offset is called the offset point AA. The first tooth profile curve L19A and the second tooth profile curve L29A are formed by connecting the offset points AA defined for all contact points A.

[0138] Figure 19 shows the relationship between the first inversion circle 13A, the second inversion circle 23A, and the contact point A when P3 < 0. As shown in Figure 19, the offset amount as the third parameter P3 is negative in the direction toward the centers O1 and O2 of the first base circle 12 and the second base circle 22, on the normal BC at the contact point A. When P3 < 0, the contact point A is offset by the third parameter P3 in the direction toward the centers O1 and O2 on the normal BC defined for all contact points A of the first cycloid curve L15A and the second cycloid curve L25A. The first tooth profile curve L19A and the second tooth profile curve L29A are formed by connecting the offset points AA defined for all contact points A.

[0139] The first cycloid curve L15A and the second cycloid curve L25A satisfy Camus' theorem, meaning that the normal BC always passes through the pitch point P regardless of the phase of the contact point A. The first tooth profile curve L19A and the second tooth profile curve L29A are drawn by offsetting the contact point A in the direction of the normal (the direction in which the normal BC extends). Therefore, Camus' theorem is also satisfied in the tooth profile shape after the offset. Furthermore, no gap occurs between the first tooth profile curve L19A and the second tooth profile curve L29A at the offset point AA. That is, in the gear pair 40 that satisfies the third setting, no angular transmission error occurs when the internal gear 10 and the external gear 20 mesh.

[0140] (Regarding the base of the tooth) Next, the tooth roots 11B and 21B of the internal gear 10 and external gear 20 will be described based on Figure 9. The tooth root 11B of the internal gear 10 should have a shape that matches the pitch of the tooth tip 21A of the external gear 20 while suppressing interference with the tooth tip 21A. Similarly, the tooth root 21B of the external gear 20 should have a shape that matches the pitch of the tooth tip 11A of the internal gear 10 while suppressing interference with the tooth tip 11A.

[0141] In the gear pair 40 of this embodiment, the third tooth profile curve L19B of the tooth root 11B of the internal gear 10 and the fourth tooth profile curve L29B of the tooth root 21B of the external gear 20 are formed based on a cycloid curve. This makes it easier to increase the rigidity of the internal gear 10 and the external gear 20 while ensuring smooth meshing between them. Note that the tooth profile curves of the tooth roots 11B and 21B of the internal gear 10 and the external gear 20 do not necessarily have to be based on a cycloid curve.

[0142] In this embodiment, the third rotation radius b3 is equal to the second rotation radius b2 (b3=b2). Also, the fourth rotation radius b4 is equal to the first rotation radius b1 (b4=b1). According to this embodiment, the pitch of the internal gear 10 and the pitch of the external gear 20 can be matched, and smooth meshing can be achieved.

[0143] In this embodiment, the absolute value of the third drawing point distance c3 is greater than or equal to the absolute value of the second drawing point distance c2 (|c3|≧|c2|). Therefore, during meshing, the third cycloid curve L15B drawn by the third drawing point 14B does not interfere with the second cycloid curve L25A drawn by the second drawing point 24A. Thus, interference between the tooth root 11B of the internal gear 10 and the tooth tip 21A of the external gear 20 can be suppressed. Furthermore, in this embodiment, it is even more preferable that the third drawing point distance c3 is equal to the second drawing point distance c2 (c3=c2). This makes it possible to form tooth roots 11B that can smoothly connect the tooth tips 11A of the internal gear 10. Furthermore, the bottom wall thickness of the internal gear 10 can be maximized, and the rigidity of the internal gear 10 can be increased.

[0144] In this embodiment, the absolute value of the fourth drawing point distance c4 is greater than or equal to the absolute value of the first drawing point distance c1 (|c4|≧|c1|). Therefore, during meshing, the fourth cycloid curve L25B drawn by the fourth drawing point 24B does not interfere with the first cycloid curve L15A drawn by the first drawing point 14A. Thus, interference between the tooth root portion 21B of the external gear 20 and the tooth tip portion 11A of the internal gear 10 can be suppressed. Furthermore, in this embodiment, it is even more preferable that the fourth drawing point distance c4 is equal to the first drawing point distance c1 (c4=c1). This makes it possible to form tooth root portions 21B that can smoothly connect the tooth tips 21A of the external gear 20. Furthermore, the tooth root diameter of the external gear 20 can be made as large as possible, and the rigidity of the external gear 20 can be increased.

[0145] As described above, when the gear pair 40 satisfies the third setting, the tooth tip portion 11A of the internal gear 10 is formed by offsetting the first cycloid curve L15A in the normal direction, and the tooth tip portion 21A of the external gear 20 is formed by offsetting the second cycloid curve L25A in the normal direction. In this case, interference with the tooth tip portion 21A of the external gear 20 can be suppressed by offsetting the third cycloid curve L15B in the normal direction for the third tooth profile curve L19B that constitutes the tooth root portion 11B of the internal gear 10. Similarly, interference with the tooth tip portion 11A of the internal gear 10 can be suppressed by offsetting the fourth cycloid curve L25B in the normal direction for the fourth tooth profile curve L29B that constitutes the tooth root portion 21B of the external gear 20. In the following description, the amount of offset when forming the third tooth profile curve L19B is called the third offset amount d3. Similarly, the amount of offset when forming the fourth tooth profile curve L29B is called the fourth offset amount d4.

[0146] Furthermore, the third offset amount d3 and the fourth offset amount d4, like the third parameter P3, can take both positive and negative values, with the direction away from the centers O1 and O2 of the base circles 12 and 22 being considered positive.

[0147] When the third cycloid curve L15B is offset by a third offset amount d3 in the normal direction to form the third tooth profile curve L19B, the third offset amount d3 is set to be in the same direction as the offset direction of the second tooth profile curve L29A so as not to interfere with the second tooth profile curve L29A during meshing. More specifically, the third offset amount d3 should be greater than or equal to the third parameter P3 (d3≧P3). This allows the third tooth profile curve L19B to be positioned radially outward from the second tooth profile curve L29A, thereby suppressing interference between the third tooth profile curve L19B and the second tooth profile curve L29A. Note that the relationship between the third offset amount d3 and the third parameter P3 that must be satisfied (d3≧P3) is valid regardless of the sign of the third offset amount d3 and the third parameter P3.

[0148] In particular, in this embodiment, it is even more preferable that the third offset amount d3 is equal to the third parameter P3 (d3=P3). This makes it possible to form tooth roots 11B that can smoothly connect the tooth tips 11A of the internal gear 10. Furthermore, the bottom wall thickness of the internal gear 10 can be maximized, and the rigidity of the internal gear 10 can be increased.

[0149] When the fourth cycloid curve L25B is offset by a fourth offset amount d4 in the normal direction to form the fourth tooth profile curve L29B, the fourth offset amount d4 is set to be in the same direction as the offset direction of the first tooth profile curve L19A so as not to interfere with the first tooth profile curve L19A during meshing. More specifically, the fourth offset amount d4 should be less than or equal to the third parameter P3 (d4 ≤ P3). This allows the fourth tooth profile curve L29B to be positioned radially inward from the first tooth profile curve L19A, thereby suppressing interference between the fourth tooth profile curve L29B and the first tooth profile curve L19A. Note that the relationship between the fourth offset amount d4 and the third parameter P3 that must be satisfied (d4 ≤ P3) holds regardless of the sign of the fourth offset amount d4 and the third parameter P3.

[0150] In particular, in this embodiment, it is even more preferable that the fourth offset amount d4 is equal to the third parameter P3 (d4=P3). This makes it possible to form tooth roots 21B that can smoothly connect the tooth tips 21A of the external gear 20. Furthermore, the tooth root diameter of the external gear 20 can be made as large as possible, and the rigidity of the external gear 20 can be increased.

[0151] (Features of this embodiment) Next, the specific configuration of the gear pair 40 in this embodiment will be described. The gear pair 40 in this embodiment satisfies all of the first setting, second setting, and third setting.

[0152] Figure 20 is a schematic diagram showing the procedure for forming the first tooth profile curve L19A in this embodiment. Figure 21 is a schematic diagram showing the procedure for forming the second tooth profile curve L29A in this embodiment.

[0153] When forming the tooth profiles of a gear pair 40, first the base circles 12 and 22 of the internal gear 10 and the external gear 20 are set. Next, the tooth profile shapes of the tooth tips 11A and 21A of the internal gear 10 and the external gear 20 are formed. Next, the tooth profile shapes of the tooth roots 11B and 21B of the internal gear 10 and the external gear 20 are formed. Then, in the internal gear 10, the connection portion 11C between the tooth tip 11A and the tooth root 11B is formed, and in the external gear 20, the connection portion 21C between the tooth tip 21A and the tooth root 21B is formed.

[0154] Before forming the gear teeth, a reference base circle is established. By determining the number of teeth of one gear and the base circle diameter of the other gear, the base circle diameter and number of teeth of the internal gear 10 and external gear 20 in the gear pair 40 can be determined. If the base circle diameter a2 and the number of teeth N of the external gear 20 are given, then the number of teeth of the internal gear 10 is N+1, and the base circle diameter a1 is a2 / {N×(N+1)}.

[0155] In forming the tooth tip portions 11A and 21A, first, a first parameter P1 satisfying a first setting and a second parameter P2 satisfying a second setting are determined. Further, using the determined first parameter P1 and second parameter P2, a first cycloid curve L15A (see FIG. 20) and a second cycloid curve L25A (see FIG. 21) are formed.

[0156] Next, a third parameter P3 satisfying a third setting is determined. Further, using the determined third parameter P3, the first cycloid curve L15A is offset in the normal direction to form a first tooth profile curve L19A (see FIG. 20), and the second cycloid curve L25A is offset in the normal direction to form a second tooth profile curve L29A (see FIG. 21).

[0157] As shown in FIG. 9, the first rolling circle radius b1 is larger than the second rolling circle radius b2 (0 < b2 < b1). Also, in the gear pair 40 of the present embodiment, both the first rolling circle radius b1 and the second rolling circle radius b2 take positive values. Therefore, in the gear pair 40 of the present embodiment, the first parameter P1 (= b2 / b1) is a value greater than 0 and less than 1 (0 < P1 < 1).

[0158] In the gear pair 40 of the present embodiment, the second parameter P2 (= (b1 + b2) - (c1 + c2)) is a value exceeding 0 (P2 > 0). In the gear pair 40 of the present embodiment, the first drawing point 14A is located inside the circle of the first rolling circle 13A. Therefore, the absolute value of the first drawing point distance c1 is smaller than the absolute value of the first rolling circle radius b1 (|c1| < |b1|). In the gear pair 40 of the present embodiment, the second drawing point 24A is located inside the circle of the second rolling circle 23A. Therefore, the absolute value of the second drawing point distance c2 is smaller than the absolute value of the second rolling circle radius b2 (|c2| < |b2|).

[0159] In the gear pair 40 of this embodiment, the third parameter P3 is a value greater than 0 (P3>0). As described above, the positive direction of the normal is the direction away from the centers O1 and O2 of the first base circle 12 and the second base circle 22. Therefore, the first cycloid curve L15A and the second cycloid curve L25A of this embodiment are offset by the third parameter P3 toward the radially outward direction of the centers O1 and O2, respectively, to form the first tooth profile curve L19A and the second tooth profile curve L29A.

[0160] Furthermore, the first parameter P1 and the second parameter P2 do not violate the above-mentioned conditions 1 to 4. Therefore, the first cycloid curve L15A and the second cycloid curve L25A satisfy Camus' theorem.

[0161] In the gear pair 40 of this embodiment, the internal gear 10 is at least partially represented by the first tooth profile curve L19A, and the external gear 20 is at least partially represented by the second tooth profile curve L29A. In particular, in this embodiment, the outer shape of the internal gear 10 is represented by the portion of the first tooth profile curve L19A that is convex radially inward, and the outer shape of the external gear 20 is represented by the portion of the second tooth profile curve L29A that is convex radially outward. Therefore, when the internal gear 10 and the external gear 20 mesh in the portions represented by the first tooth profile curve L19A and the second tooth profile curve L29A, Camus's theorem is always satisfied, and power transmission can be performed without generating angular transmission errors.

[0162] Next, the procedure for forming the tooth roots 11B and 21B will be explained based on Figure 9. The tooth roots 11B and 21B are formed using the same procedure as the tooth tips 11A and 21A. That is, in forming the tooth roots 11B and 21B, first, the third cycloid curve L15B and the second parameter P2 are used to form the fourth cycloid curve L25B.

[0163] As described above, the third rotation radius b3 is equal to the second rotation radius b2 (b3=b2), and the fourth rotation radius b4 is equal to the first rotation radius b1 (b4=b1). Also, in this embodiment, the third drawing point distance c3 is equal to the second drawing point distance c2 (c3=c2), and the fourth drawing point distance c4 is equal to the first drawing point distance c1 (c4=c1). The third offset amount d3 is in the same direction as the offset direction of the second tooth profile curve L29A and is equal to the third parameter P3 (d3=P3). The fourth offset amount d4 is in the same direction as the offset direction of the first tooth profile curve L19A and is equal to the third parameter P3 (d4=P3).

[0164] In this embodiment, the internal gear 10 is drawn with at least a portion of the third tooth profile curve L19B, and the external gear 20 is drawn with at least a portion of the fourth tooth profile curve L29B. In this embodiment, the outer shape of the tooth root 11B of the internal gear 10 is drawn with the portion of the third tooth profile curve L19B that is concave radially outward. Also, the outer shape of the tooth root 21B of the external gear 20 is drawn with the portion of the fourth tooth profile curve L29B that is concave radially inward. According to this embodiment, it is possible to increase the rigidity of the internal gear 10 and the external gear 20 while ensuring smooth meshing by preventing interference between the tooth roots and tooth tips of the internal gear 10 and the external gear 20.

[0165] Figure 22 is a schematic diagram showing the connection portion 11C of the internal gear 10 in this embodiment. The connection portion 11C of the internal gear 10 smoothly connects the first tooth profile curve L19A of the tooth tip portion 11A and the third tooth profile curve L19B of the tooth root portion 11B. Also, the connection portion 21C of the external gear 20, shown in Figure 9, has the same configuration as the connection portion 11C of the internal gear 10. That is, the connection portion 21C of the external gear 20 smoothly connects the second tooth profile curve L29A of the tooth tip portion 21A and the fourth tooth profile curve L29B of the tooth root portion 21B.

[0166] In this embodiment, the connecting portions 11C and 21C are composed of Bézier curves. That is, in the internal gear 10, the first tooth profile curve L19A and the third tooth profile curve L19B are smoothly connected by a Bézier curve. Similarly, in the external gear 20, the second tooth profile curve L29A and the fourth tooth profile curve L29B are smoothly connected by a Bézier curve. As a result, the connecting portions 11C and 21C can smoothly connect the tooth profile curves of the tooth tip portions 11A and 21A with the tooth profile curves of the tooth root portions 11B and 21B.

[0167] In particular, it is preferable that the connecting portions 11C and 21C are composed of cubic Bézier curves defined by four control points. According to this embodiment, the connecting portion 11C can smoothly change the curvature direction between a first tooth profile curve L19A that is convex radially inward and a third tooth profile curve L19B that is concave radially outward, thereby connecting them. Similarly, the connecting portion 21C can smoothly change the curvature direction between a second tooth profile curve L29A that is convex radially outward and a fourth tooth profile curve L29B that is concave radially inward, thereby connecting them.

[0168] (Summary of the embodiments) The gear pair 40 of this embodiment satisfies the above-described conditions 1 to 4. Furthermore, the first tooth profile curve L19A and the second tooth profile curve L29A of the gear pair 40 of this embodiment are drawn satisfying at least one of the following settings: first setting (P1>1 or P1<1), second setting (P2≠0), or third setting (P3≠0). According to this embodiment, the tooth profiles of the internal gear 10 and external gear 20 can be modified in various ways while satisfying Camus' theorem. In other words, the gear pair 40 of this embodiment allows for the construction of an optimal cycloid gear according to the application while suppressing angular transmission errors.

[0169] In particular, in this embodiment, the first tooth profile curve L19A and the second tooth profile curve L29A are drawn satisfying all of the settings of the first, second, and third settings. Therefore, the first tooth profile curve L19A and the second tooth profile curve L29A in this embodiment can have a more flexible curve shape compared to the tooth profile curve of the standard gear pair 940.

[0170] In this embodiment, the gear pair 40 is formed based on the first cycloid curve L15A and the second cycloid curve L25A, which are drawn using a first parameter P1 that satisfies the first setting and P1 < 1, where both the first rotation radius b1 and the second rotation radius b2 are positive values ​​(b1 > 0, b2 > 0). In addition, the gear pair 40 in this embodiment satisfies the third setting, and the first tooth profile curve L19A and the second tooth profile curve L29A are formed by offsetting the first cycloid curve L15A and the second cycloid curve L25A radially outward from the first base circle 12 and the second base circle 22 (P3 > 0).

[0171] Figure 23 is a schematic diagram of the tooth tips 911A and 921A of the standard internal gear 910 and standard external gear 920 that mesh with each other in a standard gear pair 940. In the standard gear pair 940, the tooth surfaces of the tooth tips 911A and 921A of the standard internal gear 910 and standard external gear 920 face in a direction perpendicular to the circumferential direction at the end of meshing (i.e., the circumferential ends of each tooth surface). At this time, the meshing occurs in the region near the base circle of the cycloid curve, and due to the properties of the cycloid curve, the contact occurs in the region with the smallest radius of curvature (theoretically 0). As a result, the surface pressure on the tooth surfaces becomes large at the end of meshing between the tooth tips 911A and 921A.

[0172] Figure 24 is a schematic diagram of the tooth tips 11A and 21A of the internal gear 10 and external gear 20 that mesh with each other in the gear pair 40 of this embodiment. In the gear pair 40 of this embodiment, the first cycloid curve L15A and the second cycloid curve L25A, drawn using a first parameter P1 with a value greater than 0 and less than 1, are offset radially outward to form the first tooth profile curve L19A and the second tooth profile curve L29A. According to this embodiment, the tooth surfaces at the circumferential ends of the tooth tips 11A and 21A can be inclined with respect to the radial direction. Therefore, compared to the standard gear pair 940 (see Figure 23), it is possible to suppress the increase in surface pressure on the tooth surfaces even at the end of meshing between the tooth tips 11A and 21A. According to this embodiment, the load on the tooth surfaces of the internal gear 10 and external gear 20 during meshing can be reduced. As a result, damage to the internal gear 10 and external gear 20 can be suppressed, and the lifespan of the gear pair 40 can be extended.

[0173] As shown in Figure 9, the gear pair 40 of this embodiment is formed based on the first cycloid curve L15A and the second cycloid curve L25A, which are drawn using a second parameter P2 that satisfies the second setting and satisfies P2>0. When P2>0, the absolute value of the first drawing point distance c1 is smaller than the absolute value of the first rotation radius b1, and the absolute value of the second drawing point distance c2 is smaller than the absolute value of the second rotation radius b2. Therefore, the eccentricity Ec(c1+c2) becomes smaller than that of a standard cycloid gear pair, and the base circles of the gear pair are no longer tangent to each other. A standard cycloid gear pair has the problem that assembly is extremely difficult because the meshing points are located diagonally opposite the tangent points of the base circles. By setting P2>0, the diagonal meshing is eliminated, making assembly easier. In other words, with the gear pair 40 of this embodiment, the internal gear 10 and the external gear 20 can be easily assembled regardless of the dimensional accuracy of the tooth surface shape.

[0174] <Example 1> Next, a modified example 1 of the gear pair 140 that can be adopted in the above-described embodiment will be explained. Note that components identical to those in the above-described embodiment are denoted by the same reference numerals and their descriptions are omitted.

[0175] FIG. 25 is a schematic view of the tooth tip portions 111A and 121A of the internal gear 110 and the external gear 120 that mesh with each other in the gear pair 140 of this modified example.

[0176] The gear pair 140 of this modified example satisfies the first setting and the third setting. Also, the gear pair 140 of this modified example does not satisfy the second setting. Therefore, the second parameter P2 of this modified example is 0. Note that the second parameter P2 of this modified example is an example, and the second parameter P2 may be a value greater than 0 (P2>0), or the second parameter P2 may be a value less than 0 (P2<0).

[0177] FIG. 26 is a schematic view showing the procedure for forming the second tooth profile curve L29A of the tooth tip portion 121A of the external gear 120 in this modified example. The tooth tip portion 121A first forms the second cycloid curve L25A, and then offsets the second cycloid curve L25A in the normal direction by the third parameter P3 to form the second tooth profile curve L29A.

[0178] In the gear pair 140 of this modified example, the first parameter P1 (=b2 / b1) is greater than -1 and less than 0 (-1<P1<0). In the gear pair 140 of this modified example, the first rolling circle radius b1 takes a positive value (b1>0), and the second rolling circle radius b2 takes a negative value (b2<0). For this reason, as shown in FIG. 15, the second cycloid curve L25A becomes a hypocycloid curve with a rolling circle radius of |b2| and is concave inward in the radial direction. On the other hand, the first rolling circle radius b1 is sufficiently larger than the absolute value |b2| of the second rolling circle radius b2.

[0179] As shown in FIG. 26, the second cycloid curve L25A that is concave inward in the radial direction is offset radially outside the second base circle 22 using the third parameter P3. Thereby, the second tooth profile curve L29A that is convex outward in the radial direction is formed.

[0180] In order to offset the second cycloid curve L25A radially outward from the second base circle 22, the third parameter P3 is set to a value greater than the sum of the second inversion radius b2 and the second drawing point distance c2 (b2+c2) (P3>b2+c2). In this modified example, since the second drawing point distance c2 is equal to the second inversion radius b2, the third parameter P3 only needs to be greater than twice the second inversion radius b2.

[0181] Furthermore, as shown in Figure 25, the second tooth profile curve L29A is formed, and the first cycloid curve L15A is also offset radially outward by the third parameter P3. This results in the formation of the first tooth profile curve L19A.

[0182] In this modified gear pair 140, the first rotation radius b1 takes a positive value, the second rotation radius b2 takes a negative value (b1>0, b2<0), and the second tooth profile curve L29A is formed by offsetting the second cycloid curve L25A radially outward from the second base circle 22. With this configuration, the circumferential ends of the tooth tips 111A and 121A can be inclined with respect to the radial direction. As a result, compared to the standard gear pair 940 (see Figure 23), it is possible to suppress the increase in surface pressure on the tooth surfaces even at the end of meshing between the tooth tips 111A and 121A. According to this embodiment, the load on the tooth surfaces of the internal gear 110 and external gear 120 can be reduced. Consequently, damage to the internal gear 110 and external gear 120 can be suppressed, and the lifespan of the gear pair 140 can be extended.

[0183] <Modification 2> Next, a modified example 2 of the gear pair 240 that can be adopted in the above-described embodiment will be explained. Note that components identical to those in the above-described embodiment are denoted by the same reference numerals and their descriptions are omitted.

[0184] Figure 27 is a schematic diagram of the tooth tips 211A and 221A of the internal gear 210 and external gear 220 that mesh with each other in the gear pair 240 of this modified example.

[0185] The gear pair 240 of this modified example satisfies the first setting and the third setting. Also, the gear pair 240 of this modified example does not satisfy the second setting. Therefore, the second parameter P2 of this modified example is 0. Note that the second parameter P2 of this modified example is an example, and the second parameter P2 may be a value exceeding 0 (P2 > 0), or the second parameter P2 may be a value less than 0 (P2 < 0).

[0186] In the gear pair 240 of this modified example, the first parameter P1 (= b2 / b1) is greater than -1 and less than 0 (-1 < P1 < 0). In the gear pair 240 of this modified example, the first rolling circle radius b1 takes a negative value (b1 < 0), and the second rolling circle radius b2 takes a positive value (b2 > 0). For this reason, the first cycloid curve L15A becomes an epicycloid curve and has a concave shape that is concave toward the radially outer side. The first cycloid curve L15A that is concave toward the radially outer side is offset radially inward from the first base circle 12 using the third parameter P3. Thereby, a first tooth profile curve L19A that is convex toward the radially inner side is formed.

[0187] In order to offset the first cycloid curve L15A radially inward from the first base circle 12, the third parameter P3 is set to a value greater than the sum of the first rolling circle radius b1 and the first drawing point distance c1 (b1 + c1) (P3 > b1 + c1). Note that in this modified example, since the first drawing point distance c1 is equal to the first rolling circle radius b1, the third parameter P3 only needs to be greater than twice the first rolling circle radius b1.

[0188] Also, while forming the first tooth profile curve L19A, the second cycloid curve L25A is also offset radially outward by the third parameter P3. Thereby, a second tooth profile curve L29A is formed.

[0189] In this modified gear pair 240, the first rotation radius b1 takes a negative value, and the second rotation radius b2 takes a positive value (b1<0, b2>0). The first tooth profile curve L19A is formed by offsetting the first cycloid curve L15A radially inward from the first base circle 12. This configuration allows the circumferential ends of the tooth tips 211A and 221A to be inclined with respect to the radial direction. This suppresses the increase in surface pressure on the tooth surfaces even at the end of meshing between the tooth tips 211A and 221A, compared to the standard gear pair 940 (see Figure 23). This embodiment reduces the load on the tooth surfaces of the internal gear 210 and external gear 220. As a result, damage to the internal gear 210 and external gear 220 can be suppressed, and the lifespan of the gear pair 240 can be extended.

[0190] While embodiments and variations of the present invention have been described above, the configurations and combinations thereof in the embodiments and variations are merely examples, and additions, omissions, substitutions, and other modifications are possible without departing from the spirit of the present invention. Furthermore, the present invention is not limited by the embodiments.

[0191] For example, the above embodiment described a case in which a gear pair is used in a drive system for a human-powered vehicle, but the applications of the gear pair are not limited to this embodiment. The gear pair may be used in components of a human-powered vehicle other than the drive system. The gear pair may also be used in an internal transmission of a human-powered vehicle, for example. Furthermore, the gear pair may be used in products other than human-powered vehicles. For example, the gear pair may be used in fishing equipment (e.g., fishing reels). In this embodiment, the case in which a gear pair is used in a transmission as a reduction gear was described. However, the gear pair may also be used in a transmission as a speed increaser.

[0192] For example, the configurations of the drive unit, transmission, and gear pair in the embodiments are examples only, and the drive unit, transmission, and gear pair may include configurations not shown in each embodiment, or may not include some of the configurations shown in each embodiment.

[0193] Furthermore, in the above-described embodiment, the drawing point is located inside the circle of the decumbent and draws a Carteite cycloid curve, and in the modified example, the case in which the drawing point is located on the circumference of the decumbent and draws a cycloid curve was described. However, the drawing point may be located outside the circle of the decumbent and draw a hypocycloid curve. That is, the second parameter P2 may be a negative value.

[0194] Furthermore, for example, the shape of the other parts of the tooth tip portion 11A of the internal gear 10 is not limited as long as at least a portion of it includes the first tooth profile curve L19A. The shape of the other parts of the tooth tip portion 21A of the external gear 20 is not limited as long as at least a portion of it includes the second tooth profile curve L29A. The shape of the other parts of the tooth root portion 11B of the internal gear 10 is not limited as long as at least a portion of it includes the third tooth profile curve L19B. The shape of the other parts of the tooth root portion 21B of the external gear 20 is not limited as long as at least a portion of it includes the fourth tooth profile curve L29B. [Explanation of Symbols]

[0195] 1...Human-powered vehicle, 6...Drive system, 7...Transmission, 10,110...Internal gear, 11...Internal tooth, 11B,21B...Tooth root, 12,BC1...Base circle, 12...First base circle, 13A...First rotation circle, 13B...Third rotation circle, 14A...First drawing point, 14B...Third drawing point, 20,120...External gear, 21...External tooth, 22...Second base circle, 23A...Second Rotation circle, 23B...4th rotation circle, 24A...2nd drawing point, 24B...4th drawing point, 40,140...gear pair, a1...1st base circle radius, a2...2nd base circle radius, b1...1st rotation circle radius, b2...2nd rotation circle radius, b3...3rd rotation circle radius, b4...4th rotation circle radius, BC...normal, c1...1st drawing point distance, c2...2nd drawing point distance, c3...3rd drawing point Distance, c4... Distance to the 4th drawing point, D, E, O1, O2... Center, d3... 3rd offset amount, d4... 4th offset amount, DP1, DP2, DP3, DP4, DP5, DP6... Drawing point, Ec, Ec9... Eccentricity, L29A... 2nd tooth profile curve, L19A... 1st tooth profile curve, L15A... 1st cycloid curve, L25A... 2nd cycloid curve, La1... Hypocycloid curve, La4... Epicycloid curve, L15B... 3rd cycloid curve, L19B... 3rd tooth profile curve, L25B... 4th cycloid curve, L29B... 4th tooth profile curve, N... Number of teeth, P1... 1st parameter, P2... 2nd parameter, P3... 3rd parameter, RC1, RC2... Rotation

Claims

1. An internal gear having N+1 internal teeth, at least a portion of which are drawn by the first tooth profile curve, The external gear comprises an external gear having at least a portion of its teeth N, which are drawn by a second tooth profile curve, and which meshes internally with the internal gear, The first tooth profile curve is formed based on a first cycloid curve drawn as the trajectory of a first drawing point located on, inside, or outside the circumference of a first rotation circle rolling around a first base circle. The second tooth profile curve is formed based on a second cycloid curve, which is drawn as the trajectory of a second drawing point located on, inside, or outside the circumference of a second rotation circle rolling around a second base circle. Let the radius of the first base circle be the radius a1 of the first base circle. Let the radius of the first inversion be the first inversion radius b1. The distance from the center of the first rotation circle to the first drawing point is defined as the first drawing point distance c1. Let the radius of the second base circle be the second base circle radius a2. Let the radius of the second inversion be the second inversion radius b2. The distance from the center of the second rotation circle to the second drawing point is defined as the second drawing point distance c2. Let the distance between the center of the first base circle and the center of the second base circle be the eccentricity Ec. The first rotation radius b1, the second rotation radius b2, the first drawing point distance c1, and the second drawing point distance c2 each take positive or negative values. The sign of the first drawing point distance c1 is assumed to be the same as the sign of the first rotation radius b1. The sign of the second drawing point distance c2 is assumed to be the same as the sign of the second rotation radius b2. The first cycloid curve is a hypocycloid curve with a radius of |b1| when the first radius of inversion b1 is a positive value, and an epicycloid curve with a radius of |b1| when the first radius of inversion b1 is a negative value. The second cycloid curve is an epicycloid curve with a radius of |b2| when the second radius of inversion b2 is a positive value, and a hypocycloid curve with a radius of |b2| when the second radius of inversion is a negative value. The first cycloid curve and the second cycloid curve satisfy the following conditions 1, 2, 3, and 4. a1=(N+1)×(b1+b2)...(Conditional expression 1) a2=N×(b1+b2)...(Conditional expression 2) b1:c1=b2:c2...(conditional expression 3) Ec=c1+c2...(conditional expression 4) The ratio of the second rotation radius b2 to the first rotation radius b1 (b2 / b1) is defined as the first parameter P1. The second parameter P2 is the eccentricity adjustment amount ((b1 + b2) - (c1 + c2)), which is the value obtained by subtracting the sum of the first drawing point distance c1 and the second drawing point distance c2 from the sum of the first rotation radius b1 and the second rotation radius b2. The third parameter P3 is defined as the offset amount that offsets the first cycloid curve and the second cycloid curve by the same distance in the normal direction. The first tooth profile curve and the second tooth profile curve are drawn satisfying at least one of the following first, second, or third settings: The first setting draws the first cycloid curve and the second cycloid curve using the first parameter P1 satisfying P1 > 1 or P1 < 1. The second setting draws the first cycloid curve and the second cycloid curve using the second parameter P2 that satisfies P2 ≠ 0. The third setting involves using the third parameter P3 that satisfies P3 ≠ 0 to offset the first cycloid curve and the second cycloid curve in the normal direction by the third parameter P3, thereby obtaining the first tooth profile curve and the second tooth profile curve. Gears.

2. The first tooth profile curve and the second tooth profile curve are drawn satisfying all of the settings of the first setting, the second setting, and the third setting. The gear pair according to claim 1.

3. The first and second traverse radii are both positive values ​​(b1 > 0, b2 > 0), The first cycloid curve and the second cycloid curve are drawn using the first parameter P1 that satisfies the first setting and satisfies P1 < 1. The third setting is satisfied, and the first cycloid curve and the second cycloid curve are offset radially outward from the first base circle and the second base circle to form the first tooth profile curve and the second tooth profile curve, The gear pair according to claim 1.

4. The first setting is satisfied, the first radius of rotation takes a positive value, and the second radius of rotation takes a negative value (b1 > 0, b2 < 0), The third setting is satisfied, and the second tooth profile curve is formed by offsetting the second cycloid curve radially outward from the second base circle, The gear pair according to claim 1.

5. The first setting is satisfied, the first rotation radius takes a negative value, and the second rotation radius takes a positive value (b1 < 0, b2 > 0), The third setting is satisfied, and the first tooth profile curve is formed by offsetting the first cycloid curve radially inward from the first base circle, The gear pair according to claim 1.

6. The first cycloid curve and the second cycloid curve are drawn using the second parameter P2 that satisfies the second setting and satisfies P2 > 0. The gear pair according to claim 1.

7. The outer shape of the internal tooth is drawn in the portion of the first tooth profile curve that is convex radially inward. The outer shape of the outer tooth is drawn in the portion of the second tooth profile curve that is convex radially outward. The gear pair according to claim 1.

8. The aforementioned internal gear has at least a portion of its tooth roots drawn with a third tooth profile curve. The aforementioned external gear has at least a portion of its tooth roots drawn with a fourth tooth profile curve. The third tooth profile curve is formed based on a third cycloid curve, which is drawn as the trajectory of a third drawing point located on, inside, or outside the circumference of a third rotation circle rolling around the first base circle. The fourth tooth profile curve is formed based on a fourth cycloid curve, which is drawn as the trajectory of a fourth drawing point located on, inside, or outside the circumference of a fourth inversion circle rolling around the second base circle. The radius of the third inversion, b3, is equal to the radius of the second inversion, b2 (b3 = b2). The absolute value of the third drawing point distance c3, which is the distance from the center of the third rotation circle to the third drawing point, is greater than or equal to the absolute value of the second drawing point distance c2 (|c3| ≥ |c2|), The radius of the fourth inversion, b4, is equal to the radius of the first inversion, b1 (b4 = b1). The absolute value of the fourth drawing point distance c4, which is the distance from the center of the fourth rotation circle to the fourth drawing point, is greater than or equal to the absolute value of the first drawing point distance c1 (|c4| ≥ |c1|), When the third cycloid curve is offset by a third offset amount in the normal direction to form the third tooth profile curve, the third offset amount is set to be in the same direction as the offset direction of the second tooth profile curve so as not to interfere with the second tooth profile curve during meshing. When the fourth cycloid curve is offset by a fourth offset amount in the normal direction to form the fourth tooth profile curve, the fourth offset amount is set so as not to interfere with the first tooth profile curve during meshing. The gear pair according to claim 1.

9. The third drawing point distance c3 is equal to the second drawing point distance c2 (c3 = c2), The fourth drawing point distance c4 is equal to the first drawing point distance c1 (c4 = c1), The third offset amount is equal to the third parameter P3 (d3 = P3), The fourth offset amount is equal to the third parameter P3 (d4 = P3). The gear pair according to claim 8.

10. The outer shape of the tooth root of the internal gear is drawn in the portion of the third tooth profile curve that is concave toward the radially outward direction. The outer shape of the tooth root of the external gear is drawn in the portion of the fourth tooth profile curve that is concave radially inward. The gear pair according to claim 8.

11. In the aforementioned internal gear, the first tooth profile curve and the third tooth profile curve are smoothly connected by a Bézier curve. In the external gear, the second tooth profile curve and the fourth tooth profile curve are smoothly connected by a Bézier curve. The gear pair according to claim 8.

12. The aforementioned Bézier curve is a cubic Bézier curve defined by four control points. The gear pair according to claim 11.

13. A transmission having a gear pair as described in any one of claims 1 to 12.

14. A drive system for a human-powered vehicle, including the transmission described in claim 13.

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