Gear mechanism

Abstract

Provided is a gear mechanism having an outer-toothed circular arc gear that is provided with M circular arc teeth and that rotates around a first central axis, and an outer-toothed non-circular arc gear that is provided with N non-circular arc teeth and that rotates around a second central axis separated by a predetermined distance D from the first central axis, wherein the gear mechanism is characterized in that: the circular arc teeth of the outer-toothed circular arc gear have a circular arc gear tooth tip part, and a circular arc gear tooth side part positioned on a side part of the circular arc gear tooth tip part and provided with a circular arc shape having a radius r; the non-circular arc teeth of the external teeth-type non-circular arc gear have a non-circular arc gear tooth tip part, and a non-circular arc gear tooth side part that are positioned on a side part of the non-circular arc gear tooth tip part and that come into contact with the circular arc gear tooth side part; the shape of at least part of the non-circular arc gear tooth side part is formed such that an epitrochoid curve drawn with a virtual circle of a radius D×N / (M+N) around the second central axis as a constant circle, a virtual circle of a radius D×M / (M+N) around the first central axis as a dynamic circle, and the center of the circular arc gear tooth side part as a drawing point becomes an offset epitrochoid curve that is offset by a length r; and the number M of teeth of the external teeth-type circular arc gear is 4 to 10 (inclusive).

Description

gear mechanism

[0001] The present invention relates to a gear mechanism.

[0002] BACKGROUND ART Gear mechanisms including an externally toothed gear that rotates about a first central axis and an externally toothed gear that rotates about a second central axis that is spaced a predetermined distance from the first central axis are already well known.

[0003] Japanese Patent Application Laid-Open No. 2012-82893

[0004] In the past, some of these gear mechanisms had a drawback in that while one externally toothed gear rotates at a constant speed, the other externally toothed gear would wobble, causing variations in speed (called speed variation). Therefore, there was a demand for a gear mechanism with a new tooth shape that does not have this drawback.

[0005] Furthermore, in view of commercial merit, there has been a demand for a gear mechanism that is free from the above drawbacks and is also compact.

[0006] The present invention has been made in view of the above-mentioned problems, and an object of the present invention is to provide a gear mechanism that is effective in suppressing speed variations and is compact, thereby offering great commercial merit.

[0007] The main invention for achieving the above object is a gear mechanism having an externally toothed arc-shaped gear having M arc-shaped teeth and rotating around a first central axis, and an externally toothed non-arcuar gear having N non-arcuar teeth and rotating around a second central axis separated by a predetermined distance D from the first central axis, wherein the arc-shaped teeth of the externally toothed arc-shaped gear have arc-shaped gear tooth tip portions and arc-shaped gear tooth side portions located on the sides of the arc-shaped gear tooth tip portions and having an arc shape of radius r, and the non-arcuar tooth of the externally toothed non-arcuar gear have non-arcuar gear tooth tip portions and non-arcuar gear tooth side portions located on the sides of the non-arcuar gear tooth tip portions and in contact with the arc-shaped gear tooth side portions, and at least a part of the shape of the non-arcuar gear tooth side portions is The gear mechanism is formed so that when a virtual circle of radius D×N / (M+N) centered on the second central axis is a fixed circle, a virtual circle of radius D×M / (M+N) centered on the first central axis is a moving circle, and the center of the side of the arc-shaped gear tooth is taken as the drawing point, the epitrochoid curve drawn is an offset epitrochoid curve offset by a length r, and the number of teeth M of the externally toothed arc-shaped gear is 4 or more and 10 or less.

[0008] Other features of the present invention will become apparent from the description of this specification and the accompanying drawings.

[0009] 1 is an explanatory diagram for explaining a gear mechanism 1 according to the present embodiment. It is an explanatory diagram for explaining the arc-shaped teeth 14 of the externally toothed arc-shaped gear 10 according to the present embodiment. It is a diagram showing how to draw the epitrochoid curve EP. It is a diagram showing another way to draw the epitrochoid curve EP. It is an explanatory diagram for explaining the behavior of a cam mechanism including a cam 60 relating to the epitrochoid curve EP and a cam follower 62a with a radius of zero. It is an explanatory diagram for explaining an offset epitrochoid curve OEP. It is an explanatory diagram for explaining the behavior of a cam mechanism including a cam 60 relating to the offset epitrochoid curve OEP and a cam follower 62a relating to a circle of radius r. It is an explanatory diagram for explaining the non-circular teeth 34 of the externally toothed non-circular gear 30 according to the present embodiment. It is a diagram showing the correspondence relationship of tooth sides. It is a conceptual diagram showing how the externally toothed arc-shaped gear 10 and the externally toothed non-circular gear 30 are in contact at two points. It is an explanatory diagram for explaining the contact ratio condition. It is a diagram showing the pitch angle θ1 and the straddle angle θ2 for each of three cases. Fig. 1 is an explanatory diagram for explaining an undercut limit. Fig. 2 is a diagram showing the relationship between the number of teeth N of the externally toothed non-circular gear 30 and the value of the left side of the conditional equation. Fig. 3 is an explanatory diagram for explaining a gear mechanism 100 according to a second embodiment. Fig. 4 is a diagram showing the relationship between the number of teeth M of the externally toothed arc gear 10 and the value of the left side of the conditional equation.

[0010] At least the following matters will become clear from the description of this specification and the accompanying drawings.

[0011] A gear mechanism having an externally toothed arc-shaped gear having M arc-shaped teeth and rotating around a first central axis, and an externally toothed non-arcuar gear having N non-arcuar teeth and rotating around a second central axis separated from the first central axis by a predetermined distance D, wherein the arc-shaped teeth of the externally toothed arc-shaped gear have arc-shaped gear tooth tip portions and arc-shaped gear tooth side portions located on the sides of the arc-shaped gear tooth tip portions and having an arc shape of radius r, and the non-arcuar tooth of the externally toothed non-arcuar gear have non-arcuar gear tooth tip portions and non-arcuar gear tooth side portions located on the sides of the non-arcuar gear tooth tip portions and in contact with the arc-shaped gear tooth side portions, and at least a part of the shape of the non-arcuar gear tooth side portions is a virtual circle of radius D×N / (M+N) centered on the second central axis as a fixed circle, a virtual circle of radius D×M / (M+N) centered on the first central axis as a moving circle, and the center of a tooth side of the arc-shaped gear as a drawing point, the epitrochoid curve drawn is an offset epitrochoid curve offset by a length r, and the number of teeth M of the externally toothed arc-shaped gear is 4 or more and 10 or less.

[0012] Such a gear mechanism can suppress speed variations and can also be made compact, making it possible to realize a gear mechanism that has great commercial merits.

[0013] A gear mechanism having an externally toothed arc-shaped gear having M arc-shaped teeth and rotating around a first central axis, and an externally toothed non-arcuar gear having N non-arcuar teeth and rotating around a second central axis separated from the first central axis by a predetermined distance D, wherein the arc-shaped teeth of the externally toothed arc-shaped gear have arc-shaped gear tooth tip portions and arc-shaped gear tooth side portions located on the sides of the arc-shaped gear tooth tip portions and having an arc shape of radius r, and the non-arcuar tooth of the externally toothed non-arcuar gear have non-arcuar gear tooth tip portions and non-arcuar gear tooth side portions located on the sides of the non-arcuar gear tooth tip portions and in contact with the arc-shaped gear tooth side portions, and at least a part of the shape of the non-arcuar gear tooth side portions is a virtual circle of radius D×N / (M+N) centered on the second central axis as a fixed circle, a virtual circle of radius D×M / (M+N) centered on the first central axis as a moving circle, and the center of a tooth side of the arc-shaped gear as a drawing point, the epitrochoid curve drawn is an offset epitrochoid curve offset by a length r, and the number of teeth N of the externally toothed non-circular gear is 3 or more and 10 or less.

[0014] Such a gear mechanism can suppress speed variations and can also be made compact, making it possible to realize a gear mechanism that has great commercial merits.

[0015] Regarding the Gear Mechanism 1 According to the Present Embodiment: Next, the gear mechanism 1 according to the present embodiment will be described with reference to Fig. 1. Fig. 1 is an explanatory diagram for explaining the gear mechanism 1 according to the present embodiment.

[0016] The gear mechanism 1 includes two externally toothed gears (external gears) that mesh with each other. As will be described in detail later, the teeth of one gear are arc-shaped, while the teeth of the other gear are not. Therefore, for convenience, the former gear is referred to as the externally toothed arc-shaped gear 10, and the latter gear is referred to as the externally toothed non-circular gear 30.

[0017] The externally toothed arc gear 10 is a gear that rotates around a first central axis 12 and has M (eight in this embodiment) teeth (for convenience, referred to as arc teeth 14). In other words, the number of teeth M of the externally toothed arc gear 10 is eight.

[0018] The externally toothed non-circular gear 30 is a gear that rotates around a second central axis 32 that is a predetermined distance (i.e., axis distance D) away from the first central axis 12, and has N (16 in this embodiment) teeth (referred to as non-circular teeth 34 for convenience). In other words, the number of teeth N of the externally toothed arc gear 10 is 16.

[0019] The arc-shaped teeth 14 and the non-arc-shaped teeth 34 mesh with each other.

[0020] The number of teeth M and the number of teeth N are not limited to 8 and 16 (the number of teeth M and the number of teeth N may be the same number).

[0021] Furthermore, the externally toothed arc-circular gear 10 has M (8) arc-shaped teeth 14, and the externally toothed non-arc gear 30 has N (16) arc-shaped teeth 14, so that the number of teeth of the externally toothed non-arc-circular gear 30 is N / M (2) times the number of teeth of the externally toothed arc-circular gear 10. Based on this, the size of the externally toothed non-arc-circular gear 30 is twice that of the externally toothed arc-circular gear 10. More specifically, the value M / (M+N) times (1 / 3) the center distance D is used as the pitch radius R1 of the pitch circle PC1 of the externally toothed arc-circular gear 10, and the value N / (M+N) times (2 / 3) the center distance D is used as the pitch radius R2 of the pitch circle PC2 of the externally toothed non-arc-circular gear 30.

[0022] Regarding the Circular Tooth 14 Next, the circular tooth 14 of the externally toothed arc gear 10 according to this embodiment will be described using Figures 1 and 2. Figure 2 is an explanatory diagram for explaining the circular tooth 14 of the externally toothed arc gear 10 according to this embodiment. Note that in Figure 2, for the sake of clarity, only one circular tooth 14 is shown, and the other circular teeth 14 are omitted.

[0023] The arc-shaped tooth 14 has a tooth side portion with an arc-shaped curve that differs from the involute curve typically found in gears. That is, the arc-shaped tooth 14 has an arc-shaped gear tooth tip 16 and an arc-shaped gear tooth side portion 18 that is located on the side of the arc-shaped gear tooth tip 16 and has an arc shape with a radius r. Two arc-shaped gear tooth side portions 18 are provided (referred to as a first arc-shaped gear tooth side portion 18a and a second arc-shaped gear tooth side portion 18b, both of which have the same radius r).

[0024] The second arc-shaped gear tooth side portion 18b is located on the opposite side of the first arc-shaped gear tooth side portion 18a when viewed from the arc-shaped gear tooth tip 16. The center C2 of the second arc-shaped gear tooth side portion 18b is different from the center C1 of the first arc-shaped gear tooth side portion 18a. The distance L from the first central axis 12 to the center C1 is the same as the distance L from the first central axis 12 to the center C2 (this distance L can be set arbitrarily). The radius r and the pitch angle α of the arc shown in FIG. 2 (the face width can be adjusted by adjusting this angle) can also be set arbitrarily.

[0025] The tooth height can also be set arbitrarily, but in this embodiment, the module m (= pitch circle radius R1 × 2 / number of teeth M) is used, and the arc tooth 14 is formed by cutting an arc at a position −1.25 × m on the inside and a position + m on the outside of the pitch circle PC1 of radius R1 as the reference.

[0026] Regarding the Non-Circular Teeth 34: Next, we will explain the non-circular teeth 34 of the externally toothed non-circular gear 30 according to this embodiment. As will be explained below, the shape of the non-circular teeth 34 is an offset epitrochoid curve OEP, which is an offset from the epitrochoid curve EP.

[0027] <<<About the epitrochoid curve EP>>> A trochoid curve is defined as the curve drawn by fixed points (also called drawing points) inside or outside a circle when a circle is rolled along a curve (a circle is a special case of this) without slipping. In particular, a curve made up of two circumscribed circles (in other words, the curve drawn by drawing points inside or outside the moving circle when a moving circle is rolled along a fixed circle without slipping) is called an epitrochoid curve EP.

[0028] FIG. 3 shows how to draw an epitrochoid curve EP. In the upper left diagram, the fixed circle (second friction wheel 52) is located on the left, and the moving circle (first friction wheel 50) is located on the right. In this example, the radius of the fixed circle (second friction wheel 52) is twice the radius of the moving circle (first friction wheel 50), and the drawing point P is located within the moving circle (first friction wheel 50) and on the X-axis. From this state, the moving circle (first friction wheel 50) rotates and revolves around the fixed circle (second friction wheel 52) (upper left diagram → upper right diagram → lower left diagram → lower right diagram; θ1 represents the rotation angle, and θ2 represents the revolution angle). When the revolution angle reaches 360 degrees, the moving circle (first friction wheel 50) returns to its original position. The trajectory drawn by the drawing point P during this movement of the moving circle (first friction wheel 50) becomes the epitrochoid curve EP.

[0029] The method of drawing the epitrochoid curve EP shown in Figure 3 above follows the definition of the epitrochoid curve EP, but there are other ways to draw it. Figure 4 shows another way to draw the epitrochoid curve EP.

[0030] In the example of Fig. 3, the second friction wheel 52 was fixed, but in this example, the second friction wheel 52 rotates. Also, in the example of Fig. 3, the first friction wheel 50 revolved while rotating on its axis, but in this example, the first friction wheel 50 only rotates on its axis and does not revolve. That is, in this example, the first friction wheel 50 and the second friction wheel 52 rotate (spin) without slipping on each other, with their centers of rotation fixed (upper left diagram → upper right diagram → lower left diagram → lower right diagram. θ1 represents the rotation angle of the first friction wheel 50, and θ2 represents the rotation angle of the second friction wheel 52). When the first friction wheel 50 moves, the trajectory drawn by the drawing point P (the arrangement of the drawing point P is the same as in the example of Fig. 3) becomes an epitrochoid curve EP, but in this example, the XY coordinate system rotates together with the rotation of the second friction wheel 52 (therefore, the previously drawn trajectory moves along with the rotation of the XY coordinate system). In this way, in this example, when the second friction wheel 52 is rotated, the first friction wheel 50 rolls without slipping, and the locus of the drawing point P is drawn. The locus of the drawing point P is drawn as viewed from the XY coordinate system fixed to the second friction wheel 52. The lower right diagram of Figure 4 shows the state in which the first friction wheel 50 rotates two times (θ1 = 720 degrees), the second friction wheel 52 rotates once (θ2 = 360 degrees), the XY coordinate system returns to its original position, and the epitrochoid curve EP is drawn. As is clear from a comparison with the lower right diagram of Figure 3, the method of this example can also draw the same epitrochoid curve EP as shown in Figure 3.

[0031] Next, let us consider the behavior of the cam mechanism when we assume that the epitrochoid curve EP is the cam 60 and the drawing point P is the cam follower 62a with a radius of 0 (in other words, a diameter that is infinitely close to 0). Figure 5 is an explanatory diagram for explaining the behavior of a cam mechanism that includes a cam 60 related to the epitrochoid curve EP and a cam follower 62a with a radius of 0.

[0032] Figure 5 is basically the same as Figure 4. However, in Figure 5, the entire epitrochoid curve EP depicted in Figure 4 is shown in four complete views (the entire epitrochoid curve EP is depicted not only in the lower right view but also in the upper left, upper right, and lower left views), and this is taken as the cam 60. In addition, the depicted point P in Figure 4 is taken as the cam follower 62a with a radius of zero (in other words, a diameter infinitely close to zero), and the section from the depicted point P to the center of the first friction wheel 50 is taken as the arm 62b, and a follower 62 having the cam follower 62a and the arm 62b is assumed.

[0033] 5, when the epitrochoid curve EP rotates in accordance with the rotation of the second friction wheel 52 (upper left diagram → upper right diagram → lower left diagram → lower right diagram), the drawing point P, which moves in accordance with the rotation of the first friction wheel 50, moves on the epitrochoid curve EP. In other words, the cam 60 (epitrochoid curve EP) and the cam follower 62a (drawing point P) move in a state of engagement (contact) with each other.

[0034] Furthermore, because the first friction wheel 50 and the second friction wheel 52 rotate without slipping on each other, when the second friction wheel 52 rotates at a constant speed, the first friction wheel 50 also rotates at a constant speed. This relationship also applies to the cam 60 (epitrochoid curve EP) and the cam follower 62a (drawing point P). That is, when the second friction wheel 52 rotates at a constant speed, the cam 60 (epitrochoid curve EP), which rotates along with the second friction wheel 52, also rotates at a constant speed, and the cam follower 62a (drawing point P), which rotates along with the first friction wheel 50, which rotates at a constant speed, also rotates at a constant speed. In this way, the cam 60 (epitrochoid curve EP) and the cam follower 62a (drawing point P) rotate at a constant speed while engaged (contacting) with each other. That is, even though the cam 60 (epitrochoid curve EP) rotates at a constant speed, the cam follower 62a (drawing point P) is unstable and the speed varies (hereinafter referred to as speed variation). This is appropriately suppressed.

[0035] <<<Regarding the Offset Epitrochoid Curve OEP>>> In the above, the epitrochoid curve EP was assumed to be the cam 60, and the drawing point P was assumed to be the cam follower 62a with a radius of 0 (in other words, a diameter infinitely close to 0). However, here, we will define an offset epitrochoid curve OEP associated with the epitrochoid curve EP, and consider the behavior of the cam mechanism when we assume that this offset epitrochoid curve OEP is the cam 60 and that a circle of radius r centered at the drawing point P on the epitrochoid curve EP is the cam follower 62a. Figure 6 is an explanatory diagram for explaining the offset epitrochoid curve OEP. Figure 7 is an explanatory diagram for explaining the behavior of a cam mechanism including a cam 60 associated with the offset epitrochoid curve OEP and a cam follower 62a associated with the circle of radius r.

[0036] A tangent line TA is drawn at each point on the epitrochoid curve, and a point is taken that is offset inward from each point in the normal direction to the tangent line TA by a certain distance. The curve connecting these points is defined as the offset epitrochoid curve OEP. In other words, as shown in Figure 6, when the bar 70 is moved so that the line LI perpendicular to the bar 70 at the outer end 70a of the bar 70 always becomes the tangent line TA to the epitrochoid curve EP, the locus of the inner end 70b of the bar becomes the offset epitrochoid curve OEP.

[0037] An offset epitrochoid curve OEP having a length r equal to the fixed distance (i.e., an offset epitrochoid curve OEP offset by the length r from the epitrochoid curve EP) is assumed to be the cam 60, and a circle of radius r centered at the drawing point P on the epitrochoid curve EP is assumed to be the cam follower 62a. That is, in Figure 7, the offset epitrochoid curve OEP offset by the length r from the epitrochoid curve EP is shown in all four diagrams, and this is assumed to be the cam 60. In addition to this, a circle of radius r centered at the drawing point P is assumed to be the cam follower 62a, and an arm 62b is assumed to extend from the drawing point P to the center of the first friction wheel 50, and a follower 62 having the cam follower 62a and the arm 62b is assumed.

[0038] 7, when the offset epitrochoid curve OEP rotates in conjunction with the rotation of the second friction wheel 52 (epitrochoid curve EP) (upper left diagram → upper right diagram → lower left diagram → lower right diagram), the cam follower 62a, which moves in conjunction with the rotation of the first friction wheel 50 (drawing point P), operates while maintaining contact with the offset epitrochoid curve OEP. In other words, the cam 60 (offset epitrochoid curve OEP offset by a length r from the epitrochoid curve EP) and the cam follower 62a (circle of radius r) move in a state of engagement (contact) with each other.

[0039] Furthermore, because the first friction wheel 50 and the second friction wheel 52 rotate without slipping against each other, when the second friction wheel 52 rotates at a constant speed, the first friction wheel 50 also rotates at a constant speed. This relationship also applies to the cam 60 (an offset epitrochoid curve OEP obtained by offsetting the epitrochoid curve EP by a length r) and the cam follower 62a (a circle with a radius r). In other words, when the second friction wheel 52 rotates at a constant speed, the cam 60 (offset epitrochoid curve OEP) that rotates along with the second friction wheel 52 also rotates at a constant speed, and the cam follower 62a (a circle with a radius r) that rotates along with the first friction wheel 50 (revolving around the center of the first friction wheel 50) also rotates at a constant speed. In this way, the cam 60 (offset epitrochoid curve OEP) and the cam follower 62a (a circle with a radius r) engage (contact) with each other and perform uniform rotational motion together. That is, even though the cam 60 (offset epitrochoid curve OEP) rotates at a constant speed, the cam follower 62a (circle of radius r) does not rattle and the speed does not vary (speed variation) and this is appropriately suppressed.

[0040] <<<Regarding the Shape of the Non-Circular Tooth 34>>> As described above, if we consider the cam 60 to be an offset epitrochoid curve OEP obtained by offsetting the epitrochoid curve EP by a length r, and the cam follower 62a to be a circle of radius r centered at the drawing point P of the epitrochoid curve EP, then this cam mechanism will exhibit an effect of appropriately suppressing speed variation (hereinafter also referred to as the speed variation suppression effect). Therefore, this matter will be applied to the design of the teeth of the gear mechanism 1.

[0041] This point will be explained using Figures 1, 2, 7 to 9. Figure 8 is an explanatory diagram for explaining the non-circular teeth 34 of the externally toothed non-circular gear 30 according to this embodiment. Figure 9 will be described later.

[0042] As described above, the arc-shaped tooth 14 has arc-shaped gear tooth side portions 18 (first arc-shaped gear tooth side portion 18a and second arc-shaped gear tooth side portion 18b) with arc-shaped curves. Here, since the arc-shaped gear tooth side portions 18 are part of a circle with radius r, the first arc-shaped gear tooth side portion 18a of one arc-shaped tooth 14 (for example, the arc-shaped gear tooth side portion 18 indicated by reference symbol TC1) can correspond to the cam follower 62a (see the upper diagrams of FIGS. 7 and 8). In this case, when an imaginary circle of radius R2 (= center distance D × number of teeth N / (number of teeth M + number of teeth N)) centered on the second central axis 32 is defined as the fixed circle (second friction wheel 52), an imaginary circle of radius R1 (= center distance D × number of teeth M / (number of teeth M + number of teeth N)) centered on the first central axis 12 is defined as the dynamic circle (first friction wheel 50), and the center C1 of the first circular gear tooth side portion TC1 is defined as the drawing point P, the drawn epitrochoid curve EP is offset by a length r to form an offset epitrochoid curve OEP (see FIG. 7 ), which corresponds to the cam 60. Therefore, if the shape of the non-circular gear tooth side portion 38 that comes into contact with the circular gear tooth side portion 18 (first circular gear tooth side portion 18 a) is set to the offset epitrochoid curve OEP (see the upper diagram in FIG. 8 ), a gear mechanism 1 that suppresses speed variations can be realized.

[0043] As described above, the shape of at least a part of the non-arc gear tooth side portion 38 according to this embodiment is formed so that, when an imaginary circle of radius R2 (= axis distance D × number of teeth N / (number of teeth M + number of teeth N)) centered on the second central axis 32 is taken as the fixed circle (second friction wheel 52), an imaginary circle of radius R1 (= axis distance D × number of teeth M / (number of teeth M + number of teeth N)) centered on the first central axis 12 is taken as the moving circle (first friction wheel 50), and the center C1 of the first arc gear tooth side portion 18 a is taken as the drawing point P, the drawn epitrochoid curve EP is an offset epitrochoid curve OEP (see FIG. 7 ) that is offset by the length r.

[0044] Like the arc-shaped tooth 14, the non-arc gear tooth 34 has a non-arc gear tooth tip 36 in addition to a non-arc gear tooth side 38. In other words, the non-arc gear tooth 34 has the non-arc gear tooth tip 36 and the non-arc gear tooth side 38 located on the side of the non-arc gear tooth tip 36.

[0045] A specific design example of the non-circular gear tooth 34 according to this embodiment is as follows. First, one first arc-shaped gear tooth side portion 18a (e.g., the arc-shaped gear tooth side portion 18 designated by reference symbol TC1) is selected, and the corresponding offset epitrochoid curve OEP is drawn. Then, for a portion of the offset epitrochoid curve OEP that may come into contact with the first arc-shaped gear tooth side portion TC1, the offset epitrochoid curve OEP is cut at a position −1.25×m inward and a position +m outward from the pitch circle PC2 of radius R2, as with the arc-shaped tooth 14, to form the non-circular gear tooth side portion 38 (designated by reference symbol TN1a) of the non-circular tooth 34 (however, the tooth height can be set arbitrarily, as with the arc-shaped tooth 14).

[0046] Furthermore, in this embodiment, the number of teeth of the externally toothed non-arc gear 30 is twice the number of teeth of the externally toothed arc-circular gear 10, so the externally toothed non-arc gear 30 rotates once while the externally toothed arc-circular gear 10 rotates twice. Therefore, there are two non-arc gear tooth side portions 38 that contact the first arc-circular gear tooth side portion TC1, and therefore the non-arc gear tooth side portion 38 (denoted by reference symbol TN1b) is also obtained by cutting the offset epitrochoid curve OEP that is point-symmetrical to the non-arc gear tooth side portion TN1a when viewed from the second center axis 32. Due to the above-described design, the non-arc gear tooth side portions TN1a and TN1b according to this embodiment have an overall shape that conforms to the offset epitrochoid curve OEP. Therefore, the non-arc gear tooth side portions TN1a and TN1b are formed so that the shape of the entire portion that contacts the arc-gear tooth side portion 18 conforms to the offset epitrochoid curve OEP.

[0047] Next, the above steps are repeated for the second arc-circular gear tooth side portion 18b (designated TC2), which is located on the opposite side of the first arc-circular gear tooth side portion TC1 from the arc-circular gear tooth tip 16 (see the lower diagram in Figure 8). That is, the offset epitrochoid curve OEP corresponding to the second arc-circular gear tooth side portion TC2 is drawn. Then, for the portion of the offset epitrochoid curve OEP that may come into contact with the second arc-circular gear tooth side portion TC2, the offset epitrochoid curve OEP is cut at a position −1.25×m inward and a position +m outward from the pitch circle PC2 of radius R2, forming the non-circular gear tooth side portion 38 (designated TN2a) of the non-circular tooth 34. Furthermore, the non-arc gear tooth side portion TN2a and the offset epitrochoid curve OEP located at a position point-symmetrical with respect to the second central axis 32 are also cut and defined as non-arc gear tooth side portion 38 (denoted by symbol TN2b). Note that non-arc gear tooth side portion TN2a (non-arc gear tooth side portion TN2b) is the tooth side portion of another (adjacent) non-arc gear tooth 34 (also referred to as second non-arc gear tooth 34b) different from the non-arc gear tooth 34 (also referred to as first non-arc gear tooth 34a) having non-arc gear tooth side portion TN1a (non-arc gear tooth side portion TN1b).

[0048] Then, by carrying out the above procedure for the other seven arc-circular teeth 14, all of the non-arcuate teeth 34 can be obtained. Fig. 9 is a diagram showing the correspondence of the tooth sides. Non-arcuate gear tooth side portions 38 obtained by carrying out the above procedure for the first arc-circular gear tooth side portion TC1 (TC3, TC5, TC7, TC9, TC11, TC13, TC15) are designated by symbols TN1a and TN1b (TN3a and TN3b, TN5a and TN5b, TN7a and TN7b, TN9a and TN9b, TN11a and TN11b, TN13a and TN13b, TN15a and TN15b), and The non-circular gear tooth side portions 38 obtained by subjecting the two-circular gear tooth side portions TC2 (TC4, TC6, TC8, TC10, TC12, TC14, TC16) to the above procedure are indicated by the symbols TN2a and TN2b (TN4a and TN4b, TN6a and TN6b, TN8a and TN8b, TN10a and TN10b, TN12a and TN12b, TN14a and TN14b, TN16a and TN16b).

[0049] Like the arc-gear tooth side portion 18, the non-arc gear tooth 34 also has two tooth sides as the non-arc gear tooth side portion 38: a first non-arc gear tooth side portion 38a (e.g., the non-arc gear tooth side portion 38 designated by the symbol TN3a) and a second non-arc gear tooth side portion 38b (e.g., the non-arc gear tooth side portion 38 designated by the symbol TN2a) provided on the opposite side of the non-arc gear tooth tip 36 from the first non-arc gear tooth side portion 38a.

[0050] In the above description, the externally toothed non-circular gear 30 is formed by carrying out the above steps when the externally toothed arc-shaped gear 10 is positioned at the rotational position shown in Fig. 9, but this rotational position may be arbitrary. For example, a similar externally toothed non-circular gear 30 can be formed by carrying out the above steps when the externally toothed arc-shaped gear 10 is positioned slightly rotated from the rotational position shown in Fig. 9.

[0051] Regarding the number of teeth M of the externally toothed circular arc gear 10: Conventional involute gears are manufactured by a conventional method (e.g., a hobbing method) using a dedicated gear processing machine equipped with a dedicated gear cutting tool. It is known that as the number of teeth of the gear to be manufactured decreases, it becomes difficult to manufacture a gear mechanism that adequately exhibits the aforementioned speed variation suppression effect using the gear cutting tool (the conventional method). In practice, it has been impossible to realize an involute gear with a number of teeth M of 10 or less that exhibits this effect.

[0052] In contrast, the externally toothed arc-shaped gear 10 according to this embodiment does not have the manufacturing constraints described above for gears with a small number of teeth. This is because, unlike involute gears, the externally toothed arc-shaped gear 10 is manufactured using the same manufacturing techniques used for cams (particularly parallel cams) and cam followers. Specifically, like cams and cam followers, the externally toothed arc-shaped gear 10 is manufactured using end milling or, for small gears, wire cutting. In other words, the profiles of the externally toothed arc-shaped gear 10 and the externally toothed non-circular gear 30 with its corresponding cam curve are digitally displayed using cam and cam follower analysis techniques. These data are then simulated on a three-dimensional CAD system to check for backlash and tooth interference. After the three-dimensional data is checked in advance, the externally toothed arc-shaped gear 10 and the corresponding externally toothed non-circular gear 30 are manufactured using end milling or wire cutting on an NC machining center.

[0053] As described above, the externally toothed arc gear 10 according to this embodiment is not subject to manufacturing constraints imposed on gears with a small number of teeth, and the number of teeth M can be set to 10 or less. This makes it possible to make the gear more compact, and furthermore, it also has great commercial merits, as it makes gears with a single-digit number of teeth more appealing to potential buyers.

[0054] As described above, in the externally toothed arc gear 10 according to this embodiment, the number of teeth M can be 10 or less, but this does not mean that the number of teeth M can be reduced indefinitely. That is, there is a lower limit to the number of teeth M (a value below which the externally toothed arc gear 10 cannot be realized that adequately suppresses speed variation under any circumstances). To achieve an externally toothed arc gear 10 that adequately suppresses speed variation, a contact ratio of 1 or greater is required, and this lower limit is derived from this condition (the condition that the contact ratio is 1 or greater; hereinafter, referred to as the contact ratio condition). In other words, a lower limit to the number of teeth M that can (possibly) satisfy the contact ratio condition is derived. This matter is explained in detail below.

[0055] <<<Regarding the Lower Limit of the Number of Teeth M of the Externally Toothed Arc-Curve Gear 10>>> FIG. 10 is a conceptual diagram showing the externally toothed arc-curve gear 10 and the externally toothed non-circular gear 30 contacting at two points. FIG. 11 is an explanatory diagram for explaining the contact ratio condition. The upper diagram shows a case where the contact ratio is greater than 1, the center diagram shows a case where the contact ratio is 1, and the bottom diagram shows a case where the contact ratio is less than 1. FIG. 12 is a diagram corresponding to FIG. 11 and shows the pitch angle θ1 and straddle angle θ2 for each of the three cases. Note that FIGS. 11 and 12 show the arc-curve teeth of the externally toothed arc-curve gear 10 with an arc radius of 0. That is, in this section, the explanation will be given assuming that the arc-curve teeth of the externally toothed arc-curve gear 10 have an arc diameter that is as close to 0 as possible (i.e., a follower having a cam follower and an arm with an arc diameter that is as close to 0 as possible).

[0056] In order to eliminate backlash between the externally toothed arc-shaped gear 10 and the externally toothed non-circular gear 30 and to ensure that both gears always rotate in unison, a meshing ratio of 1 or greater is required. A "meshing ratio of 1" means that both gears are always in contact at two or more points (see FIG. 10 ; contact points are indicated by reference numeral 80), and in reality, this cycle repeats: two-point contact (long-term) → three-point contact (momentary) → two-point contact (long-term) → three-point contact (momentary) →...

[0057] As shown in Figure 11, in order for the externally toothed arc-circular gear 10 and the externally toothed non-circular gear 30 to always be in contact at two or more points, when one arc-circular tooth (denoted by reference symbol A1) of the externally toothed arc-circular gear 10 faces the center of the externally toothed non-circular gear 30, the arc-circular teeth (denoted by reference symbol A2) on both adjacent sides (upper and lower) must be in contact with the externally toothed non-circular gear 30. Looking at Figure 11 with this condition in mind, it can be seen that the meshing ratio is 1 or more in the upper and central diagrams of Figure 11, but in the lower diagram, the arc-circular tooth denoted by reference symbol A2 is not in contact with the externally toothed non-circular gear 30 and the meshing ratio is less than 1. Note that the change in the number of contact points in the diagram above is 2-point contact (long term) → 3-point contact (long term) → 2-point contact (long term) → 3-point contact (long term) → ..., while the change in the number of contact points in the diagram below is 1-point contact (long term) → 2-point contact (long term) → 1-point contact (long term) → 2-point contact (long term) → ....

[0058] This condition can be expressed by the magnitude relationship between the pitch angle θ1 of the externally toothed non-circular gear 30 and the angle between the centers of the arcs of the externally toothed arc-circular gear 10 as seen from the center of the externally toothed non-circular gear 30 (for convenience, this angle is referred to as the straddle angle θ2). When comparing these angles, as shown in the upper diagram of FIG. 12 , if the straddle angle θ2 is greater than the pitch angle θ1, the externally toothed non-circular gear 30 is sandwiched between the two outer externally toothed arc-circular gears 10, and three-point contact can be maintained for a while even as rotation progresses from the illustrated three-point contact state, so the meshing ratio exceeds 1. Furthermore, as shown in the center diagram of FIG. 12 , if the straddle angle θ2 and the pitch angle θ1 are equal, the vertices of the two outer externally toothed arc-circular gears 10 and the externally toothed non-circular gear 30 coincide, so as rotation progresses from the illustrated three-point contact state, two-point contact occurs, and the meshing ratio is 1. Furthermore, as shown in the lower diagram of FIG. 12, when the spanning angle θ2 is smaller than the pitch angle θ1, there is one-point contact, and the meshing ratio is smaller than 1.

[0059] From the above, the conditional expression for the contact ratio condition is straddle angle θ2 - pitch angle θ1 ≧ 0. Note that θ1 and θ2 are respectively expressed as θ1 = 2π / N and θ2 = 2 tan, where θ1 is the center-to-center distance D, distance L (the distance from the center of rotation of the externally toothed arc-shaped gear 10 to the center of the arc, i.e., the length of the arm of the externally toothed arc-shaped gear 10 (follower) in FIGS. 11 and 12), the number of teeth M of the externally toothed arc-shaped gear 10, and the number of teeth N of the externally toothed non-arc-shaped gear 30. -１ (L·sin(2π / M) / (DL·cos(2π / M))). Therefore, the conditional expression is 2·tan -１ (L·sin(2π / M) / (D−L·cos(2π / M)))−2π / N≧0.

[0060] Next, in order to simplify the conditional expression, the distance L is set to a value at the round-down limit. Here, the round-down limit will be explained using Fig. 13. Fig. 13 is an explanatory diagram for explaining the round-down limit.

[0061] The left diagram of Fig. 13 corresponds to the lower right diagram of Fig. 4 (the upper left diagram of Fig. 5). That is, the left diagram of Fig. 13 illustrates the epitrochoid curve EP (cam 60) drawn by moving the drawing point P (the cam follower 62a of the follower 62). The center diagram of Fig. 13 illustrates the epitrochoid curve EP (cam 60) drawn in a similar manner, except that the length of the arm 62b of the follower 62 (i.e., the distance L) is longer than in the left diagram of Fig. 13. More specifically, the epitrochoid curve EP (cam 60) is drawn by setting the distance L equal to the radius D × M / (M + N) of the first friction wheel 50 (moving circle) (i.e., the drawing point P is located on the first friction wheel 50 (moving circle)). In addition, the right diagram of Figure 13 shows the epitrochoid curve EP (cam 60) drawn in a similar manner, with the length of the arm 62b of the follower 62 (i.e., the distance L) being longer than in the center diagram of Figure 13.

[0062] If we look at the right diagram in Figure 13, we can see that a looped portion (indicated by the symbol LO) has occurred in the epitrochoid curve EP (cam 60). This phenomenon is called undercutting, and if undercutting occurs, it goes without saying that the cam 60 cannot actually be manufactured. Therefore, it is necessary to set the distance L to a length that does not cause undercutting.

[0063] The turning point for whether or not a rounding down occurs is actually when the distance L = D x M / (M + N), i.e., the state shown in the center diagram of Figure 13. That is, if the distance L is greater than D x M / (M + N), a rounding down occurs, and if the distance L is less than D x M / (M + N), a rounding down does not occur. Therefore, the state shown in the center diagram of Figure 13 is called the rounding down limit.

[0064] Then, the above-mentioned conditional expression 2 tan -１ Substitute D×M / (M+N), which is the value at the limit of rounding down, for L in (L·sin(2π / M) / (D−L·cos(2π / M)))−2π / N≧0 to rearrange the equation. Then, the conditional expression becomes tan -１ (sin(2π / M) / ((M+N) / M-cos(2π / M)))-π / N≧0.

[0065] The reason why the value at the cut-down limit is substituted for L in the conditional expression, that is, the reason why the case where L = D × M / (M + N) is used to find the lower limit of the number of teeth M using the conditional expression is limited to this, is as follows: As is clear from Fig. 11, the shorter the distance L (i.e., the length of the arm of the follower), the more difficult it is to satisfy the conditional expression (the stricter the condition becomes), and therefore the case where L = D × M / (M + N) (the case at the cut-down limit) is the most lenient condition within which a cam mechanism can be realized (the cam 60 can actually be manufactured without cut-down occurring).

[0066] Meanwhile, the purpose of this study is to find a lower limit value for the number of teeth M that can satisfy (or has the potential to satisfy) the contact ratio condition. Therefore, it is desirable to find the lower limit value under the most lenient condition (for example, if the true lower limit value for the number of teeth M is 4 (i.e., if the number of teeth M is 4 and the contact ratio condition can actually be satisfied), if the result is 5 because of a stricter condition, the study would be inappropriate). For these reasons, when finding the lower limit value for the number of teeth M using a conditional expression, the value at the cut-down limit is substituted for L in the conditional expression.

[0067] As mentioned above, the externally toothed arc gear 10 is assumed to have arc teeth with an arc diameter that is as close to zero as possible (i.e., a follower with a cam follower and arm with an arc diameter that is as close to zero as possible), and this is also for the same reason. That is, as is clear from FIG. 11 , the larger the arc diameter is from 0, the smaller the straddle angle θ2 becomes, making it more difficult to satisfy the above condition (the condition becomes stricter). For this reason, the case where the arc diameter is as close to 0 as possible (the loosest condition) is studied.

[0068] Let's go back to the conditional expression and continue the study. The conditional expression is tan -１ (sin(2π / M) / ((M+N) / M-cos(2π / M)))-π / N≧0, which is a function of the number of teeth M and the number of teeth N.

[0069] FIG. 14 is a diagram showing the relationship between the number of teeth N of the externally toothed non-circular gear 30 and the value of the left side of the conditional equation. In this diagram, the horizontal axis represents the number of teeth N (from 1 to 100) of the externally toothed non-circular gear 30, and the vertical axis represents the value of the left side of the conditional equation. There are six graphs, each corresponding to a number of teeth M ranging from 1 to 6. That is, in FIG. 14 , the number of teeth N is changed to find the value of the left side of the conditional equation for each of the number of teeth M ranging from 1 to 6.

[0070] As can be seen from Figure 14, when the number of teeth M is 1 to 3, the value of the left-hand side never exceeds 0, regardless of the number of teeth N (it has been confirmed that when the number of teeth M is 1 to 3, the value of the left-hand side never exceeds 0, even if the number of teeth N is set to infinity). Therefore, when the number of teeth M is 1 to 3, the contact ratio condition is not met, despite the relaxed condition and regardless of the number of teeth N. On the other hand, when the number of teeth M is 4 or more, the value of the left-hand side exceeds 0, and there are cases where the contact ratio condition is met. From the above, it can be seen that the lower limit of the number of teeth M (the value below which the externally toothed arc gear 10 that adequately exhibits the speed variation suppression effect cannot be realized under any circumstances) is 4.

[0071] <<<Effectiveness of the Gear Mechanism 1 According to the Present Embodiment>>> The gear mechanism 1 according to the present embodiment comprises: an externally toothed arc-shaped gear 10 having M arc-shaped teeth 14 and rotating about a first central axis 12; and an externally toothed non-arc-shaped gear 30 having N non-arc-shaped teeth 34 and rotating about a second central axis 32 away from the first central axis 12 by a predetermined distance D. The arc-shaped teeth 14 of the externally toothed arc-shaped gear 10 have an arc-shaped gear tooth tip 16, and an arc-shaped gear tooth side portion 18 (for example, a first arc-shaped gear tooth side portion 18a designated by reference symbol TC1 in FIG. 8 ) located on a side of the arc-shaped gear tooth tip 16 and having an arc shape of radius r.

[0072] The non-arc gear tooth 34 of the externally toothed non-arc gear 30 has a non-arc gear tooth tip 36 and a non-arc gear tooth side portion 38 (for example, the non-arc gear tooth side portion 38 shown by symbols TN1a and TN1b in FIG. 8) located on the side of the non-arc gear tooth tip 36 and in contact with the arc-gear tooth side portion 18 (for example, the first arc-gear tooth side portion 18a shown by symbol TC1 in FIG. 8), and the non-arc gear tooth side portion 38 (for example, the non-arc gear tooth side portion 38 shown by symbols TN1a and TN1b in FIG. 8) is at least a part of The shape is formed so that when an imaginary circle of radius R2 (= axis distance D × number of teeth N / (number of teeth M + number of teeth N)) centered on the second central axis 32 is taken as the fixed circle (second friction wheel 52), an imaginary circle of radius R1 (= axis distance D × number of teeth M / (number of teeth M + number of teeth N)) centered on the first central axis 12 is taken as the moving circle (first friction wheel 50), and the center C1 of the first circular arc gear tooth side portion 18a is taken as the drawing point P, the drawn epitrochoid curve EP becomes an offset epitrochoid curve OEP (see Figure 7) offset by a length r.

[0073] The number of teeth M of the externally toothed arc gear 10 is 4 or more and 10 or less.

[0074] Therefore, as described above, it is possible to realize a gear mechanism 1 that exhibits the effect of suppressing speed variations and is compact, thereby offering great commercial merits.

[0075] ===Other Embodiments===The gear mechanism according to the present invention has been described above based on the above-mentioned embodiments, but the above-mentioned embodiments of the invention are intended to facilitate understanding of the present invention and do not limit the present invention. The present invention may be modified or improved without departing from the spirit and scope of the present invention, and of course, equivalents thereof are also included in the present invention.

[0076] In the above embodiment (also referred to as the first embodiment), an example of a gear mechanism 1 was given in which the gear mechanism 1 includes an externally toothed arc-shaped gear 10 and an externally toothed non-circular gear 30 having an offset epitrochoid curve OEP, and in which compactness is achieved by reducing the number of teeth M of the externally toothed arc-shaped gear 10. However, the present invention is not limited to this, and compactness may also be achieved by reducing the number of teeth N of the externally toothed non-circular gear 30.

[0077] FIG. 15 is a diagram corresponding to FIG. 1 and is an explanatory diagram for explaining a gear mechanism 100 according to a second embodiment.

[0078] Similar to the first embodiment, the gear mechanism 100 of the second embodiment comprises an externally toothed arc-shaped gear 10 having M (16 in this embodiment) arc-shaped teeth 14 and rotating around a first central axis 12, and an externally toothed non-arc-shaped gear 30 having N (8 in this embodiment) non-arc-shaped teeth 34 and rotating around a second central axis 32 that is a predetermined distance D away from the first central axis 12, and each of the arc-shaped teeth 14 of the externally toothed arc-shaped gear 10 has an arc-gear tooth tip portion 16 and an arc-gear tooth side portion 18 that is located on the side of the arc-gear tooth tip portion 16 and has an arc-shaped shape with a radius r.

[0079] Similarly to the first embodiment, the non-arc gear teeth 34 of the externally toothed non-arc gear 30 have non-arc gear tooth tip portions 36 and non-arc gear tooth side portions 38 that are located on the sides of the non-arc gear tooth tip portions 36 and are in contact with the arc-gear tooth side portions 18. The shape of at least a portion of the non-arc gear tooth side portions 38 is formed so that, when a virtual circle of radius R2 (= center distance D × number of teeth N / (number of teeth M + number of teeth N)) centered on the second central axis 32 is taken as the fixed circle, a virtual circle of radius R1 (= center distance D × number of teeth M / (number of teeth M + number of teeth N)) centered on the first central axis 12 is taken as the moving circle, and the center of the first arc-gear tooth side portion 18 a is taken as the drawing point, the resulting epitrochoid curve is an offset epitrochoid curve that is offset by a length r.

[0080] The number of teeth N of the externally toothed non-circular gear 30 is as follows: First, there are no manufacturing restrictions on gears with a small number of teeth, and this also applies to the externally toothed non-circular gear 30.

[0081] That is, conventional involute gears are manufactured by a conventional method (e.g., a hob method) using a dedicated gear processing machine equipped with a dedicated gear cutting tool. It is known that as the number of teeth of the gear to be manufactured decreases, it becomes difficult to manufacture a gear mechanism that adequately exhibits the aforementioned speed variation suppression effect using the gear cutting tool (the conventional method). In practice, it has been impossible to realize an involute gear with the number of teeth N of 10 or less that exhibits such an effect.

[0082] In contrast, the externally toothed non-circular gear 30 according to the second embodiment does not have the manufacturing constraints described above for gears with a small number of teeth. This is because, unlike involute gears, the externally toothed non-circular gear 30 is manufactured using the same manufacturing techniques used for cams (particularly parallel cams) and cam followers. Specifically, like cams and cam followers, the externally toothed non-circular gear 30 is manufactured by end milling or, for small gears, by wire cutting. In other words, the profiles of the externally toothed arc-shaped gear 10 and the externally toothed non-circular gear 30 with its corresponding cam curve are digitally displayed using a cam / cam follower analysis technique. These data are then simulated on a three-dimensional CAD system to check for backlash and tooth interference. After the three-dimensional data is checked in advance, the externally toothed arc-shaped gear 10 and the corresponding externally toothed non-circular gear 30 are manufactured by end milling or wire cutting using an NC machining center.

[0083] As described above, the externally toothed non-circular gear 30 according to the second embodiment is not subject to manufacturing constraints imposed on gears with a small number of teeth, and the number of teeth N can be set to 10 or less. This makes it possible to make the gear more compact, and furthermore, it also has great commercial merits, as it makes gears with a single-digit number of teeth more appealing to potential buyers.

[0084] As described above, the externally toothed non-circular gear 30 according to the second embodiment can have a number of teeth N of 10 or less. However, the number of teeth N cannot be reduced indefinitely, as with the externally toothed arc-circular gear 10 (first embodiment). That is, there is a lower limit to the number of teeth N (a value below which the externally toothed non-circular gear 30 that adequately suppresses speed variation cannot be realized under any circumstances). To realize an externally toothed non-circular gear 30 that adequately suppresses speed variation, the contact ratio must be 1 or greater. This lower limit is derived from the contact ratio condition, as with the externally toothed arc-circular gear 10 (first embodiment). That is, a lower limit to the number of teeth N that satisfies (or has the potential to satisfy) the contact ratio condition is derived. These points are described in detail below.

[0085] <<<<Regarding the Lower Limit of the Number of Teeth N of the Externally Toothed Non-Circular Gear 30 >>> When determining the lower limit of the number of teeth N of the externally toothed non-circular gear 30, the above-mentioned conditional expression tan -１ (sin(2π / M) / ((M+N) / M-cos(2π / M)))-π / N≧0 can be used.

[0086] FIG. 16 is a diagram showing the relationship between the number of teeth M of the externally toothed arc gear 10 and the value of the left side of the conditional equation. In this diagram, the horizontal axis represents the number of teeth M (from 1 to 100) of the externally toothed arc gear 10, and the vertical axis represents the value of the left side of the conditional equation. There are six graphs, each corresponding to a number of teeth N of 1 to 6. That is, in FIG. 16, the number of teeth M is changed for each of the number of teeth N of 1 to 6, and the value of the left side of the conditional equation is found.

[0087] As can be seen from Figure 16, when the number of teeth N is 1 to 2, the value of the left-hand side never exceeds 0, regardless of the number of teeth N (it has been confirmed that when the number of teeth N is 1 to 2, the value of the left-hand side never exceeds 0, even if the number of teeth M is set to infinity). Therefore, when the number of teeth N is 1 to 2, the contact ratio condition is not met, despite the relaxed condition, and regardless of the number of teeth M. On the other hand, when the number of teeth N is 3 or more, the value of the left-hand side exceeds 0, and there are cases where the contact ratio condition is met. From the above, it can be seen that the lower limit of the number of teeth M (the value below which the externally toothed arc gear 10 that adequately exhibits the speed variation suppression effect cannot be realized under any circumstances) is 3.

[0088] <<<Effectiveness of the Gear Mechanism 100 According to the Second Embodiment>>> The gear mechanism 100 according to the second embodiment comprises: an externally toothed arc-shaped gear 10 having M arc-shaped teeth 14 and rotating around a first central axis 12; and an externally toothed non-arc-shaped gear 30 having N non-arc-shaped teeth 34 and rotating around a second central axis 32 away from the first central axis 12 by a predetermined distance D, wherein the arc-shaped teeth 14 of the externally toothed arc-shaped gear 10 have an arc-shaped gear tooth tip 16 and an arc-shaped gear tooth side portion 18 that is located on the side of the arc-shaped gear tooth tip 16 and has an arc-shaped shape of radius r.

[0089] Similarly to the first embodiment, the non-arc gear teeth 34 of the externally toothed non-arc gear 30 have non-arc gear tooth tip portions 36 and non-arc gear tooth side portions 38 that are located on the sides of the non-arc gear tooth tip portions 36 and are in contact with the arc-gear tooth side portions 18. The shape of at least a portion of the non-arc gear tooth side portions 38 is formed so that, when a virtual circle of radius R2 (= center distance D × number of teeth N / (number of teeth M + number of teeth N)) centered on the second central axis 32 is taken as the fixed circle, a virtual circle of radius R1 (= center distance D × number of teeth M / (number of teeth M + number of teeth N)) centered on the first central axis 12 is taken as the moving circle, and the center of the first arc-gear tooth side portion 18 a is taken as the drawing point, the resulting epitrochoid curve is an offset epitrochoid curve that is offset by a length r.

[0090] The number of teeth M of the externally toothed non-circular gear 30 is 3 or more and 10 or less.

[0091] Therefore, as described above, it is possible to realize a gear mechanism 1 that exhibits the effect of suppressing speed variations and is compact, thereby offering great commercial merits.

[0092] REFERENCE SIGNS LIST 1 Gear mechanism 10 Externally toothed arc-shaped gear 12 First central shaft 14 Arc-shaped tooth 16 Arc-shaped gear tooth tip 18 Arc-shaped gear tooth side 18a First arc-shaped gear tooth side 18b Second arc-shaped gear tooth side 30 Externally toothed non-circular gear 32 Second central shaft 34 Non-circular tooth 34a First non-circular tooth 34b Second non-circular tooth 36 Non-circular gear tooth tip 38 Non-circular gear tooth side 38a First non-circular gear tooth side 38b Second non-circular gear tooth side 50 First friction wheel 52 Second friction wheel 60 Cam 62 Follower 62a Cam follower 62b Arm 70 Bar 70a Outer end 70b Inner end 80 Contact point 100 Gear mechanism A1 Arc-shaped tooth A2 Circular arc tooth C1 Center C2 Center D Center distance EP Epitrochoid curve L Distance LI Line LO Looped portion OEP Offset epitrochoid curve P Drawing point PC1 Pitch circle PC2 Pitch circle R1 Pitch circle radius R2 Pitch circle radius TA Tangent α Pitch angle of arc TC1 First circular arc gear tooth side TC2 Second circular arc gear tooth side TC3 First circular arc gear tooth side TC4 Second circular arc gear tooth side TC5 First circular arc gear tooth side TC6 Second circular arc gear tooth side TC7 First circular arc gear tooth side TC8 Second circular arc gear tooth side TC9 First circular arc gear tooth side TC10 Second circular arc gear tooth side TC11 First circular arc gear tooth side TC12 Second circular gear tooth side portion TC13 First circular gear tooth side portion TC14 Second circular gear tooth side portion TC15 First circular gear tooth side portion TC16 Second circular gear tooth side portion TN1a, TN1b Non-circular gear tooth side portion TN2a, TN2b Non-circular gear tooth side portion TN3a, TN3b Non-circular gear tooth side portion TN4a, TN4b Non-circular gear tooth side portion TN5a, TN5b Non-circular gear tooth side portion TN6a, TN6b Non-circular gear tooth side portion TN7a, TN7b Non-circular gear tooth side portion TN8a, TN8b Non-circular gear tooth side portion TN9a, TN9b Non-circular gear tooth side portion TN10a, TN10b Non-circular gear tooth side portion TN11a, TN11b Non-circular gear tooth side portion TN12a, TN12b Non-circular gear tooth side portion TN13a, TN13b Non-circular gear tooth side portion TN14a, TN14b Non-circular gear tooth side portion TN15a, TN15b Non-circular gear tooth side portion TN16a, TN16b Non-circular gear tooth side portion

Claims

1. A gear mechanism having an externally toothed arc-shaped gear having M arc-shaped teeth and rotating around a first central axis, and an externally toothed non-arc gear having N non-arc teeth and rotating around a second central axis a predetermined distance D away from the first central axis, wherein the arc-shaped teeth of the externally toothed arc-shaped gear have an arc-shaped gear tooth tip portion and an arc-shaped gear tooth side portion located on a side of the arc-shaped gear tooth tip portion and having an arc shape of radius r, and the non-arc-shaped teeth of the externally toothed non-arc gear have a non-arc-shaped gear tooth tip portion and a non-arc-shaped gear tooth side portion located on a side of the non-arc-shaped gear tooth tip portion and in contact with the arc-shaped gear tooth side portion, and at least a part of the shape of the non-arc-shaped gear tooth side portion is a virtual circle of radius D x N / (M + N) centered on the second central axis is a fixed circle, a virtual circle of radius D x M / (M + N) centered on the first central axis is a moving circle, and the center of the circular arc gear tooth side portion is a drawing point, the epitrochoid curve drawn is an offset epitrochoid curve offset by a length r, and the number of teeth M of the externally toothed circular gear is 4 or more and 10 or less.

2. A gear mechanism having an externally toothed arc gear having M arc teeth and rotating around a first central axis, and an externally toothed non-arc gear having N non-arc teeth and rotating around a second central axis a predetermined distance D away from the first central axis, wherein the arc teeth of the externally toothed arc gear have an arc gear tooth tip portion and an arc gear tooth side portion located on a side of the arc gear tooth tip portion and having an arc shape of radius r, and the non-arc gear of the externally toothed non-arc gear have a non-arc gear tooth tip portion and a non-arc gear tooth side portion located on a side of the non-arc gear tooth tip portion and in contact with the arc gear tooth side portion, and the shape of at least a part of the non-arc gear tooth side portion is a virtual circle of radius D x N / (M + N) centered on the second central axis is a fixed circle, a virtual circle of radius D x M / (M + N) centered on the first central axis is a moving circle, and the center of the circular gear tooth side portion is a drawing point, the epitrochoid curve drawn is an offset epitrochoid curve offset by a length r, and the number of teeth N of the externally toothed non-circular gear is 3 or more and 10 or less.

Images