GEAR PAIR, GEARBOX AND DRIVE UNIT

Abstract

A gear pair 40, 140 comprises an internal gear 10, 110 with internal teeth 11 having the number of teeth N + 1, at least one section of which is described by a first tooth profile curve L19A, and an external gear 20, 120 with external teeth 21 having the number of teeth N, at least one section of which is described by a second tooth profile curve L29A, and is in inscribed tooth mesh with the internal gear 10, 110, wherein the first tooth profile curve L19A and the second tooth profile curve L29A are formed on the basis of cycloidal curves L15A, L25A, which lie as loci of first and second drawing points 14B 24B on circumferences inside or outside of first and second rolling circles 13A, 23A, which roll on first and second base circles 12, 22, and on the basis of first and second parameters P1, P2, which are defined as a combination of a ratio of rolling circle radii b1, b2 and drawing point distances, where the formed cycloidal curves L15A,L25A are offset by a third parameter P3 to obtain the first tooth profile curve L19A and the second tooth profile curve L29A.

Description

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

[0002] In related technology, a cycloid gear pair is known which includes an inner gear and an outer gear formed by a tooth profile curve consisting of a combination of a hypocycloid curve and an epicycloid curve, see for example JP 3 729 867 B.

[0003] Cycloidal gears have the problem that adjusting the tooth profile to reduce surface pressure or the like increases the angular transmission error.

[0004] Taking into account the problem mentioned above, an objective of the present invention is to provide a gear pair, a transmission and a drive unit that have a tooth profile curve that is optimal for the respective application and at the same time suppress an angular transmission error.

[0005] A gear pair according to a first aspect of the present invention comprises an internal gear with internal teeth having the number N + 1 teeth, at least one section of which is described by a first tooth profile curve, and an external gear with external teeth having the number N teeth, at least one section of which is described by a second tooth profile curve, and which is in inscribed tooth mesh with the internal gear, wherein the first tooth profile curve is formed on the basis of a first cycloidal curve, which is drawn as the locus of a first drawing point that lies on a circumference inside or outside a first rolling circle that rolls on a first base circle, wherein the second tooth profile curve is formed on the basis of a second cycloidal curve, which is drawn as the locus of a second drawing point that lies on a circumference inside or outside a second rolling circle that rolls on a second base circle.where a radius of the first base circle is defined as the first base circle radius a1, a radius of the first rolling circle is defined as the first rolling circle radius b1, a distance from a center point of the first rolling circle to the first drawing point is defined as the first drawing point distance c1, a radius of the second base circle is defined as the second base circle radius a2, a radius of the second rolling circle is defined as the second rolling circle radius b2, a distance from a center point of the second rolling circle to the second drawing point is defined as the second drawing point distance c2, and a distance between a center point of the first base circle and a center point of the second base circle is defined as the eccentricity amount Ec, where the first rolling circle radius b1, the second rolling circle radius b2, the first drawing point distance c1, and the second drawing point distance c2 are each positive or negative values,wherein a positive and negative sign of the first drawing point distance c1 corresponds to a positive and negative sign of the first rolling circle radius b1, a positive and negative sign of the second subtraction distance c2 corresponds to a positive and negative sign of the second rolling circle radius b2, wherein, if the first rolling circle radius b1 is a positive value, the first cycloid curve is a hypocycloid curve with a rolling circle radius |b1|, if the first rolling circle radius b1 is a negative value, the first cycloid curve is an epicycloid curve with a rolling circle radius |b1|, if the second rolling circle radius b2 is a positive value, the second cycloid curve is an epicycloid curve with a rolling circle radius |b2|, if the second rolling circle radius is a negative value, the second cycloid curve is a hypocycloid curve with a rolling circle radius |b2|. The first cycloid curve and the second cycloid curve satisfy the following conditional expressions 1, 2,3 und 4:, a1=(N+1)×(b1+b2) a2=N×(b1+b2) b1:c1=b2:c2 Ec=c1+c2

[0006] The ratio (b2 / b1) of the second rolling circle radius b2 to the first rolling circle radius b1 is defined as the first parameter P1; an eccentricity adjustment value ((b1 + b2) - (c1 + c2)), which is the sum of the first rolling circle radius b1 and the second rolling circle radius b2 minus the sum of the first drawing point distance c1 and the second drawing point distance c2, is defined as the second parameter P2; an offset amount for offsetting the first cycloidal curve and the second cycloidal curve by the same distance in a normal direction is defined as the third parameter P3; the first tooth profile curve and the second tooth profile curve are drawn such that they satisfy at least one of the following first, second, and third settings, where the first setting is to draw the first cycloidal curve and the second cycloidal curve using the first parameter P1, which satisfies P1 > 1 or P1 < 1; the second setting is toto draw the first cycloidal curve and the second cycloidal curve using the second parameter P2, which satisfies P2 ≠ 0, and the third setting consists of using the third parameter P3, which satisfies P3 ≠ 0, and offsetting the first cycloidal curve and the second cycloidal curve by the third parameter P3 in the normal direction to obtain the first tooth profile curve and the second tooth profile curve.

[0007] According to the above embodiment, the first and second tooth profile curves are drawn such that they satisfy at least one of the following first, second, and third conditions, making it possible to use a tooth profile that differs from that of a conventional standard cycloidal gear. Accordingly, it is possible to provide a gear pair with an optimal tooth profile curve according to the application, for example, to reduce surface pressure, improve the arrangement, and increase transmission efficiency. Furthermore, according to the above embodiment, the first and second tooth profile curves satisfy conditions 1 through 4, thus fulfilling Camus' theorem for the gear pair.This means that, according to this design, it is possible to provide a gear pair that enables uniform meshing with a reduced angular transmission error while simultaneously increasing the degree of freedom in the tooth profile.

[0008] According to a second aspect of the present invention, the gear pair according to the first aspect is designed such that the first tooth profile curve and the second tooth profile curve are drawn in such a way that they satisfy all first settings, second settings and third settings.

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

[0010] According to a third aspect of the present invention, the gear pair according to the first or second aspect is designed such that the first rolling circle radius b1 and the second rolling circle radius b2 are both positive values ​​(b1 > 0, b2 > 0), the first setting is satisfied and the first cycloidal curve and the second cycloidal curve are drawn using the first parameter P1, which satisfies P1 < 1, and the third setting is satisfied and the first tooth profile curve and the second tooth profile curve are formed by offsetting the first cycloidal curve and the second cycloidal curve radially outwards from the first base circle and the second base circle.

[0011] According to the above design, it is possible to suppress an increase in surface pressure on the tooth surfaces at a contact point between the outer and inner gears. Consequently, it is possible to extend the service life of the gear pair.

[0012] According to a fourth aspect of the present invention, the gear pair according to the first aspect is designed such that the first setting is fulfilled, the first rolling circle radius is a positive value and the second rolling circle radius is a negative value (b1 > 0, b2 < 0) and the third setting is fulfilled, and the second tooth profile curve is formed by offsetting the second cycloidal curve radially outwards from the second base circle.

[0013] According to the above design, it is possible to suppress an increase in surface pressure on the tooth surfaces at a contact point between the outer and inner gears. Consequently, it is possible to extend the service life of the gear pair.

[0014] According to a fifth aspect of the present invention, the gear pair according to the first aspect is designed such that the first setting is fulfilled, the first rolling circle radius is a negative value and the second rolling circle radius is a positive value (b1 < 0, b2 > 0) and the third setting is fulfilled, and the first tooth profile curve is formed by offsetting the first cycloidal curve radially inwards from the first base circle.

[0015] According to the above design, it is possible to suppress an increase in surface pressure on the tooth surfaces at a contact point between the outer and inner gears. Consequently, it is possible to extend the service life of the gear pair.

[0016] According to a sixth aspect of the present invention, the gear pair is designed according to one of the first to fifth aspects such that the second setting is fulfilled and the first cycloidal curve and the second cycloidal curve are drawn using the second parameter P2, which satisfies P2 > 0.

[0017] According to the above design, a gap can be created between the inner gear and the outer gear in an eccentric direction, making it easy to arrange the gear pair.

[0018] According to a seventh aspect of the present invention, the gear pair according to one of the first to sixth aspects is designed such that a radially inwardly convex section of the first tooth profile curve describes an outer shape of the internal toothing and a radially outwardly convex section of the second tooth profile curve describes an outer shape of the external toothing.

[0019] According to the above design, a tooth tip of the inner gear can be formed by the first tooth profile curve, and a tooth tip of the outer gear can be formed by the second tooth profile curve. Therefore, it is possible to provide a gear pair in which the tooth tips mesh uniformly.

[0020] According to an eighth aspect of the present invention, the gear pair according to one of the first to seventh aspects is designed such that the inner gear has at least one section of a tooth root line described by a third tooth profile curve, the outer gear has at least one section of a tooth root described by a fourth tooth profile curve, the third tooth profile curve being formed on the basis of a third cycloidal curve drawn as the locus of a third drawing point located on a circumference, inside or outside a third rolling circle rolling on the first base circle, the fourth tooth profile curve being formed on the basis of a fourth cycloidal curve drawn as the locus of a fourth drawing point located on a circumference, inside or outside a fourth rolling circle rolling on the second base circle, a third rolling circle radius b3 being a radius of the third rolling circle,equal to the second rolling circle radius b2 (b3 = b2), an absolute value of a third drawing point distance c3, which is a distance from a center point of the third rolling circle to the third drawing point, is equal to or greater than an absolute value of the second drawing point distance c2 (|c3| ≥ |c2|), a fourth rolling circle radius b4, which is a radius of the fourth rolling circle, is equal to the first rolling circle radius b1 (b4 = b1), an absolute value of a fourth drawing point protrusion c4, which is a distance from a center point of the fourth rolling circle to the fourth drawing point, is equal to or greater than an absolute value of the first drawing point protrusion c1 (|c4| ≥ |c1|), if the third tooth profile curve is formed by offsetting the third cycloidal curve by a third offset amount in the normal direction, the third offset amount is specified in the same direction as an offset direction of the second tooth profile curve,so that it does not disturb the second tooth profile curve during combing, and if the fourth tooth profile curve is formed by offsetting the fourth cycloidal curve by a fourth offset amount in the normal direction, the fourth offset amount is defined in the same direction as an offset direction of the first tooth profile curve, so that it does not disturb the first tooth profile curve during combing.

[0021] According to the above embodiment, when the internal and external gears mesh, it is possible to prevent the third tooth profile curve, which forms the root of the internal gear, from interfering with the second tooth profile curve of the external gear. Similarly, when the internal and external gears are engaged, it is possible to prevent the fourth tooth profile curve, which forms the root of the external gear, from interfering with the first tooth profile curve of the internal gear.

[0022] According to a ninth aspect of the present invention, the gear pair according to the eighth aspect is designed such that 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) and the fourth offset amount is equal to the third parameter P3 (d4 = P3).

[0023] According to the above embodiment, uniform meshing can be achieved by avoiding interference between the third tooth profile curve, which forms the root of the internal gear, and the second tooth profile curve of the external gear. Similarly, uniform meshing can be achieved by avoiding interference between the fourth tooth profile curve, which forms the root of the external gear, and the first tooth profile curve of the internal gear.

[0024] According to a tenth aspect of the present invention, the gear pair according to the eighth or ninth aspect is designed such that a radially outwardly concave section of the third tooth profile curve describes an outer shape of the tooth root of the inner gear and a radially inwardly concave section of the fourth tooth profile curve describes an outer shape of the tooth root of the outer gear.

[0025] According to the above design, 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 cycloidal curve. Therefore, it is possible to provide a gear pair that meshes uniformly by avoiding interference between the tooth tips and the tooth roots.

[0026] According to an eleventh aspect of the present invention, the gear pair according to one of the eighth to tenth aspects is designed such that the first tooth profile curve and the third tooth profile curve in the inner gear are uniformly connected by a Bezier curve and the second tooth profile curve and the fourth tooth profile curve in the outer gear are uniformly connected by a Bezier curve.

[0027] According to the above embodiment, in the internal gear, the connecting section between the first and third tooth profile curves can be uniformly connected by a Bézier curve. Similarly, in the external gear, the connecting section between the second and fourth tooth profile curves can be uniformly connected by a Bézier curve.

[0028] According to a twelfth aspect of the present invention, the gear pair according to the eleventh aspect is designed such that the Bezier curve is a cubic Bezier curve defined by four control points.

[0029] According to the above embodiment, a tooth profile with a uniformly changing curvature direction can be formed 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 Bezier curve.

[0030] According to a thirteenth aspect of the present invention, a transmission comprises the gear pair according to one of the first twelve aspects.

[0031] According to the above design, it is possible to provide a gearbox in which an angular transmission error is suppressed.

[0032] According to a fourteenth aspect of the present invention, a drive unit for a human-powered vehicle includes the transmission according to the thirteenth aspect.

[0033] According to the above design, it is possible to provide a drive unit in which an angle transmission error is suppressed.

[0034] According to the present invention, it is possible to provide a gear pair, a transmission and a drive unit that have an optimal tooth profile curve according to an application, while suppressing an angular transmission error.

[0035] A more complete appreciation of the invention and many of its associated advantages will easily become apparent when one considers the following detailed description in conjunction with the accompanying drawings, wherein Fig. 1 shows a side view depicting a human-powered vehicle with a drive unit according to one embodiment; Fig. 2 a schematic diagram of the drive unit according to the embodiment; Fig. 3 is a schematic diagram that represents types of cycloid curves; Fig. 4 is a schematic diagram that represents types of cycloid curves; Fig. 5 is a schematic diagram of a standard gear pair; Fig. 6 a partially enlarged view of the in Fig. The standard gear pair shown in section 5 is; Fig. 7 a partially enlarged view of the in Fig. The standard gear pair shown in section 5 depicts the orbits of the rolling circle centers; Fig. 8 is a front view of a gear pair of the embodiment; Fig. 9 a partially enlarged view of the in Fig. The gear pair of the embodiment shown in section 8 is; Fig. 10 is a diagram that represents a cycloidal curve, drawn in a case where a first rolling circle radius and a fourth rolling circle radius are a positive value and a negative value, respectively; Fig. 11 is a diagram that represents a cycloid curve, drawn in a case where a second rolling circle radius or a third rolling circle radius is a positive value or a negative value, respectively; Fig. 12 is a diagram that schematically represents the course of the engagement between a tooth tip of an internal gear and a tooth tip of an external gear in a cycloidal gear; Fig. 13 is a schematic diagram of a first rolling circle and a second rolling circle, which draw a contact point between the inner gear and the outer gear of the cycloidal gear; Fig. 14 is a diagram that represents a relationship between the first rolling circle, the second rolling circle and the contact point in a case where a first parameter exceeds 1; Fig. 15 is a diagram illustrating a relationship between the first rolling circle, the second rolling circle and the contact point in a case where the first parameter is equal to or greater than -1 and less than 0; Fig. 16 a diagram that represents a relationship between the first rolling circle, the second rolling circle and the contact point in a case where a second parameter is positive; Fig. 17 a diagram that represents a relationship between the first rolling circle, the second rolling circle and the contact point in a case where the second parameter is negative; Fig. 18 a diagram that shows a relationship between the first rolling circle, the second rolling circle and the contact point in a case where a third parameter is positive; Fig. 19 a diagram that represents a relationship between the first rolling circle, the second rolling circle and the contact point in a case where the third parameter is negative; Fig. 20 is a diagram that represents a method for forming a first tooth profile curve of the tooth tip of the internal gear of the embodiment; Fig. 21 is a diagram that represents a method for forming a second tooth profile curve of the tooth tip of the external gear of the embodiment; Fig. 22 is a schematic diagram representing a connecting section of the internal gear of the embodiment; Fig. 23 is a schematic diagram of the tooth tips of a standard internal gear and a standard external gear meshing together in the standard gear pair; Fig. 24 is a schematic diagram of the tooth tips of the inner gear and the outer gear which mesh together in the gear pair of the embodiment; Fig. 25 is a schematic diagram of the tooth tips of an internal gear and an external gear meshing together in a gear pair of a first modification example; Fig. 26 is a diagram that illustrates a method for forming a second tooth profile curve of the tooth tip of the external gear of the first modification example; and Fig. 27 is a schematic diagram of tooth tips of an internal gear and an external gear meshing together in a gear pair of a second modification example.

[0036] A gear pair, a transmission, and a drive unit according to an embodiment of the present invention are described with reference to the drawings, wherein identical reference numerals in the different drawings denote the same or identical elements. In the description of the embodiment, configurations with the same or similar functions are identified by the same reference numerals. A redundant description of these configurations is unnecessary. The drawings are schematic or conceptual, and the ratio between the thickness and width of the individual parts, the size ratio between parts, and the like do not necessarily correspond to those in reality.

[0037] Fig. Figure 1 is a side view showing a human-powered vehicle 1 equipped with a drive unit 6 according to the present embodiment. The human-powered vehicle 1 comprises a vehicle body frame 2, a rear wheel 3, a front wheel 4, a drive train 5, and the drive unit 6. The vehicle body frame 2 is supported by the rear wheel 3 and the front wheel 4.

[0038] The drivetrain 5, for example, is a chain-driven drivetrain. The 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 a crank axis J1, and crank arms 5f located at both ends of the crankshaft 5e. The crankshaft 5e is mounted on the vehicle body frame 2 such that it can rotate about 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 rotates together with the rear wheel 3 around the central axis of the rear wheel 3. The chain 5d is wound 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] Fig. Figure 2 is a schematic representation of the drive unit 6. The drive unit 6 is connected to the crankshaft 5e. The drive unit 6 includes a motor 8, a gearbox 7 connected to the motor 8, a power transmission unit 9 connected to the gearbox 7, and a housing 6a that accommodates the motor 8, the gearbox 7, and the power transmission unit 9. The power of the motor 8 is transmitted to the crankshaft 5e via the gearbox 7 and the power transmission unit 9. Accordingly, the drive unit 6 provides a driving force for the human-powered vehicle 1.

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

[0043] The gearbox 7 reduces the rotational speed of the power input from the motor 8 and transmits it to the power transmission unit 9. The gearbox 7 includes a gear pair 40. The gear pair 40 also includes an internal gear 10 and an external gear 20. The internal gear 10 is, for example, attached to the housing 6a. Furthermore, the external gear 20 oscillates and rotates due to the power of the motor 8 while engaged with the internal gear 10. The gearbox 7 extracts, for example, the oscillating rotation of the external gear 20 as a rotation about a center point O1 and transmits it to the power transmission unit 9.

[0044] The power transmission unit 9 includes at least one gear (not shown). A gear (not shown) of the power transmission unit 9 engages with a gear (not shown) located on the outer circumferential surface of the crankshaft 5e. The power transmission unit 9 transmits the power from the gearbox 7 to the drive train 5.

[0045] Fig. 3 and Fig. Figure 4 shows a schematic representation of a cycloidal curve. The inner gear 10 and the outer gear 20, which form the gear pair 40, are both cycloidal gears. First, the cycloidal curve formed by the cycloidal gear is shown with reference to Fig. 3 and Fig. 4 described.

[0046] The cycloidal curve is defined by a locus formed by drawing the points DP1, DP2, DP3, DP4, DP5, and DP6 as the rolling circles RC1 and RC2 roll on the circumference of a base circle BC1. The base circle BC1 is defined relative to the internal gear 10 and the external gear 20. The base circle BC1 is an imaginary circle that serves as the reference point for the tooth profile curve. The diameter of the base circle BC1 is defined differently when defining the tooth profile of the internal gear 10 and when defining the tooth profile of the external gear 20. The diameter of the base circle BC1 when defining the tooth profile of the internal gear 10 is φ / N × (N + 1), where φ is the diameter of the base circle BC1 when defining the tooth profile of the external gear 20, and N is the number of teeth.

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

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

[0049] Generally, a cycloidal curve drawn as the locus of points on a rolling circle outside the base circle is called an epicycloid curve, and a cycloidal curve drawn as the locus of points on a rolling circle inside the base circle is called a hypocycloid curve. Conversely, a cycloidal curve drawn as the locus of points inside a rolling circle is called a foreshortened cycloid curve, and a cycloidal curve drawn as the locus of points outside the rolling circle is called a stretched cycloid curve.

[0050] As in the Fig. 3 and Fig. As shown in Figure 4, the cycloid curve has different shapes depending on the combination of the rolling circles RC1 and RC2 and the drawing points DP1, DP2, DP3, DP4, DP5, and DP6. The multitude of cycloid curves with different shapes includes a hypocycloid curve La1, a shortened hypocycloid curve La2, a stretched hypocycloid curve La3, an epicycloid curve La4, a shortened epicycloid curve La5, and a stretched epicycloid curve La6.

[0051] As in Fig. As shown in Figure 3, the hypocycloid curve La1 is drawn through the locus of drawing point DP1 when the rolling circle RC1 rolls on the base circle BC1. Drawing point DP1 is in contact with the base circle BC1. When the rolling circle RC1 rolls circumferentially within the base circle BC1, drawing point DP1 passes radially through the base circle BC1 and again comes into contact with it. Accordingly, the hypocycloid curve La1 is drawn in a concave shape, concave radially inward. When the rolling circle RC1 completes one revolution around the base circle BC1, the hypocycloid curve La1 is drawn such that a multitude of concave segments are continuously arranged in the circumferential direction of the base circle BC1.

[0052] The truncated hypocycloid curve La2 is drawn through the locus of drawing point DP2 as the rolling circle RC1 rolls on the base circle BC1. Since drawing point DP2 lies inside the rolling circle RC1, the truncated hypocycloid curve La2 does not touch the base circle BC1. As the rolling circle RC1 completes one revolution of the base circle BC1, the truncated hypocycloid curve La2 is drawn inside the base circle BC1 such that convex sections, projecting radially outward from the base circle BC1, and concave sections, projecting radially inward into the base circle BC1, are arranged alternately in the circumferential direction of the base circle BC1.

[0053] The stretched hypocycloid curve La3 is drawn through the locus of drawing point DP3 as the rolling circle RC1 rolls on the base circle BC1. Since drawing point DP3 lies outside the rolling circle RC1, the stretched hypocycloid curve La3 intersects the base circle BC1. The stretched hypocycloid curve La3 itself also intersects radially inside the base circle BC1. When the rolling circle RC1 completes one revolution around the base circle BC1, the foreshortened hypocycloid curve La2 is drawn such that its intersecting segments and concave segments, which are concave radially inward toward the base circle BC1, are arranged alternately around the circumference of the base circle BC1.

[0054] As in Fig. As shown in Figure 4, the epicycloid curve La4 La1 is drawn through the locus of drawing point DP4 when the rolling circle RC2 rolls on the base circle BC1. Since the rolling circle RC2 is located outside the base circle BC1, the epicycloid curve La4 is drawn such that convex sections projecting radially outward from the base circle BC1 are arranged continuously in the circumferential direction of the base circle BC1.

[0055] The shortened epicycloid curve La5 is drawn through the locus of the drawing point DP5 when the rolling circle RC2 rolls on the base circle BC1. Since the rolling circle RC2 is located outside the base circle BC1, the shortened epicycloid curve La5 is drawn outside the base circle BC1 such that concave sections, which are concave radially inward toward the base circle BC1, and convex sections, which project radially outward from the base circle BC1, are arranged alternately in the circumferential direction of the base circle BC1.

[0056] The stretched epicycloid curve La6 is drawn through the locus of the drawing point DP6 when the rolling circle RC2 rolls on the base circle BC1. Since the rolling circle RC2 is located outside the base circle BC1, the stretched epicycloid curve La6 is drawn such that its intersecting segments and convex segments, which project radially outward from the base circle BC1, are continuous in the circumferential direction of the base circle BC1.

[0057] Due to the property of the rolling circles RC1 and RC2 to roll on the base circle BC1 without slippage, the normal line to each point on these cycloidal curves La1, La2, La3, La4, La5 and La6 is a straight line that runs from each point on the cycloidal curves La1, La2, La3, La4, La5 and La6 through the contact point between the rolling circles RC1 and RC2, which corresponds to that point, and the base circle BC1.

[0058] Fig. Figure 5 is a schematic diagram of a gear pair 940 of a standard cycloidal drive. The gear pair 40 of the present embodiment has a configuration that was developed from the gear pair 940 of a standard cycloidal gear, which is described below. For this reason, the gear pair 940 of a standard cycloidal drive will be described first.

[0059] In the following description, a gear pair of a standard cycloidal drive is referred to as the standard gear pair 940, and an internal gear and an external gear forming the standard gear pair 940 are referred to as the standard internal gear 910 and standard external gear 920, respectively. The number of teeth N + 1 of the standard external gear 920 is exactly one less than the number of teeth N of the standard internal gear 910 (N being a natural number). The standard external gear 920 is in inscribed mesh with the standard internal gear 910. A first base circle 912 and a second base circle 922 are specified to have radii of N + 1:N and are arranged to be partially inscribed. The center point O1 of the first base circle 912 and the center point O2 of the second base circle 922 are arranged at positions that are spaced apart by an eccentricity amount Ec9.

[0060] The tooth profile of the standard internal gear 910 is drawn on the basis of the first base circle 912. The standard internal gear 910 includes a tooth tip 911A, which is arranged radially inside relative to the first base circle 912, and a tooth root 911B, which is arranged radially outside relative to the first base circle 912.

[0061] Similarly, the tooth profile of the standard external gear 920 is drawn based on the second base circle 922. The standard external gear 920 includes a tooth tip 921A, which is located radially outside the second base circle 922, and a tooth root 921B, which is located radially inside the second base circle 922.

[0062] Fig. 6 and Fig. Figure 7 shows partially enlarged views of the tooth profile design of the standard 940 gear pair. Fig. 5 illustrate. As in Fig. As shown in Figure 6, the tooth tip 911A of the standard internal gear 910 is formed from a first cycloidal curve L915A. The first cycloidal curve L915A is drawn as the locus of a first drawing point 914A, which lies on the circumference of a first rolling circle 913A that rolls on the first base circle 912 while being inscribed within the first base circle 912. That is, the first cycloidal curve L915A is a hypocycloid curve.

[0063] The tooth root 911B of the standard internal gear 910 is formed by a third cycloidal curve L915B. The third cycloidal curve L915B is drawn as the locus of a third drawing point 914B, which lies on the circumference of a third rolling circle 913B that rolls on the first base circle 912 while circumscribing the first base circle 912. That is, the third cycloidal curve L915B is an epicycloidal curve.

[0064] The tooth tip 921A of the standard external gear 920 is formed by a second cycloidal curve L925A. The second cycloidal curve L925A is drawn as the locus of a second drawing point 924A, which lies on the circumference of a second rolling circle 923A that rolls on the second base circle 922 and thereby circumscribes the second base circle 922. That is, the second cycloidal curve L925A is an epicycloidal curve.

[0065] The tooth root 921B of the standard external gear 920 is formed by a fourth cycloidal curve L925B. The fourth cycloidal curve L925B is drawn as the locus of a fourth drawing point 924B, which lies on the circumference of a fourth rolling circle 923B that rolls on the second base circle 922 while being inscribed within the second base circle 922. That is, the fourth cycloidal curve L925B is a hypocycloidal curve.

[0066] The parameters of the standard gear pair 940 are defined as follows. The radius of the first base circle 912 is defined as the first base circle radius a91. The radius of the second base circle 922 is defined as the second base circle radius a92. The radius of the first rolling circle 913A is defined as the first rolling circle radius b91. The radius of the second rolling circle 923A is defined as the second rolling circle radius b92. The radius of the third rolling circle 913B is defined as the third rolling circle radius b93. The radius of the fourth rolling circle 923B is defined as the fourth rolling circle radius b94.

[0067] In the standard gear pair 940, the first rolling circle radius b91, the second rolling circle radius b92, the third rolling circle radius b93 and the fourth rolling circle radius b94 are all the same size (b91 = b92 = b93 = b94).

[0068] Next, the angular transmission error in the standard 940 gear pair is confirmed. Fig. Figure 6 shows a contact point A between the first cycloid curve L915A and the second cycloid curve L925A. Fig. Figure 6 also shows a tangent point B between the first rolling circle 913A and the first base circle 912 in a state in which the contact point A and the first drawing point 914A coincide. Fig. Figure 6 further shows a tangent point C between the second rolling circle 923A and the second base circle 922 in a state in which the contact point A and the second drawing point 924A coincide.

[0069] The first cycloidal curve L915A and the second cycloidal curve L925A are tangent to each other at point A. Due to the property of the cycloidal curve described above, the normal line to point A of L915A is a straight line that includes point A and point B of tangency, and the normal line to point A of L925A is a straight line that includes point A and point C of tangency. Therefore, line segments AB and AC coincide with the common normal line to both the first cycloidal curve L915A and the second cycloidal curve L925A at point A. In the following description, the straight line passing through point B of tangency, point A of contact, and point C of tangency is referred to as the normal line BC.

[0070] Since the same number of tooth tips 911A and tooth roots 911B are arranged on the circumference of the first base circle 912 as the number of teeth N + 1 of the standard internal gear 910, the first base circle radius a91 is equal to N + 1 times the sum of the first rolling circle radius b91 and the third rolling circle radius b93: a91=(N+1)×(b91+b93)

[0071] Since the same number of tooth tips 921A and tooth roots 921B are arranged on the circumference of the second base circle as the number of teeth N of the outer gear, the radius of the second base circle a92 is N times the sum of the second rolling circle radius b92 and the fourth rolling circle radius b94: a92=N×(b93+b94)

[0072] Fig. Figure 7 shows a path (central path DO) of a center point D of the first rolling circle 913A and a path (central path EO) of a center point E of the second rolling circle 923A.

[0073] As described above, the length of line segment BO1 (i.e., the first base circle radius a91) and the length of line segment CO2 (i.e., the second base circle radius a92) are in the ratio N + 1:N. From the formula for calculating the lengths of the first base circle radius a91 and the second base circle radius a92, it follows that the sum of the first rolling circle radius b91 and the third rolling circle radius b93 is equal to the sum of the second rolling circle radius b92 and the fourth rolling circle radius b94. Since, as described above, the first through fourth base circle radii b1, b2, b3, and b4 are all equal, the difference between the length of line segment BO1 (i.e., the first base circle radius a91) and the length of line segment CO2 (i.e., the second base circle radius a92) is two rolling circles (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, since the base circles are tangent to each other. Therefore, the distance between the center D of the first rolling circle 913A and the center O1 of the first base circle 912 (the length of line segment DO1) is equal to the distance between the center E of the second rolling circle 923A and the center O2 of the second base circle 922 (the length of line segment EO2). Furthermore, since the first cycloidal curve L915A and the second cycloidal curve L925A are tangent at the point of contact A, center D, point of contact A, and center E lie on a straight line, and the distance between center D and center E (the length of line segment DE) is equal to Ec9 (Ec9 = b91 + b92).

[0074] This means that in the standard gear pair 940, the lengths of line segment DO1 and EO2 are equal, and the lengths of line segment DE and eccentricity magnitude Ec9 are equal. Therefore, the quadrilateral 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 to each other, irrespective of the meshing position of the standard internal gear 910 and the standard external gear 920.

[0075] It is assumed that on the normal BC there exists a division point P at which triangle BO1P is similar to triangles BDA and CEA. As described above, line segment DE and line segment O1O2 are always parallel to each other, even when the contact point A moves (i.e., even when the standard external gear 920 oscillates and rotates). Therefore, the similarity relationship between triangle BO1P, triangle BDA, and triangle CEA is always maintained, regardless of the phase of the contact point A. Consequently, the normal BC always passes through a division point P, regardless of the phase of the contact point A. It follows that the standard gear pair 940 satisfies Camus' theorem. Furthermore, in the standard gear pair 940, if elastic deformations are disregarded, the angular transmission error becomes zero, enabling uniform power transmission.

[0076] In the associated technique, attempts were made to construct cycloidal gears formed by modifying the parameters of the standard gear pair 940 described above, with the aim of reducing surface pressure. As examples, attempts were made to construct a gear pair in which the first rolling circle radius b91 and the second rolling circle radius b92 are different, a gear pair in which the first rolling circle radius b91 and the distance to the rolling point are different, and a gear pair in which the second rolling circle radius b92 and the distance to the drawing point are different.

[0077] However, in conventional cycloidal gears, where each parameter is changed, the design is not based on Camus' theorem, so the angular transmission error cannot be reduced to zero and uniform power transmission is not possible. The inventor has developed a design method in which the parameters of the standard 940 gear pair are changed within a range that satisfies Camus' theorem, and the angular transmission error becomes zero even for a gear pair made of cycloidal gears that deviate from the standard cycloidal gears.

[0078] Fig. Figure 8 is a front view of the gear pair 40 of the present embodiment. Fig. Image 9 is a partially enlarged view of Fig. 8. As in Fig. As shown in Figure 8, the gear pair 40 includes an internal gear 10 and an external gear 20, which is in inscribed tooth mesh with the internal gear 10.

[0079] The internal gear 10 is a cycloidal gear centered on a center point O1. The internal gear 10 has nine internal teeth 11 that project radially inward relative to the center point O1. At least one section of the internal teeth 11 is described by a first tooth profile curve L19A, which will be explained later, and at least one section of the internal teeth 11 is described by a third tooth profile curve L19B, which will be explained later.

[0080] The external gear 20 is a cycloidal gear centered on a center point O2. The external gear 20 has eight external teeth 21 that project radially outwards relative to the center point O2. At least one section of the external teeth 21 is described by a second tooth profile curve L29A, which will be described later, and at least one section of the external teeth 21 is described by a fourth tooth profile curve L29B, which will be described later.

[0081] In the gear pair 40 of the present embodiment, the number of teeth of the outer gear 20 can be only one tooth less than the number of teeth of the inner gear 10. That is, if a natural number N is used and the number of teeth of the outer gear 20 is N, the number of teeth of the inner gear 10 is expressed as N + 1. A first base circle 12 of the inner gear 10 and a second base circle 22 of the outer gear 20 are defined such that their radii are N + 1:N. The center O1 of the first base circle 12 and the center O2 of the second base circle 22 are arranged at positions spaced apart from each other by an eccentricity Ec, which will be described later.

[0082] The gear pair 40 of the present embodiment forms the Fig. 2. Gearbox 7 is shown. In gearbox 7, the internal gear 10 is attached to the housing 6a, and the external gear 20 is connected to the output shaft of the motor 8. When the output shaft of the motor 8 rotates, the external gear 20 can rotate about its center point O2 while oscillating about its center point O1 of the internal gear 10. The meshing position of the external gear 20 relative to the internal gear 10 changes as the external gear 20 oscillates and rotates. As a result of this changing meshing position, the external gear 20 rotates by the difference in the number of teeth between the external gear 20 and the internal gear 10 each time the output shaft of the motor 8 rotates once. In the present embodiment, the outer gear 20 rotates by one tooth each time the output shaft of the motor 8 rotates once, since the difference in the number of teeth is 1.

[0083] The design of the gearbox 7 is not limited to the present embodiment. For example, the gearbox 7 can be connected to the motor 8 and the housing 6a in such a way that the rotational speed of the output shaft increases relative to the rotational speed of the output shaft of the motor 8. Furthermore, the gearbox 7 can include a plurality of gear pairs 40.

[0084] As in Fig. Figure 9 shows the tooth profile of the internal gear 10, based on the first base circle 12. The internal gear 10 includes a tooth tip 11A, a tooth root 11B, and a connecting section 11C. The tooth tip 11A is a radially inwardly convex section of the tooth profile of the internal gear 10. The tooth root 11B is a radially outwardly concave section of the tooth profile of the internal gear 10. The connecting section 11C is a section that joins the tooth tip 11A and the tooth root 11B.

[0085] The first tooth profile curve L19A of the tooth tip 11A is formed on the basis of a first cycloidal curve L15A. The first cycloidal curve L15A is drawn as the locus of a first drawing point 14A, which lies on the circumference, inside or outside a first rolling circle 13A, which rolls on the first base circle 12 while being inscribed in the first base circle 12.

[0086] Similarly, the tooth root 11B is drawn by the third tooth profile curve L19B. In the internal gear 10, the third tooth profile curve L19B is formed based on the third cycloidal curve L15B. The third cycloidal curve L15B is drawn as the locus of a third drawing point 14B, which lies on the circumference, inside or outside a third rolling circle 13B, which rolls on the first base circle 12 while circumscribing the first base circle 12.

[0087] The tooth profile of the external gear 20 is drawn based on the second base circle 22. The external gear 20 includes a tooth tip 21A, a tooth root 21B, and a connecting section 21C. The tooth tip 21A is a radially outward convex section of the tooth profile of the external gear 20. The tooth root 21B is a radially inward concave section of the tooth profile of the external gear 20. The connecting section 21C is a section that joins the tooth tip 21A and the tooth root 21B.

[0088] The tooth tip 21A is defined by a second tooth profile curve L29A. In the outer gear 20, the second tooth profile curve L29A is formed based on the second cycloidal curve L25A. The second cycloidal curve L25A is drawn as the locus of a second drawing point 24A, which lies on the circumference, inside or outside a second rolling circle 23A that rolls on the second base circle 22 while circumscribing the second base circle 22.

[0089] Similarly, the tooth root 21B is drawn by the fourth tooth profile curve L29B. In the outer gear 20, the fourth tooth profile curve L29B is formed based on the fourth cycloidal curve L25B. The fourth cycloidal curve L25B is drawn as the locus of a fourth drawing point 24B, which lies on the circumference, inside or outside a fourth rolling circle 23B, which rolls on the second base circle 22 while being inscribed in the second base circle 22.

[0090] Here, the parameters of the gear pair 40 of the present embodiment are defined as follows. The radius of the first base circle 12 is defined as the first base circle radius a1. The radius of the first rolling circle 13A is defined as the first rolling circle radius b1. The distance from the center of the first rolling circle 13A to the first drawing point 14A is defined as the absolute value of a first drawing point distance c1. The radius of the second base circle 22 is defined as the second base circle radius a2. The radius of the second rolling circle 23A is defined as the second rolling circle radius b2. The distance from the center of the second rolling circle 23A to the second drawing point 24A is defined as the absolute value of a second drawing point distance c2. The radius of the third rolling circle 13B is defined as the third rolling circle radius b3.The distance from the center of the third rolling circle 13B to the third drawing point 14B is defined as the absolute value of a third drawing point distance c3. The radius of the fourth rolling circle 23B is defined as the fourth rolling circle radius b4. The distance from the center of the fourth rolling circle 23B to the fourth drawing point 24B is defined as the absolute value of a fourth drawing point distance c4. The distance between the center O1 of the first base circle 12 and the center O2 of the second base circle 22 is defined as the eccentricity value Ec.

[0091] Here, it is assumed that the first rolling circle radius b1, the second rolling circle radius b2, the third rolling circle radius b3, and the fourth rolling circle radius b4 can each be either a positive or a negative value, where (b1 > 0 or b1 < 0, b2 > 0 or b2 < 0, b3 > 0 or b3 < 0, b4 > 0 or b4 < 0). Similarly, it is assumed that the first drawing point spacing c1, the second drawing point spacing c2, the third drawing point spacing c3, ​​and the fourth drawing point spacing c4 can each be either a positive or a negative value, where (c1 > 0 or c1 < 0, c2 > 0 or c2 < 0, c3 > 0 or c3 < 0, c4 > 0 or c4 < 0).The signs of the first drawing point spacing c1 coincide with the signs of the first rolling circle radius b1, the signs of the second drawing point spacing c2 coincide with the signs of the second rolling circle radius b2, the signs of the third drawing point spacing c3 coincide with the signs of the third rolling circle radius b3, and the signs of the fourth drawing point spacing c4 coincide with the signs of the fourth rolling circle radius b4. Furthermore, the first base circle radius a1, the second base circle radius a2, and the eccentricity Ec of the distance between the center O1 of the first base circle radius 12 and the center O2 of the second base circle radius 22 can only take positive values. Since the internal gear 10 meshes radially with the external gear 20, the first base circle radius a1 is naturally larger than the second base circle radius a2 (a1 > a2).

[0092] Fig. Figure 10 is a diagram representing a cycloidal curve, plotted in a case where the first rolling circle radius b1 and the fourth rolling circle radius b4 have positive and negative values, respectively. The base circle BC1 in Fig. 10 is either the first base circle 12 or the second base circle 22.

[0093] In a case where the first rolling circle radius b1 is a positive value, the first rolling circle 13A is inscribed in the base circle BC and during rolling in the circumferential direction (in Fig. 10 counterclockwise) to one side, thereby drawing one of the hypocycloid curves La1, La2, and La3 as the locus of the first drawing point 14A. Similarly, in a case where the fourth rolling circle radius b4 is a positive value, the fourth rolling circle 23B is inscribed in the base circle BC and, during rolling in the circumferential direction (in Fig. 10 counterclockwise) to one side, whereby one of the hypocycloid curves La1, La2 and La3 is drawn as the locus of the fourth drawing point 24B.

[0094] In a case where the first rolling circle radius b1 is a negative value, the first rolling circle 13A is circumscribed around the base circle BC and during rolling in the circumferential direction (in Fig. 10 clockwise) to the other side, whereby one of the epicycloid curves Lb1, Lb2 and Lb3 is drawn as the locus of the first drawing point 14A. Similarly, in a case where the fourth rolling circle radius b4 is a negative value, the fourth rolling circle 23B is circumscribed around the base circle BC and, while rolling in the circumferential direction (in Fig. 10 clockwise) to the other side, whereby one of the epicycloid curves Lb1, Lb2 and Lb3 is drawn as the locus of the fourth drawing point 24B.

[0095] Fig. Figure 11 is a diagram illustrating a cycloidal curve plotted in a case where the second rolling circle radius b2 or the third rolling circle radius b3 is a positive value. The base circle BC1 in Fig. 11 is either the first base circle 12 or the second base circle 22.

[0096] In a case where the second rolling circle radius b2 is a positive value, the second rolling circle 23A is circumscribed around the base circle BC and during rolling in the circumferential direction (in Fig. 11 clockwise) to the other side, whereby one of the epicycloid curves La4, La5 and La6 is drawn as the locus of the second drawing point 24A. Similarly, in a case where the third rolling circle radius b3 is a positive value, the third rolling circle 13B is circumscribed around the base circle BC and, during rolling in the circumferential direction (in Fig. 11 clockwise) to the other side, whereby one of the epicycloid curves La4, La5 and La6 is drawn as the locus of the third drawing point 14B.

[0097] In a case where the second rolling circle radius b2 is a negative value, the second rolling circle 23A is inscribed in the base circle BC and during rolling in the circumferential direction (in Fig. 11 counterclockwise) to one side, thereby drawing one of the hypocycloid curves Lb4, Lb5, and Lb6 as the locus of the second drawing point 24A. Similarly, in a case where the third rolling circle radius b3 is a negative value, the third rolling circle 13B is inscribed in the base circle BC and, during rolling in the circumferential direction (in Fig. 11 counterclockwise) to one side, whereby one of the hypocycloid curves Lb4, Lb5 and Lb6 is drawn as the locus of the third drawing point 14B.

[0098] The relationship between the values ​​of the first rolling circle radius b1 and the first drawing point distance c1 and the first cycloidal curve L15A is described.

[0099] First, a case is described in which the first rolling circle radius b1 and the first drawing point spacing c1 are both positive values. In this case, the first cycloidal curve L15A is a hypocycloid curve with a rolling circle radius |b1| if the absolute value of the first drawing point spacing c1 is equal to the absolute value of the first rolling circle radius b1. The first cycloidal curve L15A is a truncated hypocycloid curve if the absolute value of the first drawing point spacing c1 is smaller than the absolute value of the first rolling circle b1. The first cycloidal curve L15A is a stretched hypocycloid curve if the absolute value of the first drawing point spacing c1 is larger than the absolute value of the first rolling circle b1.

[0100] Next, a case is described in which the first rolling circle radius b1 and the first drawing radius c1 are both negative values. In this case, the first cycloidal curve L15A is an epicycloidal curve with a rolling circle radius |b1| if the absolute value of the first drawing radius c1 is equal to the absolute value of the first rolling circle radius b1. The first cycloidal curve L15A is a truncated epicycloidal curve if the absolute value of the first drawing point distance c1 is smaller than the absolute value of the first rolling circle radius b1. The first cycloidal curve L15A is a stretched epicycloidal curve if the absolute value of the first drawing point distance c1 is larger than the absolute value of the first rolling circle radius b1.

[0101] In the Fig. In the example shown, the first rolling circle radius b1 and the first drawing point distance c1 are positive values, and the first cycloid curve L15A is a truncated hypocycloid curve.

[0102] The relationship between the values ​​of the second rolling circle radius b2 and the second drawing point distance c2 and the second cycloidal curve L25A is described.

[0103] First, a case is described in which the second rolling circle radius b2 and the second drawing point distance c2 are both positive values. In this case, the second cycloidal curve L25A is an epicycloidal curve with a rolling circle radius |b2| if the absolute value of the second drawing point distance c2 is equal to the absolute value of the second rolling circle radius b2. The second cycloidal curve L25A is a truncated epicycloidal curve if the absolute value of the second drawing point radius c2 is smaller than the absolute value of the second rolling circle b2. The second cycloidal curve L25A is a stretched epicycloidal curve if the absolute value of the second drawing point radius c2 is larger than the absolute value of the second rolling circle b2.

[0104] Next, a case is described in which the second rolling circle radius b2 and the second drawing radius c2 are both negative values. In this case, the second cycloidal curve L25A is a hypocycloid curve with a rolling circle radius |b2| if the absolute value of the second drawing radius c2 is equal to the absolute value of the second rolling circle radius b2. The second cycloidal curve L25A is a truncated hypocycloid curve if the absolute value of the second drawing point distance c2 is less than the absolute value of the second rolling circle b2. The second cycloidal curve L25A is a stretched hypocycloid curve if the absolute value of the second drawing point distance c2 is greater than the absolute value of the second rolling circle b2.

[0105] In the Fig. In the example shown, the second rolling circle radius b2 and the second drawing point distance c2 are positive values, and the second cycloid curve L25A is a shortened epicycloid curve.

[0106] The relationship between the values ​​of the third rolling circle radius b3 and the third drawing point distance c3 and the third cycloidal curve L15B is described.

[0107] First, a case is described in which the third rolling circle radius b3 and the third drawing point distance c3 are both positive values. In this case, the third cycloid curve L15B is an epicycloid curve with a rolling circle radius |b3| if the absolute value of the third drawing point distance c3 is equal to the absolute value of the third rolling circle radius b3. The third cycloid curve L15B is a truncated epicycloid curve if the absolute value of the third drawing point distance c3 is less than the absolute value of the third rolling circle b3. The third cycloid curve L15B is a stretched epicycloid curve if the absolute value of the third drawing point distance c3 is greater than the absolute value of the third rolling circle b3.

[0108] Next, a case is described in which the third rolling circle radius b3 and the third drawing point spacing c3 both have negative values. In this case, the third cycloidal curve L15B is a hypocycloid with a rolling circle radius |b3| if the absolute value of the third drawing point spacing c3 is equal to the absolute value of the third rolling circle radius b3. The third cycloidal curve L15B is a truncated hypocycloid if the absolute value of the third drawing point spacing c3 is less than the absolute value of the third rolling circle b3. The third cycloidal curve L15B is a stretched hypocycloid if the absolute value of the third drawing point spacing c3 is greater than the absolute value of the third rolling circle b3.

[0109] In the Fig. In the example shown, the third rolling circle radius b3 and the third drawing point distance c3 are positive values, and the third cycloid curve L15B is a shortened epicycloid curve.

[0110] The relationship between the values ​​of the fourth rolling circle radius b4 and the fourth drawing point distance c4 and the fourth cycloidal curve L25B is described.

[0111] First, a case is described in which the fourth rolling circle radius b4 and the fourth drawing point spacing c4 are both positive values. In this case, the fourth cycloid curve L25B is a hypocycloid curve with a rolling circle radius |b4| if the absolute value of the fourth drawing point spacing c4 is equal to the absolute value of the fourth rolling circle radius b4. The fourth cycloid curve L25B is a truncated hypocycloid curve if the absolute value of the fourth drawing point spacing c4 is less than the absolute value of the fourth rolling circle b4. The fourth cycloid curve L25B is a stretched hypocycloid curve if the absolute value of the fourth drawing point spacing c4 is greater than the absolute value of the fourth rolling circle b4.

[0112] Next, a case is described in which the fourth rolling circle radius b4 and the fourth drawing point spacing c4 are both negative values. In this case, the fourth cycloid curve L25B is an epicycloid curve with a rolling circle radius |b4| if the absolute value of the fourth drawing point spacing c4 is equal to the absolute value of the fourth rolling circle radius b4. The fourth cycloid curve L25B is a truncated epicycloid curve in a case where the absolute value of the fourth drawing point spacing c4 is less than the absolute value of the fourth rolling circle radius b4. The fourth cycloid curve L25B is a stretched epicycloid curve in a case where the absolute value of the fourth drawing point spacing c4 is greater than the absolute value of the fourth rolling circle radius b4.

[0113] In the Fig. In the example shown, the fourth rolling circle radius b4 and the fourth drawing point distance c4 are positive values, and the fourth cycloid curve L25B is a truncated hypocycloid curve.

[0114] Fig. Figure 12 is a diagram that schematically illustrates the course of the engagement between the tooth tip 11A of the internal gear 10 and the tooth tip 21A of the external gear 20. As shown in Fig. As shown in Figure 12, a contact point A runs between the tooth tip 11A of the internal gear 10 and the tooth tip 21A of the external gear 20 on their respective tooth profiles. A roll angle α of the first rolling circle 13A, which forms the tooth tip 11A of the internal gear 10, and a roll angle β of the second rolling circle 23A, which forms the tooth tip 21A of the external gear 20, are synchronized with each other.

[0115] To produce meshing, the circumferential dimension of the tooth tip 11A of the internal gear 10 and the circumferential dimension of the tooth root 21B of the external gear 20 must be identical. Therefore, the first rolling circle radius b1 and the fourth rolling circle radius b4 are equal (b1 = b4). Similarly, the circumferential dimension of the tooth root 11B of the internal gear 10 and the circumferential dimension of the tooth tip 21A of the external gear 20 are identical. Therefore, the second rolling circle radius b2 and the third rolling circle radius b3 are equal (b2 = b3).

[0116] As described above, a natural number N is used, and the number of teeth of the internal gear, 10, is expressed as N + 1. As in Fig. As shown in Figure 9, the first rolling circle 13A and the third rolling circle 13B alternately roll N + 1 times around the circumference of the first base circle 12 to draw the first cycloidal curve L15A and the third cycloidal 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 rolling circle 13A (2π × b1) and the circumference of the third rolling circle 13B (2π × b3). 2π×a1=(N+1)×(2π×b1+2π×b3)

[0117] By transforming this expression using the fact that the radius of the third rolling circle b3 is equal to the radius of the second rolling circle b2, the following condition expression 1 can be derived as the relationship that must be satisfied between the first base circle radius a1, the first rolling circle radius b1 and the second rolling circle radius b2: a1=(N+1)×(b1+b2)

[0118] As described above, the number of teeth of the outer gear 20 is expressed as N. The second rolling circle 23A and the fourth rolling circle 23B alternately roll N times around the circumference of the second base circle 22 to trace the second cycloidal curve L25A and the fourth cycloidal curve L25B. Therefore, the circumference of the second base circle 22 (2π × a²) is N times the sum of the circumference of the second rolling circle 23A (2π × b²) and the circumference of the fourth rolling circle 23B (2π × b⁴). 2π×a2=N×(2π×b2+2π×b4)

[0119] By transforming this expression using the fact that the fourth rolling circle radius b4 is equal to the first rolling circle radius b1, the following condition expression 2 can be derived as the relationship that must be satisfied between the second basic circle radius a2, the first rolling circle radius b1 and the second rolling circle radius b2: a2=N×(b1+b2)

[0120] Note that conditions 1 and 2 above are also satisfied if either the first rolling circle radius b1 or the second rolling circle radius b2 is a negative value. For example, if the second rolling circle radius b2 is a negative value, the first rolling circle radius b1 is a value large enough relative to the absolute value |b2| of the second rolling circle radius b2 to satisfy conditions 1 and 2 above.

[0121] Fig. Figure 13 is a schematic diagram showing the first rolling circle 13A and the second rolling 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. Fig. Figure 13 shows a contact point A between the tooth tip 11A of the internal gear 10 and the tooth tip 21A of the external gear 20. Fig. Figure 13 also shows a tangent point B between the first rolling circle 13A and the first base circle 12 in a state in which the contact point A and the first drawing point 14A coincide. Fig. Figure 13 further shows a tangent point C between the second rolling circle 23A and the second base circle 22 in a state in which the contact point A and the second drawing point 24A coincide. Fig. 13 is the center point of the first rolling circle 13A, defined as center point D, and the center point of the second rolling circle 23A is defined as center point E.

[0122] Similar to the standard 940 gear pair (see Fig. 6 and Fig. 7) The contact point A is located at the intersection of the normal BC and the line DE. In the Fig. In the example shown, the first drawing point 14A is located within the first rolling circle 13A, and the second drawing point 24A is located within the second rolling circle 23A. Therefore, the first rolling circle 13A and the second rolling circle 23A partially overlap. The first drawing point 14A and the second drawing point 24A overlap at contact point A.

[0123] As in the case of the standard gear pair 940, if the gear pair 40 satisfies Camus' theorem, the division point P lies on the extension of the normal BC, regardless of the phase of the contact point A. Furthermore, to achieve this configuration, triangles BDA and CEA are always similar, regardless of the phase of the contact point A. Therefore, for the gear pair 40 to satisfy Camus' theorem, the ratio of segment BD to segment DA must be equal to the ratio of segment CE to segment EA. Here, the length of segment BD is the first rolling circle radius b1, the length of segment DA is the first drawing point distance c1, the length of segment CE is the second rolling circle radius b2, and the length of segment EA is the second drawing point distance c2. Thus, the following condition expression 3 results as a necessary condition for the case that the gear pair 40 satisfies Camus' theorem: b1:c1=b2:c2

[0124] Furthermore, in a case where the gear pair 40 satisfies Camus' theorem, triangle BDA and triangle CEA are always similar to triangle PO2C. Since the respective angles are equal in this case, line segments DA and EA are parallel to line segment O1O2. That is, quadrilateral DEO1O2 is always a parallelogram, regardless of the phase of the 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 length of line segment O1O2 is equal to the sum of the lengths of line segment DA and EA. The dimension of line O1O2 is the eccentricity Ec between the first base circle 12 and the second base circle 22.Furthermore, the dimension of line DA is the first drawing point distance c1 and the dimension of line EA is the second drawing point distance c2. Therefore, the following condition expression 4 is derived as a necessary condition in the case that the gear pair 40 satisfies Camus' theorem: Ec=c1+c2

[0125] If conditions 1 to 4 are satisfied, the gear pair 40 can satisfy Camus' theorem and the angular transmission error can be reduced. In other words, as long as conditions 1 to 4 are satisfied, the parameters of gear pair 40 can be freely adjusted without worsening the angular transmission error.

[0126] Here, a first parameter P1, a second parameter P2, and a third parameter P3 are defined for tooth tips 11A and 21A. The first parameter P1, the second parameter P2, and the third parameter P3 are described in more detail below.

[0127] In the Fig. In the gear pair 40 of the present embodiment shown in 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

[0128] In the standard gear pair 940 described above (see Fig. 6) The first rolling circle radius b1 and the second rolling circle radius b2 are equal, so the first parameter P1 is equal to 1. By setting the first parameter P1 to a value other than 1 (i.e., P1 > 1 or P1 < 1), a gear pair 40 with different properties than the standard gear pair 940 can be formed.

[0129] Here, with regard to the first parameter P1, the setting P1 > 1 or P1 < 1 is referred to as the first setting. That is, the first setting means that the first cycloidal curve L15A and the second cycloidal curve L25A are drawn using the first parameter P1, which satisfies P1 > 1 or P1 < 1.

[0130] Fig. Figure 14 is a diagram illustrating the relationship between the first rolling circuit 13A, the second rolling circuit 23A, and the contact point A in a case where P1 > 1. That is, in which Fig. In the example shown in Figure 14, the first rolling circle radius b1 is smaller than the second rolling circle radius b2 (b1 < b2). In a case where 0 < P1 < 1, the size ratio between the first rolling circle radius b1 and the second rolling circle radius b2 is reversed (b1 > b2).

[0131] Fig. Figure 15 is a diagram illustrating the relationship between the first rolling circuit 13A, the second rolling circuit 23A, and the contact point A in a case where -1 < P1 < 0. That is, in which Fig. In the example shown in 15, the first parameter P1 is less than 1 (P1 < 1). In the example shown in Fig. In the example shown in Figure 15, the first rolling circle radius b1 is a positive value and larger than the second rolling circle radius b2. Furthermore, the second rolling circle radius b2 is a negative value (b1 > 0 > b2). In this case, the second cycloidal curve L25A becomes a hypocycloidal curve with a rolling circle radius |b2|, a shortened hypocycloidal curve, or a stretched hypocycloidal curve, and has a concave shape that is radially concave inwards. For this reason, it is not possible to form the tooth tip 21A of the external gear 20 if the second cycloidal curve L25A is used unchanged as the tooth profile curve. This also applies in the case where the first rolling circle radius b1 is negative and the second rolling circle radius b2 is positive (P1 < -1). Therefore, in a case where either the first rolling circle radius b1 or the second rolling circle radius b2 is negative (i.e.,in a case where P1 < 0), to deform the cycloidal curve using a third parameter P3 to be described later (see . Fig. 25).

[0132] In the Fig. In the gear pair 40 of the present embodiment shown in Figure 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)

[0133] The sum (b1 + b2) of the first rolling circle radius b1 and the second rolling circle radius b2 is the eccentricity value between the base circles of the standard gear pair 940 (see Fig. 6) The sum (c1 + c2) of the first drawing point distance c1 and the second drawing point distance c2 is the eccentricity value between the base circles in a case where the drawing point is offset from the circumference of the rolling circle (condition expression 4). Therefore, the second parameter P2 can also be defined as the eccentricity adjustment value in a case where the drawing point is offset from the circumference of the rolling circle.

[0134] In the standard gear pair 940 (see Fig. 6) The second parameter P2 is equal to zero. By setting the second parameter P2 to a value other than 0 (i.e., P2 ≠ 0), a gear pair 40 with different properties than the standard gear pair 940 can be created.

[0135] Considering conditional expressions 1 to 4 for satisfying Camus' theorem, on the right-hand side of the above expression, representing P2, the term representing the sum (b1 + b2) of the first rolling circle radius b1 and the second rolling circle radius b2, and the term representing the sum (c1 + c2) of the first drawing point distance c1 and the second drawing point distance c2, are always positive. Furthermore, if the second parameter P2 is positive, the first drawing point 14A is located inside the first rolling circle 13A, and the second drawing point 24A is located inside the second rolling circle 23A. If the second parameter P2 is negative, the first drawing point 14A is located outside the first rolling circle 13A, and the second drawing point 24A is located outside the second rolling circle 23A.

[0136] Here, with regard to the second parameter P2, the setting P2 ≠ 0 is referred to as the second setting. That is, the second setting means that the first cycloidal curve L15A and the second cycloidal curve L25A are plotted using the second parameter P2, which satisfies P2 ≠ 0.

[0137] Fig. Figure 16 is a diagram illustrating the relationship between the first rolling circuit 13A, the second rolling circuit 23A, and the contact point A in a case where P2 > 0. In the diagram shown... Fig. In the example shown in Figure 16, 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|), and the first drawing point 14A lies within the first rolling circle 13A. Furthermore, 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|), and the second drawing point 24A lies within the second rolling circle 23A. Therefore, the cycloidal curves drawn as loci of the first drawing points 14A and the second drawing points 24A are shortened cycloidal curves La2 and La5 (see Figure 16). Fig. 3 and Fig. 4).

[0138] Fig. Figure 17 is a diagram illustrating the relationship between the first rolling circuit 13A, the second rolling circuit 23A, and the contact point A in a case where P2 < 0. In the diagram shown... Fig. In the example shown in Figure 17, the absolute value of the first drawing point distance c1 is greater than the absolute value of the first rolling circle radius b1 (|c1| > |b1|), and the first drawing point 14A lies outside the first rolling circle 13A. Furthermore, the absolute value of the second drawing point distance c2 is greater than the absolute value of the second rolling circle b2 (|c2| > |b2|), and the second drawing point 24A lies outside the second rolling circle 23A. Therefore, the cycloidal curves drawn as loci of the first drawing points 14A and the second drawing points 24A are stretched cycloidal curves La3 and La6 (see Figure 17). Fig. 3 and Fig. 4).

[0139] In the Fig. In the gear pair 40 of the present embodiment shown in Figure 9, the third parameter P3 is an offset amount that shifts the first cycloidal curve L15A and the second cycloidal curve L25A by the same distance in the direction of the normal line BC. In the tooth profile curve of the embodiment, the first cycloidal curve L15A and the second cycloidal curve L25A can be deformed by offsetting them using the third parameter P3.

[0140] In the standard gear pair 940 (see Fig. 6) The third parameter P3 is zero. By setting the third parameter P3 to a value other than 0 (i.e., P3 ≠ 0), a gear pair 40 with different properties than the standard gear pair 940 can be created.

[0141] Here, with regard to the third parameter P3, the setting P3 ≠ 0 is referred to as the third setting. This means that the third setting involves offsetting the first cycloidal curve L15A and the second cycloidal curve L25A in the normal direction by the third parameter P3, using the third parameter P3, which satisfies P3 ≠ 0, to obtain the first tooth profile curve L19A and the second tooth profile curve L29A.

[0142] Fig. Figure 18 is a diagram illustrating the relationship between the first rolling circuit 13A, the second rolling circuit 23A, and the contact point A in a case where P3 > 0. As in Fig. As shown in Figure 18, the offset amount, represented as the third parameter P3, is positive in the direction of the normal line BC at contact point A, away from the centers O1 and O2 of the first base circle 12 and the second base circle 22. In a case where P3 > 0, the contact points A are offset by the third parameter P3 in a direction away from the centers O1 and O2 along the normal line BC defined for all contact points A of the first cycloidal curve L15A and the second cycloidal curve L25A. Here, the point obtained by offsetting the contact point A 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.

[0143] Fig. Figure 19 is a diagram illustrating the relationship between the first rolling circuit 13A, the second rolling circuit 23A, and the contact point A in a case where P3 < 0. As in Fig. As shown in Figure 19, the offset amount, represented as the third parameter P3, is negative in the direction of the normal line BC at contact point A, which approaches the centers O1 and O2 of the first base circle 12 and the second base circle 22. In a case where P3 > 0, the contact points A are offset by the third parameter P3 in a direction approaching the centers O1 and O2 on the normal lines BC defined for all contact points A of the first cycloidal curve L15A and the second cycloidal 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.

[0144] Since the first cycloidal curve L15A and the second cycloidal curve L25A satisfy Camus' theorem, the normal line BC always passes through the division 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 normal direction (the direction in which the normal line BC runs). Therefore, Camus' theorem is also satisfied in the tooth profile after the offset. Furthermore, no gap occurs at the offset point AA between the first tooth profile curve L19A and the second tooth profile curve L29A. That is, in the gear pair 40, which satisfies the third setting, no angular transmission error occurs when the internal gear 10 and the external gear 20 mesh.

[0145] Next, the tooth bases 11B and 21B of the internal gear 10 and the external gear 20 are described with reference to Fig. 9 described. The tooth root 11B of the internal gear 10 can have any shape as long as it matches the pitch of the tooth tip 21A of the external gear 20 and simultaneously prevents interference with the tooth tip 21A. Furthermore, the tooth root 21B of the external gear 20 can have any shape as long as it matches the pitch of the tooth tip 11A of the internal gear 10 and prevents interference with the tooth tip 11A.

[0146] In the gear pair 40 of the present 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 based on a cycloidal curve. This makes it easier to increase the stiffness of the internal gear 10 and the external gear 20 while simultaneously ensuring uniform meshing between the internal gear 10 and the external gear 20. 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 cycloidal curve.

[0147] In the present embodiment, the third rolling circle radius b3 is equal to the second rolling circle radius b2 (b3 = b2). Furthermore, the fourth rolling circle radius b4 is equal to the first rolling circle radius b1 (b4 = b1). According to the present embodiment, the pitch of the internal gear 10 and the pitch of the external gear 20 can be matched, thereby achieving uniform meshing.

[0148] In the present embodiment, the absolute value of the third drawing point spacing c3 is equal to or greater than the absolute value of the second drawing point spacing c2 (|c3| ≥ |c2|). Therefore, the third cycloidal curve L15B, drawn by the third drawing point 14B, does not interfere with the second cycloidal curve L25A, drawn by the second drawing point 24A, during engagement. This suppresses interference between the tooth root 11B of the internal gear 10 and the tooth tip 21A of the external gear 20. Furthermore, in the present embodiment, it is advantageous if the third drawing point spacing c3 is equal to the second drawing point spacing c2 (c3 = c2). This allows tooth roots 11B to be formed, enabling a uniform connection between the tooth tips 11A of the internal gear 10. Furthermore, the base thickness of the internal gear 10 can be maximized and the stiffness of the internal gear 10 can be increased.

[0149] In the present embodiment, the absolute value of the fourth drawing point spacing c4 is equal to or greater than the absolute value of the first drawing point spacing c1 (|c4| ≥ |c1|). Therefore, the fourth cycloidal curve L25B, drawn by the fourth drawing point 24B, does not interfere with the first cycloidal curve L15A, drawn by the first drawing point 14A, during engagement. This suppresses interference between the tooth root 21B of the external gear 20 and the tooth tip 11A of the internal gear 10. Furthermore, in the present embodiment, it is advantageous if the fourth drawing point spacing c4 is equal to the first drawing point spacing c1 (c4 = c1). This allows tooth roots 21B to be formed that provide a uniform connection between the tooth tips 21A of the external gear 20. Furthermore, the tooth root diameter of the outer gear 20 can be maximized and the stiffness of the outer gear 20 can be increased.

[0150] As described above, in a case where the gear pair 40 fulfills the third setting, the tooth tip 11A of the internal gear 10 is formed by offsetting the first cycloidal curve L15A in the normal direction, and the tooth tip 21A of the external gear 20 is formed by offsetting the second cycloidal curve L25A in the normal direction. In this case, for the third tooth profile curve L19B, which forms the tooth root 11B of the internal gear 10, a collision with the tooth tip 21A of the external gear 20 can be suppressed by offsetting the third cycloidal curve L15B in the normal direction. Similarly, for the fourth tooth profile curve L29B, which forms the tooth root 21B of the external gear 20, a disturbance of the tooth tip 11A of the internal gear 10 can be suppressed by offsetting the fourth cycloidal curve L25B in the normal direction. In the following description, the offset amount during the formation of the third tooth profile curve L19B is referred to as the third offset amount d3.Similarly, the offset amount in the formation of the fourth tooth profile curve L29B is referred to as the fourth offset amount d4.

[0151] Like the third parameter P3, the third offset amount d3 and the fourth offset amount d4 can also take on both positive and negative values, with the direction away from the centers O1 and O2 of the base circles 12 and 22 being positive.

[0152] In a case where the third cycloidal curve L15B is offset by the third offset amount d3 in the normal direction to form the third tooth profile curve L19B, the third offset amount d3 is set in the same direction as the offset direction of the second tooth profile curve L29A so that it does not interfere with the second tooth profile curve L29A during interlacing. More precisely, the third offset amount d3 can be equal to or greater than the third parameter P3 (d3 ≥ P3). Accordingly, the third tooth profile curve L19B can be positioned radially outside the second tooth profile curve L29A, and interference between the third tooth profile curve L19B and the second tooth profile curve L29A can be suppressed. The magnitude relationship that must be satisfied between the third offset amount d3 and the third parameter P3 (d3 ≥ P3) is determined regardless of whether the third offset amount d3 and the third parameter P3 are positive or negative.

[0153] In the present embodiment, it is particularly advantageous 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 provide a uniform connection between the tooth tips 11A of the internal gear 10. Furthermore, the root thickness of the internal gear 10 can be maximized, and the stiffness of the internal gear 10 can be increased.

[0154] In a case where the fourth cycloidal curve L25B is offset in the normal direction by the fourth offset amount d4 to form the fourth tooth profile curve L29B, the fourth offset amount d4 is set in the same direction as the offset direction of the first tooth profile curve L19A to avoid interfering with the first tooth profile curve L19A during engagement. More precisely, the fourth offset amount d4 can be equal to or less than the third parameter P3 (d4 ≤ P3). Accordingly, the fourth tooth profile curve L29B can be positioned radially inward from the first tooth profile curve L19A, and any interference between the fourth tooth profile curve L29B and the first tooth profile curve L19A can be suppressed. The magnitude relationship that must be satisfied between the fourth offset amount d4 and the third parameter P3 (d4 ≤ P3) is determined regardless of whether the fourth offset amount d4 and the third parameter P3 are positive or negative.

[0155] In the present embodiment, it is particularly advantageous if the fourth offset amount d4 is equal to the third parameter P3 (d4 = P3). This makes it possible to form tooth roots 21B that provide a uniform connection between the tooth tips 21A of the external gear 20. Furthermore, the tooth root diameter of the external gear 20 can be maximized and the stiffness of the external gear 20 increased.

[0156] Next, a specific embodiment of the gear pair 40 of the present model is described. The gear pair 40 of the present model fulfills all first, second, and third settings.

[0157] Fig. Figure 20 is a schematic diagram illustrating a method for forming the first tooth profile curve L19A of the present embodiment. Fig. Figure 21 is a schematic diagram illustrating a method for forming the second tooth profile curve L29A of the present embodiment.

[0158] In forming the tooth profile of the gear pair 40, the base circles 12 and 22 of the internal gear 10 and the external gear 20 are first defined. Then, the tooth profiles of the tooth tips 11A and 21A of the internal gear 10 and the external gear 20 are formed. Next, the tooth profiles of the tooth roots 11B and 21B of the internal gear 10 and the external gear 20 are formed. Finally, the connecting section 11C between the tooth tip 11A and the tooth root 11B is formed in the internal gear 10, and the connecting section 21C between the tooth tip 21A and the tooth root 21B is formed in the external gear 20.

[0159] Before forming the gear profile, a base circle is defined to serve as a reference. By determining the number of teeth of one of the gears and the base circle diameter of the other gear, the base circle diameters and the number of teeth of the inner gear 10 and the outer gear 20 in the gear pair 40 are determined. If the base circle diameter a2 and the number of teeth N of the outer gear 20 are given, the number of teeth of the inner gear 10 is N + 1 and the base circle diameter a1 is a2 / {N × (N + 1)}.

[0160] During the formation of tooth tips 11A and 21A, the first parameter P1, which fulfills the first setting, and the second parameter P2, which fulfills the second setting, are determined. Furthermore, the first cycloidal curve L15A (see Fig. 20) and the second cycloidal curve L25A (see Fig. 21) formed using the determined first parameter P1 and the second parameter P2.

[0161] Next, the third parameter P3 is determined, which satisfies the third setting. Using the determined third parameter P3, the first cycloidal curve L15A is offset in the normal direction to form the first tooth profile curve L19A (see Fig. 20), and the second cycloidal curve L25A is offset in the normal direction to form the second tooth profile curve L29A (see Fig. 21).

[0162] As in Fig. As shown in Figure 9, the first rolling circle radius b1 is larger than the second rolling circle radius b2 (0 < b2 < b1). In the gear pair 40 of the present embodiment, the first rolling circle radius b1 and the second rolling circle radius b2 are both 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).

[0163] In the gear pair 40 of the present embodiment, the second parameter P2 (= (b1 + b2) - (c1 + c2)) has a value greater than 0 (P2 > 0). In the gear pair 40 of the present embodiment, the first drawing point 14A is located within the first rolling circle 13A. Therefore, the absolute value of the first drawing point distance c1 is less 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 within the second rolling circle 23A. Therefore, the absolute value of the second drawing point distance c2 is less than the absolute value of the second rolling circle radius b2 (|c2| < |b2|).

[0164] In the gear pair 40 of the present embodiment, the third parameter P3 is a value greater than 0 (P3 > 0). As described above, the positive normal direction 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 cycloidal curve L15A and the second cycloidal curve L25A of the present embodiment are offset radially outward from the centers O1 and O2 by the third parameter P3 to form the first tooth profile curve L19A and the second tooth profile curve L29A, respectively.

[0165] It should be noted that the first parameter P1 and the second parameter P2 do not violate the aforementioned conditional expressions 1 to 4. Therefore, the first cycloidal curve L15A and the second cycloidal curve L25A satisfy Camus' theorem.

[0166] In the gear pair 40 of the present embodiment, at least one section of the inner gear 10 is described by the first tooth profile curve L19A, and at least one section of the outer gear 20 is described by the second tooth profile curve L29A. In particular, in the present embodiment, a radially inwardly convex section of the first tooth profile curve L19A describes the outer shape of the inner gear 10, and a radially outwardly convex section of the second tooth profile curve L29A describes the outer shape of the outer gear 20. Therefore, the inner gear 10 and the outer gear 20 always satisfy Camus' theorem when they mesh at the section described by the first tooth profile curve L19A and the section described by the second tooth profile curve L29A, and the force can be transmitted without an angular transmission error.

[0167] Next, a procedure for shaping tooth bases 11B and 21B will be described with reference to Fig. 9 described. The tooth feet 11B and 21B are formed using the same procedure as the tooth apexes 11A and 21A. That is, in the formation of the tooth feet 11B and 21B, the third cycloidal curve L15B and the second parameter P2 are first used to form the fourth cycloidal curve L25B.

[0168] As described above, the third rolling circle radius b3 is equal to the second rolling circle radius b2 (b3 = b2), and the fourth rolling circle radius b4 is equal to the first rolling circle radius b1 (b4 = b1). In the present embodiment, the third drawing point spacing c3 is equal to the second drawing point spacing c2 (c3 = c2), and the fourth drawing point spacing c4 is equal to the first drawing point spacing c1 (c4 = c1). The third offset amount d3 lies 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 lies 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).

[0169] In the present embodiment, at least one section of the internal gear 10 is described by the third tooth profile curve L19B, and at least one section of the external gear 20 is described by the fourth tooth profile curve L29B. In the present embodiment, a radially outwardly concave section of the third tooth profile curve L19B describes the outer shape of the tooth root 11B of the internal gear 10. Furthermore, a radially inwardly concave section of the fourth tooth profile curve L29B describes the outer shape of the tooth root 21B of the external gear 20. According to the present embodiment, it is possible to increase the stiffness of the internal gear 10 and the external gear 20 while simultaneously ensuring uniform meshing by preventing collisions between the tooth roots and the tooth tips of the internal gear 10 and the external gear 20.

[0170] Fig. Figure 22 is a schematic diagram illustrating a connecting section 11C of the internal gear 10 of the present embodiment.

[0171] The connecting section 11C of the internal gear 10 connects the first tooth profile curve L19A of the tooth tip 11A and the third tooth profile curve L19B of the tooth root 11B uniformly. The connecting section 21C of the gear 10 also connects the first tooth profile curve L19A of the tooth tip 11A and the third tooth profile curve L19B of the tooth root 11B. Fig. The external gear 20 shown in Figure 9 has a similar design to the connecting section 11C of the internal gear 10. That is, the connecting section 21C of the external gear 20 connects the second tooth profile curve L29A of the tooth tip 21A and the fourth tooth profile curve L29B of the tooth root 21B uniformly.

[0172] In the present embodiment, the connecting sections 11C and 21C are formed from Bézier curves. That is, in the internal gear 10, the first tooth profile curve L19A and the third tooth profile curve L19B are uniformly 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 uniformly connected by a Bézier curve. Accordingly, the connecting sections 11C and 21C can uniformly connect the tooth profile curves of the tooth tips 11A and 21A and the tooth profile curves of the tooth roots 11B and 21B.

[0173] In particular, the connecting sections 11C and 21C are preferably formed with a cubic Bézier curve defined by four control points. According to the present embodiment, the connecting section 11C can uniformly change the direction of curvature between the first tooth profile curve L19A, which is radially convex inwards, and the third tooth profile curve L19B, which is radially concave outwards, and connect them. Similarly, the connecting section 21C can uniformly change the direction of curvature between the second tooth profile curve L29A, which is radially convex outwards, and the fourth tooth profile curve L29B, which is radially concave inwards, and connect them.

[0174] According to the gear pair 40 of the present embodiment, the aforementioned condition expressions 1 to 4 are satisfied. Furthermore, the first tooth profile curve L19A and the second tooth profile curve L29A of the gear pair 40 of the present embodiment are designed such that they satisfy at least one of the first settings (P1 > 1 or P1 < 1), the second settings (P2 ≠ 0), or the third settings (P3 ≠ 0). According to the present embodiment, the shapes of the tooth profiles of the internal gear 10 and the external gear 20 can be modified in various ways while still satisfying Camus' theorem. That is, according to the gear pair 40 of the present embodiment, it is possible to design a cycloidal gear optimal for any application while simultaneously suppressing the angular transmission error.

[0175] In particular, in the present embodiment, the first tooth profile curve L19A and the second tooth profile curve L29A are drawn such that they all satisfy the first setting, the second setting, and the third setting. Therefore, the first tooth profile curve L19A and the second tooth profile curve L29A of the present embodiment can have a curved shape with a higher degree of freedom relative to the tooth profile curves of the standard gear pair 940.

[0176] The gear pair 40 of the present embodiment is formed on the basis that the first rolling circle radius b1 and the second rolling circle radius b2 are both positive values ​​(b1 > 0, b2 > 0), the first setting is fulfilled, and the first cycloidal curve L15A and the second cycloidal curve L25A are drawn using the first parameter P1, which satisfies P1 < 1. Furthermore, the gear pair 40 of the present embodiment fulfills the third setting, and the first cycloidal curve L15A and the second cycloidal curve L25A are offset radially outwards relative to the first base circle 12 and the second base circle 22 to form the first tooth profile curve L19A and the second tooth profile curve L29A (P3 > 0).

[0177] Fig. Figure 23 is a schematic diagram of the tooth tips 911A and 921A of the standard internal gear 910 and the standard external gear 920, which mesh together in the 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 the standard external gear 920 point in a direction perpendicular to the circumferential direction at the end of the engagement (i.e., at the circumferential ends of the respective tooth surfaces). At this point, the engagement occurs in the region near the base circle of the cycloidal curve, and due to the nature of the cycloidal curve, the contact occurs in the region where the radius of curvature is smallest (theoretically 0). Therefore, at the end of the engagement, the surface pressure of the tooth surfaces between the tooth tips 911A and 921A is high.

[0178] Fig. Figure 24 is a schematic diagram of the tooth tips 11A and 21A of the internal gear 10 and the external gear 20, which mesh together in the gear pair 40 of the present embodiment. In the gear pair 40 of the present embodiment, the first cycloidal curve L15A and the second cycloidal curve L25A, which are drawn using the first parameter P1, which is a value greater than 0 and less than 1, are offset radially outwards to form the first tooth profile curve L19A and the second tooth profile curve L29A. According to the present embodiment, the tooth surfaces at the circumferential end sections of the tooth tips 11A and 21A can be inclined relative to the radial direction. Therefore, compared to the case of the standard gear pair 940 (see Figure 24), the tooth profile is not as described above. Fig. 23) It is possible to prevent the surface pressure on the tooth surfaces from increasing at the end of meshing between the tooth tips 11A and 21A. According to the present embodiment, the load on the tooth surfaces of the inner gear 10 and the outer gear 20 during meshing can be reduced. This can suppress damage to the inner gear 10 and the outer gear 20 and extend the service life of the gear pair 40.

[0179] As in Fig. As shown in Figure 9, the gear pair 40 of the present embodiment is formed based on the fact that the second setting is satisfied, and the first cycloidal curve L15A and the second cycloidal curve L25A are drawn using the second parameter P2, which 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 rolling circle radius b1, and the absolute value of the second drawing point distance c2 is smaller than the absolute value of the second rolling circle radius b2. Therefore, the eccentricity magnitude Ec (c1 + c2) is smaller than that of the standard cycloidal gear pair, and the base circles of the gear pair are no longer tangential to each other. Standard cycloidal gear pairs have the problem that the arrangement is extremely difficult because engagement points exist at the diagonal angles of the tangent points of the base circle and the tangent points of the base circle.Setting P2 > 0 eliminates the diagonal meshing, thus simplifying the arrangement. That is, according to the gear pair 40 of the present embodiment, the internal gear 10 and the external gear 20 can be easily arranged regardless of the dimensional accuracy of the tooth surface shapes.

[0180] Next, a gear pair 140 of a first modification example is described, which can be used in the embodiment described above. Furthermore, the same components as in the embodiment described above are designated with the same reference numerals, and their description is omitted.

[0181] Fig. Figure 25 is a schematic diagram of the tooth tips 111A and 121A of an internal gear 110 and an external gear 120 meshing together in a gear pair 140 of the present modification design.

[0182] The gear pair 140 of this modification example fulfills the first and third settings. However, the gear pair 140 of this modification example does not fulfill the second setting. Therefore, the second parameter P2 of this modification example is zero. It should be noted that the second parameter P2 of this modification example is merely an example and can be a value greater than 0 (P2 > 0) or a value less than 0 (P2 < 0).

[0183] Fig. Figure 26 is a schematic diagram illustrating a method for forming a second tooth profile curve L29A of the tooth tip 121A of the external gear 120 of the present modification example. The tooth tip 121A first forms a second cycloidal curve L25A and then offsets the second cycloidal curve L25A in the normal direction by the third parameter P3 to form a second tooth profile curve L29A.

[0184] In gear pair 140 of the present modification example, the first parameter P1 (= b2 / b1) is greater than -1 and less than 0 (-1 < P1 < 0). In gear pair 140 of the present modification example, the first rolling circle radius b1 is a positive value (b1 > 0) and the second rolling circle radius b2 is a negative value (b2 < 0). Therefore, as in Fig. Figure 15 shows that the second cycloidal curve L25A becomes a hypocycloidal curve with a rolling circle radius |b2| and has a concave shape that is radially concave inwards. On the other hand, the first rolling circle radius b1 is sufficiently large relative to the absolute value |b2| of the second rolling circle radius b2.

[0185] As in Fig. As shown in Figure 26, the second cycloidal curve L25A, which is radially concave inwards, is offset radially outwards from the second base circle 22 using the third parameter P3. Accordingly, a second tooth profile curve L29A is formed, which is radially convex outwards.

[0186] To offset the second cycloidal curve L25A radially outwards from the second base circle 22, the third parameter P3 is set to a value greater than the sum (b2 + c2) of the second rolling circle radius b2 and the second drawing point distance c2 (P3 > b2 + c2). Since, in the present modification example, the second drawing point distance c2 is equal to the second rolling circle radius b2, the third parameter P3 can be greater than twice the second rolling circle radius b2.

[0187] As in Fig. As shown in Figure 25, the second tooth profile curve L29A is formed, and the first cycloidal curve L15A is also offset radially outwards by the third parameter P3. Accordingly, the first tooth profile curve L19A is formed.

[0188] In the gear pair 140 of the present modification example, the first rolling circle radius b1 is a positive value and the second rolling circle radius b2 is a negative value (b1 > 0, b2 < 0), and the second tooth profile curve L29A is formed by offsetting the second cycloidal curve L25A radially outward from the second base circle 22. According to this embodiment, the circumferential end sections of the tooth tips 111A and 121A can be inclined relative to the radial direction. Accordingly, compared to the case of the standard gear pair 940 (see Fig. 23) It is possible to prevent the surface pressure on the tooth surfaces from increasing at the end of the meshing between the tooth tips 111A and 121A. According to the present embodiment, the load on the tooth surfaces of the internal gear 110 and the external gear 120 can be reduced. This can suppress damage to the internal gear 110 and the external gear 120 and extend the service life of the gear pair 140.

[0189] Next, a gear pair 240 of a second modification is described, which can be used in the embodiment described above. Furthermore, the same components as in the embodiment described above are designated with the same reference numerals, and their descriptions are omitted.

[0190] Fig. Figure 27 is a schematic diagram of the tooth tips 211A and 221A of an internal gear 210 and an external gear 220 meshing together in a gear pair 240 of the present modification example.

[0191] The gear pair 240 of this modification example fulfills the first and third settings. However, the gear pair 240 of this modification example does not fulfill the second setting. Therefore, the second parameter P2 of this modification example is zero. It should be noted that the second parameter P2 of this modification example is merely an example and can be a value greater than 0 (P2 > 0) or a value less than 0 (P2 < 0).

[0192] In the gear pair 240 of the present modification example, the first parameter P1 (= b2 / b1) is greater than -1 and less than 0 (-1 < P1 < 0). In the gear pair 240 of the present modification example, the first rolling circle radius b1 is a negative value (b1 < 0) and the second rolling circle radius b2 is a positive value (b2 > 0). Therefore, the first cycloidal curve L15A becomes an epicycloidal curve and has a concave shape, which is radially concave outwards. The first cycloidal curve L15A, which is radially concave outwards, is offset radially inwards from the first base circle 12 using the third parameter P3. Accordingly, a first tooth profile curve L19A is formed, which is radially convex inwards.

[0193] To shift the first cycloidal curve L15A radially inward from the first base circle 12, the third parameter P3 is set to a value greater than the sum (b1 + c1) of the first rolling circle radius b1 and the first drawing point distance c1 (P3 > b1 + c1). Since, in the present modification example, the first drawing point distance c1 is equal to the first rolling circle radius b1, the third parameter P3 can be greater than twice the first rolling circle radius b1.

[0194] Additionally, the first tooth profile curve L19A is generated, and the second cycloidal curve L25A is also offset radially outwards by the third parameter P3. Accordingly, the second tooth profile curve L29A is generated.

[0195] In the gear pair 240 of the present modification example, the first rolling circle radius b1 is a negative value and the second rolling circle radius b2 is a positive value (b1 < 0, b2 > 0), and the first tooth profile curve L19A is formed by offsetting the first cycloidal curve L15A radially inward from the first base circle 12. According to this embodiment, the circumferential end sections of the tooth tips 211A and 221A can be inclined relative to the radial direction. Accordingly, compared to the case of the standard gear pair 940 (see Fig. 23) It is possible to prevent the surface pressure on the tooth surfaces from increasing at the end of the meshing between the tooth tips 211A and 221A. According to the present embodiment, the load on the tooth surfaces of the internal gear 210 and the external gear 220 can be reduced. This can suppress damage to the internal gear 210 and the external gear 220 and extend the service life of the gear pair 240.

[0196] Although the embodiment of the present invention and its modification examples have been described above, each configuration and combination thereof in the embodiment and the modification examples are merely examples, and additions, omissions, substitutions, and other modifications of the embodiment are possible without departing from the spirit of the present invention. Furthermore, the present invention is not limited to the embodiment described above.

[0197] In the embodiment described above, for example, the case was described in which the gear pair is used in a drive unit for a human-powered vehicle, but the application of the gear pair is not limited to the present embodiment. The gear pair can, for example, be used in a component other than the drive unit among the components for a human-powered vehicle. The gear pair can also be used, for example, in an internal gearbox of a human-powered vehicle. Furthermore, the gear pair can be used in products other than human-powered vehicles. For example, the gear pair can be used in fishing equipment (for example, a fishing reel). In the present embodiment, the case described was in which the gear pair is used in a gearbox as a speed reducer.However, the gear pair can also be used in a gearbox as a speed amplifier.

[0198] The configurations of the drive unit, the transmission and the gear pair in the embodiments are merely examples, and the drive unit, the transmission and the gear pair may include configurations that are not shown in the individual embodiments, or may not include some of the configurations shown in the individual embodiments.

[0199] Cases have been described in which, in the embodiment above, the drawing points are arranged inside the rolling circle to draw a foreshortened cycloidal curve, and in the modification example, the drawing points are arranged on the circumference of the rolling circle to draw a cycloidal curve. However, the drawing points can also be arranged outside the rolling circle to draw a hypocycloidal curve. That is, the second parameter P2 can be a negative value.

[0200] For example, as long as at least one section of the tooth tip 11A of the internal gear 10 contains the first tooth profile curve L19A, the shape of the other sections is not restricted. As long as at least one section of the tooth tip 21A of the external gear 20 contains the second tooth profile curve L29A, the shape of the other sections is not restricted. As long as at least one section of the tooth root 11B of the internal gear 10 contains the third tooth profile curve L19B, the shape of the other sections is not restricted. As long as at least one section of the tooth root 21B of the external gear 20 contains the fourth tooth profile curve L29B, the shape of the other sections is not restricted.

[0201] The phrase “at least one” in this revelation means “one or more” of a desired choice. For example, the phrase “at least one of” in this revelation means “only a single choice” or “both of two choices” when the number of choices is two. In another example, the phrase “at least one of” in this revelation means “only a single choice” or “any combination of two or more choices” when the number of choices is two or more. Furthermore, the term “and / or” in this revelation means “either one or both.” For example, the phrase “at least one of A and B” includes (1) A alone, (2) B alone, and (3) both A and B. The phrase “at least one of A, B, and C” includes (1) A alone, (2) B alone, (3) C alone, (4) both A and B, (5) both B and C, (6) both A and C, and (7) all A, B, and C.In other words, the expression “at least one of A and B” in this revelation does not mean “at least one of A and at least one of B”. REFERENCE MARK 1 Human-powered vehicle 2 Vehicle body frames 3 rear wheel 4 front wheel 5 Powertrain 5a crank 5b Front sprocket 5c Rear sprocket 5D chain 5e Crankshaft 5f crank arm 6 Drive unit 6a Housing 7 gearboxes 9 Power transmission unit 10, 110, 210 internal gear 11 Inner tooth 11A, 21A Tooth tip 11B, 21B Tooth base 11C, 21C connection section 12 First basic circle 13A First rolling circle 13B Third Rolling Circle 14A First drawing point 14B Third drawing point 20, 120, 220 Outer gear 21 Outer tooth 22 Second basic circle 23A Second rolling circuit 23B Fourth Rolling Circle 24A Second drawing point 24B Fourth drawing point 40, 140, 240 gear pair 111A, 121A Tooth tip 211A, 221A Tooth tip 910 Standard internal gear 911A, 921A Tooth tip 911B, 921B Tooth base 912 First basic circle 913A First rolling circle 913B Third rolling circle 914A First drawing point 914B Third drawing point 920 Standard external gear 922 Second basic circle 923A Second rolling circle 923B Fourth rolling circle 924A Second drawing point 924B Fourth drawing point 940 Standard gear pair A contact point a1 first base circle radius a2 second base circle radius a91 first base circle radius a92 second base circle radius AA offset point Point of tangency B, C b1 First rolling circle radius b2 Second rolling circle radius b3 Third rolling circle radius b4 Fourth rolling circle radius b91 First rolling circle radius b92 Second rolling circle radius b93 Third rolling circle radius b94 Fourth rolling circle radius BC Normal line BC1 Base Circle c1 First drawing point spacing c2 Second drawing point spacing c3 Third drawing point spacing c4 Fourth drawing point spacing D, E, O1, O2 Center d3 Third offset amount d4 Fourth offset amount, DO, EO Zentralbahn DP1, DP2, DP3 Drawing point DP4, DP5, DP6 drawing point Ec, Ec9 eccentricity value J1 crank axle J2 pivot axis L15A First cycloidal curve L15B Third cycloid curve L19A First tooth profile curve L19B Third tooth profile curve L25A Second cycloidal curve L25B Fourth Cycloid Curve L29A Second tooth profile curve L29B Fourth tooth profile curve L915A First cycloidal curve L915B Third cycloid curve L925A Second cycloidal curve L925B Fourth Cycloid Curve La1, La2, La3 hypocycloid curve La4, La5, La6 epicycloid curve Lb1, Lb2, Lb3 epicycloid curve Lb4, Lb5, Lb6 hypocycloid curve N Number of teeth P Division point P1 First parameter P2 Second parameter P3 Third parameter RC1, RC2 rolling circle α, β Roll angle QUOTES INCLUDED IN THE DESCRIPTION

[0000] This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited patent literature

[0000] JP 3 729 867

[0002]

Claims

[1] Gear pair (40, 140), comprising: an internal gear (10, 110) with internal teeth (11) with the number of teeth N + 1, at least one section of which is described by a first tooth profile curve (L19A), and an external gear (20, 120) with external teeth (21) with the number of teeth N, at least one section of which is described by a second tooth profile curve (L29A), and is in inscribed tooth mesh with the internal gear (10, 110), wherein the first tooth profile curve (L19A) is formed on the basis of a first cycloidal curve (L15A) which is drawn as the locus of a first drawing point (14A) which rolls on a circumference inside or outside a first rolling circle (13A) on a first base circle (12), wherein the second tooth profile curve (L29A) is formed on the basis of a second cycloidal curve (L25A) which is formed as the locus of a second drawing point (24B) on a circumference inside or outside a second rolling circle (23A) rolling on a second base circle (22), where a radius of the first base circle (12) is defined as the first base circle radius (a1), where a radius of the first rolling circle (13A) is defined as the first rolling circle radius (b1), where a distance from a center point (D) of the first rolling circle (13A) to the first drawing point (14A) is defined as the first drawing point distance (c1), where a radius of the second base circle (22) is defined as the second base circle radius (a2), where a radius of the second rolling circle (23A) is defined as the second rolling circle radius (b2), where a distance from a center point (E) of the second rolling circle (23A) to the second drawing point (24B) is defined as the second drawing point distance (c2), where the distance between a center point (O1) of the first base circle (12) and a center point (O2) of the second base circle (22) is defined as the eccentricity value (Ec), where the first rolling circle radius (b1), the second rolling circle radius (b2), the first drawing point distance (c1) and the second drawing point distance (c2) are each a positive or negative value, where a positive and negative sign of the first drawing point spacing (c1) corresponds to a positive and negative sign of the first rolling circle radius (b1), wherein a positive and negative sign of the second drawing point spacing (c2) corresponds to a positive and negative sign of the second rolling circle (b2), wherein, if the first rolling circle radius (b1) is a positive value, the first cycloidal curve (L15A) is a hypocycloidal curve (La1) with a rolling circle radius |b1|, where, if the first rolling circle radius (b1) is a negative value, the first cycloid curve (L15A) is an epicycloid curve (La4) with a rolling circle radius |b1|, where, if the second rolling circle radius (b2) is a positive value, the second cycloid curve (L25A) is an epicycloid curve (La4) with a rolling circle radius |b2|, where, if the second rolling circle radius b2 is a negative value, the second cycloid curve (L25A) is a hypocycloid curve (La1) with a rolling circle radius |b2|, where the first cycloidal curve (L15A) and the second cycloidal curve (L25A) satisfy the following condition expressions 1, 2, 3 and 4: a1=(N+1)×(b1+b2) a2=N×(b1+b2) b1:c1=b2:c2 Ec=c1+c2 where a ratio of the second rolling circle radius (b2) to the first rolling circle radius (b1) is defined as the first parameter (P1), wherein an eccentricity adjustment amount is defined as a sum of the first rolling circle radius (b1) and the second rolling circle radius (b2) minus a sum of the first drawing point distance (c1) and the second drawing point distance (c2), is defined as the second parameter (P2), where an offset amount for shifting the first cycloidal curve (L15A) and the second cycloidal curve (L25A) by the same distance in a normal direction is defined as a third parameter (P3), wherein the first tooth profile curve (L19A) and the second tooth profile curve (L29A) are drawn such that they satisfy at least one of the following first, second and third settings, where the first setting consists of drawing the first cycloidal curve (L15A) and the second cycloidal curve (L25A) using the first parameter (P1) that satisfies P1 > 1 or P1 < 1, where the second setting consists of drawing the first cycloidal curve (L15A) and the second cycloidal curve (L25A) using the second parameter (P2) which satisfies P2 ≠ 0, and where the third setting consists of using the third parameter (P3) which satisfies P3 ≠ 0, and offsetting the first cycloidal curve (L15A) and the second cycloidal curve (L25A) by the third parameter (P3) in the normal direction to obtain the first tooth profile curve (L19A) and the second tooth profile curve (L29A). [2] The gear pair (40, 140) according to claim 1, wherein the first tooth profile curve (L19A) and the second tooth profile curve (L29A) are drawn such that they satisfy all first, second and third settings. [3] The gear pair (40, 140) according to claim 1 or 2, where the first rolling circle radius (b1) and the second rolling circle radius (b2) are both positive values, where the first setting is satisfied and the first cycloidal curve (L15A) and the second cycloidal curve (L25A) are drawn using the first parameter (P1) which satisfies P1 < 1, and where the third setting is fulfilled and the first tooth profile curve (L19A) and the second tooth profile curve (L29A) are formed by offsetting the first cycloidal curve (L15A) and the second cycloidal curve (L25A) radially outwards from the first base circle (12) and the second base circle (22). [4] The gear pair (40, 140) according to claim 1, where the first setting is fulfilled, the first rolling circle radius (b1) is a positive value and the second rolling circle radius (b2) is a negative value, and where the third setting is fulfilled and the second tooth profile curve (L29A) is formed by offsetting the second cycloidal curve (L25A) radially outwards from the second base circle (22). [5] The gear pair (40, 140) according to claim 1, where the first setting is fulfilled, the first rolling circle radius (b1) is a negative value and the second rolling circle radius (b2) is a positive value, and where the third setting is fulfilled and the first tooth profile curve (L19A) is formed by offsetting the first cycloidal curve (L15A) radially inwards from the first base circle (12). [6] The gear pair (40, 140) according to any one of claims 1 to 5, wherein the second setting is satisfied and the first cycloidal curve (L15A) and the second cycloidal curve (L25A) are drawn using the second parameter (P2) which satisfies P2 > 0. [7] Gear pair (40, 140) according to one of claims 1 to 6, wherein a radially inwardly convex section of the first tooth profile curve (L19A) describes an outer shape of the internal toothing (11) and wherein a radially outwardly convex section of the second tooth profile curve (L29A) describes an outer shape of the external toothing (21). [8] Gear pair (40, 140) according to one of claims 1 to 7, wherein the internal gear (10, 110) has at least one section of a tooth root (11B) described by a third tooth profile curve (L19B), wherein the outer gear (20, 120) has at least one section of a tooth root (21B) described by a fourth tooth profile curve (L29B), wherein the third tooth profile curve (L19B) is formed on the basis of a third cycloidal curve (L15B) which is drawn as the locus of a third drawing point (14B) which lies on a circumference inside or outside a third rolling circle (13B) which is on the first base circle (12) wherein the fourth tooth profile curve (L29B) is formed on the basis of a fourth cycloidal curve (L25B) which is drawn as the locus of a fourth drawing or reference point (24B) which lies on a circumference inside or outside a fourth rolling circle (23B) which rolls on the second base circle (22), where a third rolling circle radius (b3), which is a radius of the third rolling circle (13B), is equal to the second rolling circle radius (b2), wherein an absolute value of a third drawing point distance (c3), which is a distance from a center point of the third rolling circle (13B) to the third drawing point (14B), is equal to or greater than an absolute value of the second drawing point distance (c2), where a fourth rolling circle radius (b4), which is a radius of the fourth rolling circle (23B), is equal to the first rolling circle radius (b1), wherein an absolute value of a fourth drawing point distance (c4), which is a distance from a center point of the fourth rolling circle (23B) to the fourth drawing point (24B), is equal to or greater than an absolute value of the first drawing point distance (c1), wherein, if the third tooth profile curve (L19B) is offset by a third offset amount (d3) in the normal direction by offsetting the third cycloidal curve (L15B), the third offset amount (d3) is specified in the same direction as an offset direction of the second tooth profile curve (L29A) so that it does not disturb the second tooth profile curve (L29A) during engagement, and wherein, if the fourth tooth profile curve (L29B) is formed by offsetting the fourth cycloidal curve (L25B) by a fourth offset amount (d4) in the normal direction, the fourth offset amount (d4) is specified in the same direction as an offset direction of the first tooth profile curve (L19A) so that it does not disturb the first tooth profile curve (L19A) during the intervention. [9] The gear pair (40, 140) according to claim 8, where the third drawing point distance (c3) is equal to the second drawing point distance (c2), where the fourth drawing point distance (c4) is equal to the first drawing point distance (c1), where the third offset amount (d3) is equal to the third parameter (P3) and where the fourth offset amount (d4) is equal to the third parameter (P3). [10] Gear pair (40, 140) according to claim 8 or 9, wherein a radially outwardly concave section of the third tooth profile curve (L19B) describes an outer shape of the tooth root (11B) of the internal gear (10, 110), and wherein a radially inwardly concave section of the fourth tooth profile curve (L29B) describes an outer shape of the tooth root (21B) of the external gear (20, 120). [11] Gear pair (40, 140) according to one of claims 8 to 10, wherein the first tooth profile curve (L19A) and the third tooth profile curve (L19B) in the internal gear (10, 110) are smoothly connected by a Bézier curve, and wherein the second tooth profile curve (L29A) and the fourth tooth profile curve (L29B) in the outer gear (20, 120) are smoothly connected by a Bézier curve. [12] Gear pair (40, 140) according to claim 11, wherein the Bezier curve is a cubic Bezier curve defined by four control points. [13] Gearbox (7) with the gear pair (40, 140) according to one of claims 1 to 12. [14] Drive unit (6) for a human-powered vehicle (1) comprising the transmission (7) according to claim 13.

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